Recent Developments in Earthquake Seismology: Present and Future of Seismological Analysis 3031475372, 9783031475375

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Rohtash Kumar Raghav Singh Shyam Kanhaiya Satya Prakash Maurya   Editors

Recent Developments in Earthquake Seismology Present and Future of Seismological Analysis

Recent Developments in Earthquake Seismology

Rohtash Kumar • Raghav Singh Shyam Kanhaiya • Satya Prakash Maurya Editors

Recent Developments in Earthquake Seismology Present and Future of Seismological Analysis

Editors Rohtash Kumar Banaras Hindu University Varanasi, India Shyam Kanhaiya Veer Bahadur Singh Purvanchal University Jaunpur, India

Raghav Singh Banaras Hindu University Varanasi, India Satya Prakash Maurya Banaras Hindu University Varanasi, India

ISBN 978-3-031-47538-2 ISBN 978-3-031-47537-5 https://doi.org/10.1007/978-3-031-47538-2

(eBook)

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Paper in this product is recyclable.

In memory of Late Dr. Rohtash Kumar, The first corresponding editor of this book

Acknowledgments

First and foremost, the editors would like to thank their authors for contributing book chapter. This book would not have taken shape without the support of all the contributing authors belonging to geologically and geographically diverse places and institutions. We particularly acknowledge Chhavi Chaudhari, M. L. Sharma, Shusil Gupta, Parveen Kumar, Rinku Mahanta, Vipul Silwal, M.L. Sharma from IIT Roorkee, India; Sandeep, Monika, Amritansh Rai, Prashant Kumar Singh, Ankit Singh, Dipankan Srivastava, Pankhudi Thakur, Shatrughan Singh, Indrajit Das from BHU Varanasi, India; and Ranjit Das, Claudio Menesesa, Marcelo Saavedrab, Genesis Seranob, Franz Machacab, Roberto Mirandabc, BryanA, Urra-Calfuñirc from Chile for contributing book chapter. The editors from the bottom of their hearts are indebted to all of them for the time they took to pen down their findings and research so that it can be disseminated to a larger audience. One of the editors (Dr. S.P. Maurya) would like to thank the financial support from UGC, Govt. of India (grant no. M-14-585), and Institute of Eminence (IoE-BHU) with grant no. 6031B. The book would not have been completed without their support. Additionally, we would like to express our gratitude to Dr. Rohtash Kumar, who originally wrote the book’s proposal. Sadly, he passed away at a very young age, and we have just finished writing this book in his honor. His help in both our personal and professional lives will always be appreciated. We also like to thank a few of my colleagues who supported us in finishing this book after the tragic passing of Dr. Rohtash Kumar, the book’s original corresponding editor. This book would not have been a reality without the typesetting work and continuous support of Banaras Hindu University Varanasi research students Dr. Prabodh Kumar, Mr. Amritansh Rai, Mr. Ankit Singh, Mr. Ravi Kant, Mr. Nitin Verma, Ms. G. Hema, and Mr. Ajay Kumar. They have been the backbone of the entire process. From organizing the book chapters, figures, and tables, their effort has been

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Acknowledgments

noteworthy. A big thank you to all. We also thank the Department of Geophysics, BHU Varanasi and Department of Earth and Planetary Science, Veer Bahadur Singh Purvanchal University, Jaunpur, UP, India for their support in completing this book. Last but not least, to the efforts of all those behind the scenes and whose names are not captured here, we would like to take a bow to show our gratitude towards you.

Contents

1

Earthquake Occurrence Models . . . . . . . . . . . . . . . . . . . . . . . . . . . Chhavi Chaudhari, M. L. Sharma, and Shusil Gupta

2

Estimation and Validation of Arias Intensity Relation Using the 1991 Uttarkashi and 1999 Chamoli Earthquakes Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Parveen Kumar, Sandeep, and Monika

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1

15

Exploring the Concept of Self-Similarity and High-Frequency Decay Kappa-Model and fmax-Model Using Strong-Motion Surface and Borehole Data of Japan: A Statistical Approach . . . . . Rohtash Kumar, Raghav Singh, Amritansh Rai, Sandeep, S. P. Singh, S. P. Maurya, and Prashant Kumar Singh

25

Body Waves– and Surface Waves–Derived Moment Tensor Catalog for Garhwal-Kumaon Himalayas . . . . . . . . . . . . . . Rinku Mahanta, Vipul Silwal, and M. L. Sharma

47

Exploring GRACE and GPS and Absolute Gravity Data on the Relationship Between Hydrological Changes and Vertical Crustal Deformation in South India . . . . . . . . . . . . . . Ankit Singh, Rohtash Kumar, Amritansh Rai, Raghav Singh, and S. P. Singh

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Moho Mapping of Northern Chile Region Using Receiver Function Analysis and HK Stacking . . . . . . . . . . . . . . . . . . . . . . . . Amritansh Rai, Rohtash Kumar, Dipankan Srivastava, Raghav Singh, Ankit Singh, and S. P. Maurya Coulomb Stress Change of the 2012 Indian Ocean Doublet Earthquake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pankhudi Thakur, Rohtash Kumar, Ranjit Das, Amritansh Rai, Raghav Singh, Ankit Singh, and S. P. Maurya

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Contents

8

Earthquake Source Dynamics and High-Frequency Decal Characteristics of Japanese Arc Region . . . . . . . . . . . . . . . . . 109 Ankit Singh, Rohtash Kumar, and Amritansh Rai

9

Lapse-Time Dependence of Coda Quality Factor Within the Lithosphere of Northern Ecuador . . . . . . . . . . . . . . . . . . . . . . . 121 Amritansh Rai, Rohtash Kumar, Ankit Singh, Raghav Singh, Indrajit Das, and S. P. Maurya

10

Coda Q Estimates of the Bilaspur Region of Himachal Lesser Himalaya . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Vandana, S. C. Gupta, Ashwani Kumar, and Himanshu Mittal

11

Data-Driven Spatiotemporal Assessment of Seismicity in the Philippine Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Amritansh Rai, Rohtash Kumar, Ankit Singh, Pankhudi Thakur, Raghav Singh, S. P. Maurya, and Ranjit Das

12

Determination and Identification of Focal Mechanism Solutions for the 2016 Kumamoto Earthquake from Waveform Inversion Using ISOLA Software . . . . . . . . . . . . . . . . . . 165 Ankit Singh, Rohtash Kumar, Amritansh Rai, Shatrughan Singh, Raghav Singh, Satya Prakash, and Pnkhudi Thakur

13

Regression Relations for Magnitude Conversion of Northeast India and Northern Chile and Southern Peru . . . . . . . . . . . . . . . . . 179 Ranjit Das, Claudio Meneses, Marcelo Saavedra, Genesis Serrano, Franz Machaca, Roberto Miranda-Yáñez, and Bryan A. Urra-Calfuñir

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

List of Figures

Fig. 1.1

Fig. 1.2

Fig. 1.3

Fig. 1.4

Fig. 1.5

Fig. 1.6

Fig. 1.7

Fig. 1.8

Fig. 1.9

Fig. 1.10

The Himalayas and Characterization of three regions on the basis of tectonics and recorded seismicity of magnitude MW ⩾ 5.0 for the time period 1255–2017 . . . . . . . . . . . . . . . . . . . . . . . . . . Magnitude Frequency Distribution and magnitude of completeness in the subdivision of Himalaya using the EMR method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variation of Cumulative rate of Nmin w.r.t. Mmax in North-West Himalaya using (a) Constant seismicity and (b) Constant Moment Release models . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . Variation of Cumulative rate of Nmin w.r.t. Mmax in Garhwal Himalaya using (a) Constant seismicity and (b) Constant Moment Release models . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . Variation of Cumulative rate of Nmin w.r.t. Mmax in Nepal Himalaya using (a) Constant seismicity and (b) Constant Moment Release models . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . Hazard assessment in North-West Himalaya: (a) annual occurrence rate of earthquake magnitude and (b) probability of earthquake occurrence in the specific time period . . . . . . . . . . . . . . Hazard assessment Garhwal Himalaya: (a) annual occurrence rate of earthquake magnitude and (b) probability of earthquake occurrence in a specific time period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hazard assessment in Nepal Himalaya: (a) annual occurrence rate of earthquake magnitude and (b) probability of earthquake occurrence in a specific time period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hazard Maps of PGA having 10% probability of exceedance in 50 years using Boore and Atkinson (2008) for (a) Constant seismicity and (b) Constant Moment Release Models . . . . . . . . . . . . . Hazard Maps of PGA having 2% probability of exceedance in 50 years using Boore and Atkinson (2008) for (a) Constant seismicity and (b) Constant Moment Release Models . . . . . . . . . . . . .

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Fig. 2.1

Fig. 2.2

Fig. 2.3

Fig. 2.4

Fig. 3.1 Fig. 3.2

Fig. 3.3 Fig. 3.4 Fig. 3.5 Fig. 3.6 Fig. 3.7 Fig. 3.8 Fig. 3.9

Fig. 3.10 Fig. 3.11

List of Figures

Seismicity during 1935–2021 of Uttarakhand Himalaya, India report by the bulletin of ISC (International Seismological Centre). The blue color star symbols represent the epicentre of the Uttarkashi and Chamoli earthquakes. (The figure is modified after Valdiya (1980) and Célérier et al. (2009)) . . . . . . . . . . . . . . . . . . . . The comparison of Arias intensity values obtained from empirical and observed data for the 1991 Uttarkashi and 1999 Chamoli earthquakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (a) The blue color box shows the location of the study region for which Arias intensity maps are prepared. The Arias intensity map for (b) the Uttarkashi earthquake and (c) the Chamoli earthquake. The variation of Arias intensity values along the profile (d) AB and (e) CD. The symbol star denotes the location of the epicentres of the Uttarkashi and Chamoli earthquakes . . . . . The Arias intensity maps for future scenario earthquakes (Mw 8.5) correspond to the epicentre of the (a) Uttarkashi and (b) Chamoli earthquakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Map showing KIK-NET sites and the epicentres of earthquakes used in the study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Average observed acceleration and displacement spectra along with the theoretical source model with fmax-model (solid line) and κ-model (dotted line) . . . .. . . .. . . .. . . .. . . .. . .. . . .. . . .. . . .. . . .. . . .. . Plot showing the fmax-distance model on epicentral distance with an empirical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plot showing the dependence of fmax-model on earthquake magnitude .. . . .. . . .. . . .. . . .. . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . Dependency of power coefficient (s) on seismic magnitude . . . . . . Surface and borehole P(f) of fmax-model for all earthquakes used in the study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plot showing FAS of direct shear wave on the semi-log scale with fe and fx with a best-fit line to estimate the slop (λ) . . . . . . . . . . Dependency of κ-model on seismic magnitude (Mw) . . . . . . . . . . . . . . Observed and predicted value of surface data kappa κ(s) and borehole data kappa κ(w) along with their residuals estimated using multivariate regression analysis (MVLR) . . . . . . . . Relationship between fmax-model and κ-model . . . . . . . . . . . . . . . . . . . . . Stress drop variation with seismic moment (M0) and earthquake source radius (r). (Red and black dots are corresponding to surface and borehole values, respectively) . . . . . . . . . . . . . . . . . . . . . . .

17

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21 27

30 31 32 32 33 34 35

38 38

40

List of Figures

Fig. 4.1

Fig. 4.2

Fig. 4.3

Fig. 4.4

Fig. 4.5

Fig. 4.6

Fig. 5.1 Fig. 5.2 Fig. 5.3 Fig. 5.4

The seismicity map of the G-K region of the Himalayan arc covering a period of 2010 to 2021. The color contrast signifies the focal depth of each event, while the size of each circle corresponds to the magnitudes of the earthquakes. The thick black lines in the map represents the active faults in the region (Dasgupta et al., 2000) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Illustrations of the locations of 18 broadband stations (depicted as blue inverted triangles) and 16 earthquake events (represented by circles) for which MT inversion is performed in this study. The variation in color signifies the focal depth of each event, while the size of the circles corresponds to the magnitudes of the earthquakes . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . .. . . The difference between raw waveform data (Upper set of three waveforms) and processed data (Lower set of three waveforms) after removal of instrument response and applying rotation. The processed data is used for the CAP method . . . . . . . . . . . . . . . . . . . MT solutions and waveform comparisons for the event 2021091100282800. Columns represent P wave components (vertical and radial), Rayleigh wave components (vertical, radial, and transverse Love wave) respectively. Stations are ordered by increasing epicentral distance, with observed and synthetic waveforms in black and red, respectively. Body waves are filtered at 3–10 s and surface waves are filtered at 16–40 s. Numbers below each station indicate epicentral distance and azimuth. Three values beneath each waveform pair include cross-correlation time shift, percentage of misfit, and amplitude ratio. Header lines are as per Silwal (2015) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The depth and magnitude search to find out the minimum misfit over grid points. In this case, the optimum depth was found at 6 km and magnitude, Mw 4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The beachball diagram representing MT catalog of 16 earthquakes is shown in this figure. The results shows as distribution of thrust, normal and strike-slip oriented mechanisms rather than a preferred thrust solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GPS stations at Lucknow, Hyderabad and Bangalore. (Courtesy NEVADA GEODETIC LABORATORY) . . .. . .. . .. . . .. The plot showing vertical crustal deformation obtained from GRACE in Lucknow region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vertical crustal deformation obtained from GPS stationed at Lucknow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vertical crustal deformation obtained from GRACE data for Hyderabad region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Fig. 5.5 Fig. 5.6 Fig. 5.7 Fig. 5.8 Fig. 5.9 Fig. 5.10 Fig. 6.1 Fig. 6.2

Fig. 6.3

Fig. 6.4 Fig. 6.5 Fig. 6.6 Fig. 6.7

Fig. 6.8

Fig. 6.9

Fig. 6.10

List of Figures

Vertical crustal deformation obtained from GPS stationed at Hyderabad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vertical crustal deformation obtained from GRACE data for Bangalore region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vertical crustal deformation obtained from GPS stationed at Bangalore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GRACE TWS analysis for Lucknow region . . . . . .. . . . . . . . . . . . .. . . . . GRACE TWS analysis for Hyderabad region . . . . . . . . . . . . . . . . . . . . . . GRACE TWS analysis for Bangalore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Seismotectonic of Northern Chile region . . . . . . . . . . . . . . . . . . . . . . . . . . . Teleseismic Events for stations (a) AC05, (b) AC06, (c) AF01, (d) CO10. The seismic stations are located by triangles, while events are shown with dots on the map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Typical “flow” chart of a receiver-function analysis. First, the seismogram is rotated to a suitable coordinate system and deconvolved to remove the source and path effect. The deconvolved output is the receiver function, which can be inverted to obtain velocity structure beneath the seismic station .. . .. . .. . . .. Seismograph recording three-component (radial, transverse, and vertical) seismic wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rotation of the original three-component seismogram to new RTZ coordinate system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Illustration of the water-level deconvolution from (Ligorrfa & Ammon, 1999) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Receiver functions for station AC04 shown over 30 s. The (left) radial and (right) transverse components, sorted by back azimuth of incoming wave field within 10° bins. Slowness information is averaged out. The top traces show the receiver functions further averaged over all back azimuth and slowness values. Negative polarity arrivals are dominant at early record. Faint positive peak can be seen around 6 s which is coming from Moho discontinuity . . . . .. . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . .. . . . . . . Receiver functions for station AC05 shown over 30 s. Here positive peak is dominant at 7 s which is consistent with Ps conversions at Moho . .. . . .. . . . .. . . .. . . .. . . .. . . .. . . .. . . . .. . . .. . . .. . . .. . Receiver Functions over Station AC07 for 30 s. Figure format is same as earlier. Strong peak is observed at 5 s which is identified as Moho Ps phase. PpPs phase is observed at 15 s and PsPs phase is observed around 20 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . Receiver Function over Station CO10 for 30 s. Figure format is same as before. The seismogram is dominated by negative phase arrivals. Faint positive peak is observed around 5 s. Strong positive peak is observed at 12 s . . . . . . . . . . . . . . . . . . . . . . . . . . . .

74 74 75 76 76 77 84

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87 88 89 90

93

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List of Figures

Fig. 6.11

Fig. 7.1 Fig. 7.2 Fig. 7.3 Fig. 7.4 Fig. 8.1 Fig. 8.2 Fig. 8.3 Fig. 8.4

Fig. 8.5

Fig. 8.6 Fig. 8.7 Fig. 9.1

Fig. 9.2

Fig. 9.3 Fig. 9.4

H-k stacking results for Vp/Vs (k) and crustal thickness (H) of all stations used in the study (a) AC04, (b) AC07, (c) AC05, (d) CO1 .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .. . . . . The Sumatran fault, subduction zone, and minor faults in the Indian Ocean Earthquake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Coulomb stress changes (bar) in the transverse and lateral directions of the fault . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Horizontal displacement vectors due to the main Sumatran fault . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vertical displacement (colors and contours) due to the main Sumatran fault . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . Acceleration time history of the SH component of the seismogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Displacement spectrum of the seismogram . . . . . . . . . . . . . . . . . . . . . . . . . The topographic map of Japan showing the major fault lines, plate boundaries and coastlines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variation of M0 with fc for EW, NS and UD channels of seismometers. Left side of the panel represents data from surface seismometers. Right side of panel represents data from well seismometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variation of fmax with Mw for EW, NS and UD channels of seismometers. Left side of the panel represents data from surface seismometers. Right side of panel represents data from well seismometers . .. . .. . . .. . .. . . .. . .. . . .. . .. . . .. . .. . . .. . .. . . .. . .. . . .. . The plot of fmax against epicentre for the surface data . . . . . . . . . . . . . The plot of fmax against epicentre for the well data . . . . . . . . . . . . . . . . Tectonic setup of the study area showing all the important fault systems along with station (blue triangle) and events (white circles) used in this study (NPDB: North Panama Deforming Belt; ECT: Ecuador-Colombia Trench; LFS: Llanos Fault System; RFS: Romeral Fault System; SMBF: Santa Marta-Bucaramanga Fault; BF: Boconó Fault) . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . An example of the seismogram recorded at OTAV (a) marked P, S and coda arrivals. A time window of 10.24 sec is shown in green shades (b) and (c) Seismogram with coda windows filtered at central frequencies of 1 Hz–2 Hz and 4 Hz–8 Hz along with estimated Qc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Seismogram with coda windows filtered at central frequencies of 4 Hz–8 Hz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Seismogram with coda windows filtered at central frequencies of 8 Hz–16 Hz . .. . .. . .. . .. .. . .. . .. . .. . .. . .. .. . .. . .. . .. . .. .. . .. . .. . .. . ..

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95 101 103 104 105 110 111 113

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115 116 116

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Fig. 9.5 Fig. 9.6 Fig. 9.7 Fig. 9.8 Fig. 10.1 Fig. 10.2

Fig. 10.3 Fig. 10.4

Fig. 10.5 Fig. 11.1

Fig. 11.2 Fig. 11.3 Fig. 11.4

Fig. 11.5 Fig. 11.6 Fig. 11.7

List of Figures

Seismogram with coda windows filtered at central frequencies of 12 Hz–24 Hz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Seismogram with coda windows filtered at central frequencies of 16 Hz–32 Hz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plots of frequency-dependent Qc at lapse time of 10 s, 20 s, 30 s, 40 s, 50 s and 60 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plot showing variation in Qavg for all lapse times versus frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Map shows the tectonic features along with instrumental stations located in the study region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plot of the event recorded at SKND station on July 5, 2009. (a) Unfiltered data-trace with coda window, (b) to (e) bandpass filtered displacement amplitudes of coda window at 1–2 Hz, 4–8 Hz, 8–16 Hz, and 16–32 Hz, respectively, and the RMS amplitude values multiplied with lapse time along with the best square fits of selected coda window at central frequencies of 1.5, 6, 12 and 24 Hz, respectively. The Qc is determined from the slope of the best square line. Abbreviations are P: P-wave arrival time; S: S-wave arrival time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Map showing the spatial distribution reference to a single station . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plots of quality factors and central frequencies for all distance ranges with linear regression frequency-dependent relationship (f), Qc = Q0fn at lapse time 30 s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Comparison of Qc values for the Bilaspur region of Himachal Lesser Himalaya, India with the existing Q studies in India . . . . . . The topographic map of Philippines Island showing the distribution of earthquake events of magnitude M > 7.8 (Yellow stars) along with plate boundaries . . . . . . . . . . . . . . . . . . . . . . . . . Histogram of temporal distribution of the earthquake events from 1940 to 2022 in the Philippines island . . . . . . . . . . . . . . . . . . . . . . . . Distribution of event’s depth throughout the period of 1940 to 2022 in Philippines Island . . . .. . . . . .. . . . . .. . . . .. . . . . .. . . . . .. . . . . .. . Zmap generated map showing the distribution of magnitude of completion (Mc) for the study region. Mc can be seen to be varied from 4.0 to 5.1 with majority of the study region having the Mc = 4.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plot of the cumulative number of earthquakes for the study region against magnitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spatial distribution of b-values in the study region during the period of 1973–2022 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spatial distribution of Z-values in the study region during the period of 1973–2022 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

129 129 130 131 135

139 142

142 143

148 153 154

155 156 157 158

List of Figures

Fig. 11.8

Fig. 11.9

Fig. 12.1 Fig. 12.2

Fig. 12.3 Fig. 12.4

Fig. 12.5 Fig. 12.6 Fig. 12.7

xvii

Plot showing the (a) annual probability of occurrence of earthquake of certain magnitude, (b) the period after which the earthquake of certain magnitude will occur again (recurrence period) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Plots showing the variation of b-values in 5 different time windows of 10 Years for the time periods (a) 1973–1982, (b) 1983–1992, (c) 1993–2002, (d) 2003–2012 and (e) 2013–2022, respectively, starting from the top left and moving clockwise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 Topographic map of Japan showing the major fault lines, plate boundaries, and coastlines generated by Zmap . . . . . . . . . . . . . . Correlation between observed and synthetic waveforms and focal mechanism of solutions is plotted against the depth of the source. The DC% value scale has been shown on the right side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plot of correlation v/s time shift. Source position and DC% . . . . . . Plot of an observed and synthetic waveform. Black represents the observed waveform and red represents the synthetic waveforms. The blue color number represents the VR between the waveforms .. . . .. . .. . .. . .. . .. . .. . .. . .. . . .. . .. . .. . .. . .. . .. . Plot of SNR v/s frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plot of power spectrum v/s frequency . . . . . . .. . . . . . . . . .. . . . . . . . . . .. . . Amplitude response of the PZ files of the instrument . . . . . . . . . . . . .

166

172 172

173 175 175 176

List of Tables

Table 2.1 Table 3.1 Table 3.2 Table 3.3 Table 3.4 Table 4.1 Table 4.2 Table 4.3

Table 4.4

The geographical location of the stations used in the present work . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . The fmax-models available in Japan region . . . . . . . . . . . . . . . . . . . . . . . . Statistics of fmax-model with multivariate regression analysis (MVLR) . . . .. . .. . . .. . .. . . .. . .. . . .. . .. . . .. . .. . . .. . .. . . .. . .. . . .. . .. . . .. . Statistics of κ-model with multivariate regression analysis (MVLR) . . . .. . .. . . .. . .. . . .. . .. . . .. . .. . . .. . .. . . .. . .. . . .. . .. . . .. . .. . . .. . Comparison of observed kappa values with other worldwide values estimated by various researchers . .. . . . . .. . . . .. . . . . .. . . . .. . . Event information of 16 earthquakes provided by ISC . . . . . . . . . . Detail information of the location of 18 seismic stations used in this study .. . . .. . . .. . . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . Velocity and resolution variation with depth after Mahesh et al. (2013). Vp and Vs are velocities of P and S waves, respectively. Qp and Qs denote the quality factors employed to quantify the attenuation of seismic waves . . .. . . .. . . .. . . .. . .. . . .. . . .. . .. . . .. . Summary of all 16 fault-plane solutions obtained after performing MT estimation, as well as, depth and magnitude search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18 33 33 36 37 50 53

53

59

Table 6.1

Moho Depth and Possion’s ratio for all the stations . . . . . . . . . . . . .

Table 8.1

Obtained kappa value for all stations of surface as well as for wells . . .. .. . .. .. . .. .. . .. .. . .. .. . .. .. . .. .. . .. .. . .. .. . .. .. . .. .. . .. 117

Table 9.1

Average quality factor at different lapse times and frequencies for OTAV station . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

Table 10.1

Site characteristics and epicentral locations of the recording stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 Various central frequencies with low-cut and high-cut frequency bands are used for filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

Table 10.2

97

xix

xx

Table 10.3

Table 10.4

List of Tables

Q values calculated in different distance ranges, where N is the number of data points and SD is the standard deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 shows the maximum depth of ellipsoid volume formulation given by Pulli (1984) at Sknd station at different distance ranges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

Table 12.1

The obtained focal plane solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

Table 13.1

Error estimations of different types of magnitudes (Wason et al., 2018) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

Chapter 1

Earthquake Occurrence Models Chhavi Chaudhari, M. L. Sharma, and Shusil Gupta

1.1

Introduction

The Seismic Hazard Assessment (SHA) is generally based on two approaches, namely probabilistic and deterministic. A popular technique for SHA is called probabilistic seismic hazard analysis (PSHA), which forecasts a correlation between the maximum ground motions or response spectra and the annual rate of exceedance and return period. Through the use of a mathematical model, PSHA incorporates the occurrence frequencies and ground motions for all earthquakes in an area. PSHA often involves several logic trees, recurrence times, seismic sources, and ground motion attenuation relationships. The rate of occurrence of earthquake events for identified seismogenic source zone is the necessary part of PSHA. The earthquake frequency-size distribution has attracted the attention of numerous researchers. It was initiated by Ishimoto and Iida (1939) and continued by Gutenberg and Richter (1944), and it became one of the frequently used magnitude-frequency relationships in seismology. There are various statistical distributions that have been described which may better reflect seismic gap regions as compared with classical method G-R relationship. In this chapter, two models, namely Constant moment release (CMR) model and Constant seismicity (CS) model, have been described. The Himalayan area has been used as a case study to see the results of these two models.

C. Chaudhari · M. L. Sharma (✉) · S. Gupta Department of Earthquake Engineering, Indian Institute of Technology Roorkee, Roorkee, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 R. Kumar et al. (eds.), Recent Developments in Earthquake Seismology, https://doi.org/10.1007/978-3-031-47538-2_1

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1.1.1

C. Chaudhari et al.

Constant Seismicity (CS) Model

The Gutenberg-Richter’s (1954) relationship, which calculates the yearly occurrence exceedance rates in a designated seismogenic source zone, is the most often used relationship to assess the seismicity of seismogenic sources. According to Cornell and Vanmarcke (1969), a lower threshold magnitude Mmin and an upper bound magnitude Mmax are used to construct the recurrence relation. A temporal sequence of earthquake numbers and an earthquake size distribution exist if the catalogue completion threshold is constant across time. The truncated density function, n(M), outlining the happening rate of earthquakes per unit magnitude at magnitude i can thus be defined as: nð M Þ =

N ðM min Þ  β  e - βðM - M min Þ H ðM max - M Þ Þ 1 - e - βðM max - M min Þ

ð1:1Þ

Here, the Heaviside step function is denoted by H () and β = b*ln 10 (b is known as seismicity constant in GR relationship). The corresponding cumulative distribution function is obtained as: N ðM Þ = N ðM min Þ

e - β M - e - βM max H ðM max - M Þ e - βM min - e - βM max

ð1:2Þ

According to the relationship shown in Eq. 1.2, the occurrence rate of earthquakes N(M ) with magnitudes larger than or identical to the threshold magnitude Mmin does not change but the N(M) diminishes exponentially to zero as M approaches Mmax. So, the term “constant seismicity exponential recurrence model” is used to describe this model. The stages of completeness for various magnitude varieties are a crucial step for modified G-R.

1.1.2

Constant Moment Release (CMR) Model

In CS model, the overall frequency of earthquakes with magnitudes larger than the minimum is unrelated to the maximum magnitude Mmax. Conversely, a lower value of Mmax indicates that there is a lesser moment release in the seismogenic source region that does not correspond to the physical significance of the source region according to the CS model. This may be remedied by limiting the moment release degree that is necessary in a particular location. As a result, the increase in the overall number of minors to moderate earthquakes compensates for the decrease in Mmax. As a result, it is feasible to alter the CMR models utilising the N(Mmin), which was _ 0 ðM max Þ, which was found geologically calculated using the moment release rate M for the given Mmax (Anderson, 1979; Molnar, 1979; Chatelain et al., 1980; Shedlock et al., 1980). The CMR model often makes the following presumptions: (1) If creep

1 Earthquake Occurrence Models

3

is not specifically stated, the complete slide on a fault or within a seismic source is seismic. (2) The average value of the slip rate across large time intervals applies to the future time period of interest, while short-term changes in the slip rate are insignificant. (3) Surface slip rates are typical of slip rates at seismogenic depths and throughout the whole fault segment of interest. By balancing the seismic moment release rate (SMRR) caused by the regular great time period slip rate that can be obtained by geological or geodetic field study. The long-term mean yearly occurrence rate, denoted by the symbol N(Mmin) is calculated under these assump_ 0 = μAS, tions. First, the seismic moment rate can be calculated using the formula M where S is the slip rate in centimetres per year (Brune, 1968). “A” stands for the plane area of the fault rupture in cm2, and μ represents the crustal rock’s modulus of rigidity in dyne/cm2. Shaping the seismic moment linked through the sources is required for the CMR constraint method’s assessment of the overall occurrence rate. The seismic moment linked through any size, according to Kostrov (1974), is determined by the relations as: _ 0 = 2μDLW E_ M

ð1:3Þ

where L stands for length, W denotes seismogenic source width, E_ stands for strain _ 0 is the total seismic moment rate that has been released as a result of rate and M strain rate (Kostrov, 1974; Chatelain et al., 1980; Savage & Simpson, 1997). To calculate the seismic moment, the rate of strain must be precisely measured. The _ ij in the seismogenic source zone is directly related to seismic moment rate tensor M the tensor of strain rate ɛij, which has been calculated using GSRM, and this relation _ ij = 2μAD_εij . A seismogenic zone volume’s SMRR has is based on Kostrov (1974) M been translated from the estimated strain rate at the earth’s surface using this connection (Ward, 1998; Choudhary & Sharma, 2017; WGCEP, 1995). Due to the 2-D strain rate tensor, this relationship measurement is not particular and does not like the double-couple tool proposed by Savage and Simpson (1997). They then proposed a variant to get over this restriction by giving the best resemblance between _ 0 and the rate of crustal strain. the rate of scalar moment M _ 0 = 2μADMaxðε_ 1 , ε_ 2 Þ M

ð1:4Þ

where the two main parts of the strain rate tensor are ε_ 1 and ε_ 2 . The frequencymagnitude figures of earthquakes with a given slope (b) and seismogenic source zone maximum magnitude have been considered to be best modelled by the exponential distribution. So, hypothetically, the SMRR resulting from all earthquakes up to magnitude Mmax can be calculated as: M_ 0 =

M max M min

M 0 ðM ÞnðM ÞdM

ð1:5Þ

4

C. Chaudhari et al.

where M is seismic moment of magnitude, which can be calculated by log M0(M) = 16 + 1.5  M in dyne-cm (Hanks & Kanamori, 1979). n(M), the exponential density function, is defined in terms of the upper bound magnitude Mmax and the occurrence rate N(Mmin). In order to express the estimated seismic moment rate during an earthquake, which is given by Eq. 1.5, in dyne-cm units, use the form _ 0 . Equation 1.6 can be represented as follows following integration: M _ 0 ðM max Þ  M_ 0 ðM Þ = N ðM min Þ  e - βðM - M min Þ  M

b d-b

ð1:6Þ

_ 0 ðM max Þ denotes the moment released by the maximum In these expressions, M possible magnitude of Mmax. Because of the power-law nature of the earthquake magnitude dispersal and the shortage of historical and instrumental earthquake archives for relatively lesser seismic areas, the GR law provides estimates for tiny space-time volumes that are extremely uncertain and occasionally unsteady (McCaffrey, 1997; Arora & Sharma, 1998; Holt et al., 2000). The law is catalogue dependent and gives no indication of the greatest magnitude. It is crucial to apply statistical techniques that closely examine the distribution’s tail, or the variety of its extreme standards, in addition to the main distributions.

1.2

Seismic Hazard Parameter Estimation

The seismic hazard modelling depends on individual tectonic setup and the environment, which implies that model applicability varies with the region, which becomes more complex within the fact that even within the same geological environment, earthquake frequency varies greatly. Various studies have been carried out worldwide to recognize the seismicity processes for different regions, but with such scientific rise, we are quite incapable of modelling real situation. Thus, most of the studies conclude that no single methodology can capture the physical phenomena of earthquake occurrence in specific regions. To model and analyse an earthquake process, one must understand the entire tectonic environment, incorporating route impacts, the rupture mechanism, the source, and the focal mechanism, within the local site circumstances. The stress accumulates due to tectonic plate movement, which is released in the form of earthquakes of several extents ranging from micro seismic measures to macro seismic measures. The quality of the dataset also plays a domineering characteristic of modelling in a pragmatic view. For case study, the Himalayas region has been selected. The orogeny of the Himalaya is characterised by the creation of major earthquakes, making it one of the world’s most active zones. The following sections discuss these study areas by applying different models of earthquake occurrences. The stress regime conditions along the Himalayan belt are highly heterogeneous due to different convergence rates in the various segments of the Himalaya. To accompany the heterogeneity in the Himalaya region, we selected three sub-regions

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Fig. 1.1 The Himalayas and Characterization of three regions on the basis of tectonics and recorded seismicity of magnitude MW ⩾ 5.0 for the time period 1255–2017

in the Himalaya, viz. the North-West Himalaya, Garhwal Himalaya and Nepal region (Fig. 1.1). To incorporate the diversity of stress rates in SHA, we have considered Constant Seismicity and CMR models. Constant Seismicity model is derived from compiled earthquake catalogue, and for implication of CMR model, global strain rate data is utilized. The estimated seismicity for all three regions using both recurrence models have been compared. The seismicity parameters gathered employing two separate approaches were employed to determine the likelihood of an earthquake occurrence of a certain magnitude during a given time period (Shanker & Sharma, 1997; Sharma and Dimri, 2003; Sharma, 2001, 2003; Lindholm et al., 2006; Mahajan et al., 2010; Kushwaha et al., 2021). These recurrence probabilities have been represented using the Poissonian distribution, which calculates the likelihood of the number of earthquakes occurring in a given location and time frame. One of the most important parameters in Probabilistic Seismic Hazard Assessment is the estimation of annual earthquake occurrence rates (Arora & Sharma, 1998; Sharma, 2001; Sharma et al., 2002; Sharma & Malik, 2006; Choudhary & Sharma, 2017, 2018a, b). The seismic hazard calculation of three unique locations spanning the Central Himalaya to the North- West Himalaya has been handled here employing the CS model and the CMR model. Three areas were chosen based on the strain rate build-up heterogeneity and successive release in the form of tectonics, seismic events and geomorphology (Fig. 1.1). The recurrence rate in the Constant Seismicity model is determined by the lower bound magnitude Mmin. Mmin was calculated for computational purposes using the Woessner and Wiemer (2005) technique, while Mmax may be found using the relationship described by Kijko (2004). Figure 1.2 depicts the magnitude frequency distribution and magnitude of completeness for the Himalaya subdivision using the EMR approach.

6 North West

104

No of event cum no of event

Cumulative Number

Mc 4.3

103

Trend line 102

101

100 3

3.5

4

4.5

5 5.5 6 Magnitude

6.5

7

7.5

8

No of event cum no of event

103

Garhwal Himalaya

Cumulative Number

Mc 4

102 Trend line

101

100

3

3.5

4

103

4.5

5 5.5 6 Magnitude

Nepal

6.5

7

7.5

No of event cum no of event

Mc 4

Cumulative Number

Fig. 1.2 Magnitude Frequency Distribution and magnitude of completeness in the subdivision of Himalaya using the EMR method

C. Chaudhari et al.

102

Trend line

101

100 3

4

5

6 7 Magnitude

8

9

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Fig. 1.3 Variation of Cumulative rate of Nmin w.r.t. Mmax in North-West Himalaya using (a) Constant seismicity and (b) Constant Moment Release models

The seismicity parametres values estimated employing the CS model for each section are mentioned in Fig. 1.2. The cumulative numbers larger than or equivalent to threshold magnitude earthquakes in the Constant Seismicity model are not dependent on the maximum magnitude Mmax. Although, a lesser Mmax value results in a lower moment release rate, which is not taken into account by the CS model, it may be avoided by confining the moment release rate in a specified zone. As a result, the decrease in Mmax is compensated for by increasing the earthquakes’ overall number N(Mmin), as illustrated in Figs. 1.3, 1.4, 1.5. Thus, adopting the N(Mmin), it is feasible to change the CS recurrence models. The seismically active region of the North-West Himalaya (fold and thrust belt) has resisted big to moderate earthquake occurrences. According to the findings of an inclusive seismological investigation of the North-West Himalaya, entire seismicity is associated with crucial thrust and undiscovered faults. The majority of the earthquakes happen at shallow depths. In 2005, an earthquake of magnitude 7.6 struck near latitude 34.493°N and longitude 73.629°E, with a focal depth of approximately 26 km. The outcomes show that the overall seismicity rate calculated employing CMR is 55.67% greater than those found using the CS model in the North-West area, indicating that gathered strain was not entirely released by previous earthquakes. This suggests that gathered strain is remunerated for by

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Fig. 1.4 Variation of Cumulative rate of Nmin w.r.t. Mmax in Garhwal Himalaya using (a) Constant seismicity and (b) Constant Moment Release models

Fig. 1.5 Variation of Cumulative rate of Nmin w.r.t. Mmax in Nepal Himalaya using (a) Constant seismicity and (b) Constant Moment Release models

supplementary tectonic activity, such as fault and locking mechanisms, or that the earthquake inventory is incomplete and insufficient. Using CS and CMR models, the predicted total seismicity N(Mmin) values are 70.56 and 109.83, respectively. The estimated yearly occurrence of earthquakes employing the CMR model rate is greater than that projected by the CS model rate for all magnitude ranges in the North-West area, as shown in Fig. 1.6. In the North-West area for CS and CMR, an earthquake of magnitude 7 Mw is predicted to occur in 60 years and 40 years, respectively, according to Fig. 1.6, which shows the likelihood of occurrences of magnitude 7 Mw and 7.5 Mw with duration of exposure (year). Using CS and CMR, an earthquake of magnitude 7.5 is expected to happen in 200 years and 300 years, respectively (Choudhary & Sharma, 2018a, b; Richa et al., 2022). A similar pattern has been seen in the Garhwal Himalaya area, where the total seismicity N(Mmin) rate derived by CS and CMR is 4.6 and 16.3, respectively. The Garhwal Himalaya area is located in the centre seismic gap and has seen less seismicity than the North-West area. The gathered energy budget in the Garhwal Himalaya implies that an earthquake with a magnitude Mw ≥ 8 is about to strike in

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Fig. 1.6 Hazard assessment in North-West Himalaya: (a) annual occurrence rate of earthquake magnitude and (b) probability of earthquake occurrence in the specific time period

Fig. 1.7 Hazard assessment Garhwal Himalaya: (a) annual occurrence rate of earthquake magnitude and (b) probability of earthquake occurrence in a specific time period

the seismic gap zone of Garhwal Himalaya (Bilham et al., 2001). Despite the fact that this region has seen the Uttarkashi earthquake (1991) with a magnitude Mw 6.5 and the Chamoli earthquake (1999) with a magnitude Mw 6.6. Preceding seismic hazard researches, however, have measured a greater likelihood of exceeding greater seismic activity in the Garhwal Himalaya area in the approaching year (Sharma, 2001), and this region has adequate prospective to generate an upcoming major earthquake (Choudhary & Sharma, 2017; Sharma, 2001). The estimated occurrence of yearly earthquakes employing the CMR rate model is 71% greater than that projected by the CS model for all magnitude ranges in the Garhwal Himalaya area, as shown in Fig. 1.7a. Using the CS and CMR models from Fig. 1.7b, this area has been characterised by an earthquake of magnitude Mw 6, which is projected to happen in 100 years and 50 years as reappearance periods of 5 years and 17 years, respectively (Choudhary & Sharma, 2017, 2018a; Maurya et al., 2023). However, an intriguing pattern in calculated findings for the Nepal region may be detected. N(Mmin), the total seismicity projected employing the CS model is estimated to be 78% greater than that computed employing the CMR model. The outcome indicates that the majority of the collected energy has been unconfined as a result of the significant earthquake occurrence (Fig. 1.8a). According to historical records, Nepal has suffered four significant earthquakes of magnitude 8 and nine earthquakes of magnitude 7.0–7.9. The Gorkha earthquake with magnitude Mw 7.8 on 25 April 25 2015 partially cracked the Main Himalayan Thrust (MHT) fault, and it is worth noting that the shallower component of the MHT remained protected

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Fig. 1.8 Hazard assessment in Nepal Himalaya: (a) annual occurrence rate of earthquake magnitude and (b) probability of earthquake occurrence in a specific time period

thereafter (Bilham et al., 2017). Using CS and CMR, a magnitude 8 earthquake will befall 700 years and 1100 years from now, respectively (Fig. 1.8b). From the result estimated, seismicity using Constant Seismicity model is lower than seismicity obtained by Constant Moment release model for North-West. It implies that strain energy is constantly stored but not released in the form of earthquakes. However, the CMS model fails to capture realistic seismicity due to insufficient catalogue. Similar behaviour of seismicity has been identified in Garhwal Himalaya, but CS and CMR models depict low seismicity in comparison to the North West region. However, the Nepal region shows different pattern because maximum stress is released due to the recently large earthquake (Nepal Gorkha Earthquke 2015) that occurred in Nepal. Strain rate data play a vital role in estimating reliable SHA in the Himalaya.

1.3

Probabilistic Seismic Hazard Assessment (PSHA)

To see the effect on PSHA of constant moment releasing constraint, a small segment of Himalaya as Uttarakhand has been selected. Uttarakhand lies in the central seismic gap of the Himalaya, a region where nonstop stress is gathering although not released with earthquakes, which is acknowledged as a seismic gap. To minimize the effect of earthquake and destruction of important structures, there is a need for seismic hazard examination of the Uttarakhand Himalaya. The PSHA is carried out based on parameter standards of the Gutenberg- Richter recurrence relationship. The estimation of parameters of the Gutenberg- Richter has been based on two models, Constant Seismicity using the past earthquake data seismicity and Moment release constraints method based on GSRM strain rate data. Further, these seismicity parameters have been used in PSHA at specific sites for an exposure time of 50 years using four New Generation Attenuation Relationships published in 2008 attenuation relationships. Uniform hazard contours for PGA have been obtained using constant seismicity and moment release constraint for a revelation time of 50 years for 90% and 98% confidence levels. For the estimation of PSHA, Uttarakhand is alienated into minor grids of size 0.2° × 0.2°. PGA has been estimated

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Fig. 1.9 Hazard Maps of PGA having 10% probability of exceedance in 50 years using Boore and Atkinson (2008) for (a) Constant seismicity and (b) Constant Moment Release Models

Fig. 1.10 Hazard Maps of PGA having 2% probability of exceedance in 50 years using Boore and Atkinson (2008) for (a) Constant seismicity and (b) Constant Moment Release Models

at the centre point of each grid for 90% and 98% likelihood of occurrence in 50 years (return period of 475 years and 2475 years). The resulting PGA distribution Uttarakhand Himalaya is shown in contour Maps Fig. 1.9a, b, respectively, considering Constant Seismicity and using Moment Release constraint. The comparison of PGA values at different sites, estimated by both models, indicates that PGA values based on Constant Moment release rate are higher than those based on Constant Seismicity model for return periods of 475 and 2475 years (Fig. 1.10a, b). It has been observed that the values of PGA obtained from the Seismic Moment Release Constraint method are higher than the PGA from constant seismicity in those regions where the occurrence of large return period earthquake events is negligible, although enough potential to trigger a large event exists. In Constant Moment release rate, the accumulated energy may be compensated to increase the number of occurrences of small to moderate earthquakes.

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Conclusion

The hazard maps indicate that the ground motion pattern remains the same for the methods, i.e. Constant Seismicity and Moment Release constraint, but the values of PGA from constant seismicity are less compared to the one obtained from seismic moment release constraint. The hazard (PGA) obtained from the Constant Seismicity is similar to the past recorded ground motion at various sites, but the hazard obtained from the seismic moment release method is very high, which reflects that higher seismicity may be released in the future. This chapter draws attention towards the use of the seismic hazard results, which should consider such models for more realistic seismic hazard parameters.

References Anderson, J. G. (1979). Estimating the seismicity from geological structures for seismic risk studies. Bulletin of the Seismological Society of America, 69, 135–158. Arora, M., & Sharma, M. L. (1998). Seismic hazard analysis – An artificial neural network approach. Current Science, 75(1), 54–59. Bilham, R., Gaur, V. K., & Molnar, P. (2001). Himalayan seismic hazard. Science, 293, 1441–1444. Bilham, R., Mencin, D., Bendick, R., & Bürgmann, R. (2017). Implications for elastic energy storage in the Himalayas from the Gorkha 2015 earthquake and other incomplete ruptures of the Main Himalayan Thrust. Quaternary International, 462, 3. Boore, M. D., & Atkinson, G. (2008). Ground-motion prediction equations for the average horizontal component of PGA, PGV, and 5% damped PSA at spectral periods between 0.01 s and 10.0 s. Earthquake Spectra, 24, 99. Brune, J. N. (1968). Seismic moment, seismicity and rate of slip along major fault zones. Journal of Geophysical Research, 73, 777–784. Chatelain, J. L., Roecker, S. W., Hatzfeld, D., & Molnar, P. (1980). Microearthquake seismicity and fault plane solutions in the Hindu Kush region and their tectonic implications. Journal of Geophysical Research: Solid Earth, 85(B3), 1365–1387. Choudhary, C., & Sharma, M. L. (2018a). Global strain rates in western to central Himalayas and their implications in seismic hazard assessment. Natural Hazards, 94(3), 1211–1224. Choudhary, C., & Sharma, M. L. (2017). Probabilistic models for earthquakes with large return periods in Himalaya region. Pure and Applied Geophysics, 174, 4313–4327. Choudhary, C., & Sharma, M. L. (2018b). Implications of constant seismicity and constant moment release models on seismic hazard, 16th Symposium on Earthquake Engineering. Cornell, C. A., & Vanmarcke, E. H. (1969). The major influences on seismic risk. Proceedings of the Fourth World Conference on Earthquake Engineering, Santiago, Chile (Vol. A-1, pp. 69–93). Gutenberg, B., & Richter, C. F. (1944). Frequency of earthquakes in California. Bulletin of the Seismological Society of America, 34(4), 1985–1988. Gutenberg, B., & Richter, C. F. (1954). Seismicity of the earth (2nd ed.). Princeton Press. Hanks, T. H., & Kanamori, H. (1979). A moment magnitude scale. Journal of Geophysical Research, 84, 2348–2350. Holt, W. E., Chamot-Rooke, N., Le Pichon, X., Haines, A. J., Shen-Tu, B., & Ren, J. (2000). Velocity field in Asia inferred from quaternary fault slip rates and global positioning system observations. Journal of Geophysical Research, 105, 19 185–19 209.

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Ishimoto, M., & Iida, K. (1939). Observations of earthquakes registered with the microseismograph constructed recently. Bulletin of the Earthquake Research Institute, 17, 443–478. Kijko, A. (2004). Estimation of the maximum earthquake magnitude, mmax. Pure and Applied Geophysics, 161(8), 1655–1681. Kostrov, V. V. (1974). Seismic moment and energy of earthquakes and seismic flow of rock, Izvestiya, Academy of Sciences, USSR. Physics of the Solid Earth, 1, 13–21. Kushwaha, P. K., Maurya, S. P., Rai, P., & Singh, N. P. (2021). Estimation of subsurface rock properties from seismic inversion and geo-statistical methods over F3-block, Netherland. Exploration Geophysics, 52(3), 258–272. Lindholm, C., Sharma, M. L., & S. Malik (2006) Seismic hazard estimation in Dehradun city, First European conference on earthquake engineering and seismology, Geneva, September 3–8, 2006. Mahajan, A. K., Thakur, V. C., Sharma, M. L., & Chauhan, M. (2010). Probabilistic seismic hazard map of NW Himalaya and its adjoining area, India. Natural Hazards, 53, 443–457. Maurya, S. P., Singh, R., Mahadasu, P., Singh, U. P., Singh, K. H., Singh, R., Kumar, R., & Kushwaha, P. K. (2023). Qualitative and quantitative comparison of the genetic and hybrid genetic algorithm to estimate acoustic impedance from post-stack seismic data of Blackfoot field, Canada. Geophysical Journal International, 233(2), 932–949. McCaffrey, R. (1997). Statistical significance of the seismic coupling coefficient. Bulletin of the Seismological Society of America, 87, 1069–1073. Molnar, P. (1979). Earthquake recurrence intervals and plate tectonics. Bulletin of the Seismological Society of America, 69, 115. Richa, Maurya, S. P., Singh, K. H., Singh, R., Kumar, R., & Kushwaha, P. K. (2022). Application of maximum likelihood and model-based seismic inversion techniques: A case study from KG basin, India. Journal of Petroleum Exploration and Production Technology, 12, 1–19. Savage, J. C., & Simpson, R. W. (1997). Surface strain accumulation and the seismic moment tensor. Bulletin of the Seismological Society of America, 87, 1345–1353. Shanker, D., & Sharma, M. L. (1997). Statistical analysis of completeness of seismicity data of the Himalayas and its effect on earthquake hazard determination. Bulletin of the Indian Society of Earthquake Technology, 34(3), 159–170. Sharma, M. L., & Dimri, R. (2003). Seismic hazard estimation and zonation of northern Indian region for bed rock ground motion. Journal of Seismology and Earthquake Engineering, 5(2), 23–34. Sharma, M. L., & Malik, Shipra (2006). Probabilistic seismic hazard analysis and estimation of spectral strong ground motion on bed rock in north east India. In Fourth international conference on earthquake engineering, Taipei, Taiwan, paper (No. 15). Sharma, M. L. (2001). Seismotectonic implications of Chamoli earthquake of March 29, 1999, Proc. Workshop on recent earthquakes of Chamoli and Bhuj, May 24–26, Roorkee, Vol II, pp. 359–368. Sharma, M. L., (2003). Seismic hazard in Northern India region, Seismological Research Letters. 74(2), March/April 2003, pp. 140–146. Sharma, M. L., Khan, M., & Arora, M. K., (2002). A GIS based approach for seismic hazard assessment, Asian Seismological commission 2002, Symposium on seismology, earthquake hazard assessment and risk management, 24–26 Nov, 2002, Kathmandu, Nepal, p. 43. Shedlock, K. M., Mcguire R. K., & Herd D. G., (1980). Earthquake recurrence in the San Francisco Bay Region, California, from the fault slip and seismic moment, USGS Open File Report, 1980, pp. 80–999. Ward, S. N. (1998). On the consistency of earthquake moment release and space geodetic strain rates. Geophysical Journal International, 135(3), 1011–1018. WGCEP. (1995). Seismic hazard in Southern California: Probable earthquake, 1994 to 2024. Bulletin of Seismological of America, 85(2), 379–439. Woessner, J., & Wiemer, S. (2005). Assessing the quality of earthquake catalogues: Estimating the magnitude of completeness and its uncertainty. Bulletin of the Seismological Society of America, 95(2), 684–698.

Chapter 2

Estimation and Validation of Arias Intensity Relation Using the 1991 Uttarkashi and 1999 Chamoli Earthquakes Data Parveen Kumar, Sandeep, and Monika

2.1

Introduction

The Garhwal Himalaya is situated in the Uttarakhand state, which falls in the central seismic gap (CSG) of main to great earthquakes (Bilham, 2019; Monika et al., 2020). In modern years, this area has witnessed the 1991 Uttarkashi earthquake with magnitude Mw 6.8 and the 1999 Chamoli earthquake with magnitude (Mw 6.6), which caused heavy destruction in this region. Several researchers suggested that continuous building of stress in the CSG region threatens the occurrence of a great earthquake with magnitude Mw ≥ 8 in this area (Bilham et al., 1995; Célérier et al., 2009; Gahalaut & Kundu, 2012; Jade et al., 2017; Kumar et al., 2015a, 2021). So the possibility of happening of a great earthquake gives seismological importance to this study area. Earthquake-resistant structures can lessen earthquake destruction, and building such type of structures requires information about earthquake parameters. Parameters only having the amplitude of the ground motion, such as peak ground acceleration (PGA), are not sufficient to indicate this damage, but the parameters that include the features of amplitude, duration, and ground motion frequency content, such as Arias intensity (Ia), are more reliable in predicting the damage (e.g. Housner, 1965; Ambraseys, 1974; Evernden et al., 1981). Arias intensity measures the strength of the ground motion, and it is defined as the total energy per unit weight

P. Kumar (✉) Wadia Institute of Himalayan Geology, Dehradun, India Sandeep Banaras Hindu University, Varanasi, India Monika Wadia Institute of Himalayan Geology, Dehradun, India Banaras Hindu University, Varanasi, India © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 R. Kumar et al. (eds.), Recent Developments in Earthquake Seismology, https://doi.org/10.1007/978-3-031-47538-2_2

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kept by a simple oscillators set with uniform frequency spacing (Arias, 1970; Maurya et al., 2020; Kushwaha et al., 2020; Maurya & Singh, 2020). Several researchers have used Ia to evaluate the hazard potential of different regions. Arias intensity has been interrelated to (1) earthquake-triggered landslides (Ambraseys, 1974; Wilson and Keefer, 1985; Jibson, 2007; Lee et al., 2008; Kushwaha et al., 2021), (2) the reaction of rigid bridge constructions to ground motions during earthquakes (Harp & Wilson, 1995; Mackie & Stojadinovic, 2002), (3) destruction stages in adobe and clay constructions (Cabanas et al., 1997), and (4) liquefaction potential of soil deposits during earthquakes (Kayen & Mitchell, 1997). The vast implication of the Ia for the different aspects exhibits its significance for evaluating hazards due to earthquakes. In the present work, the strength of the ground shivering is assessed by assessing the acceleration of temporary seismic waves of the 20 October 1991 Uttarkashi earthquake of magnitude Mw 6.8 and the 28 March 1999 Chamoli earthquake of magnitude Mw 6.6 in the Garhwal area of North-West Himalaya.

2.2

Seismotectonic and Data Set

The Garhwal region is localed in the state of Uttarakhand, India, and it is part of North-West Himalaya. This region comprises major thrusts from south to north (Fig. 2.1): (1) the Himalayan Frontal Thrust (HFT), which separates the IndoGangetic plane existing in the South from the molassic Siwalik of Mio-Pliocene ages (Siwalik Himalaya), situated to the North of HFT; (2) the Main Boundary Thrust (MBT), which is the boundary of the Siwalik Himalaya and Lesser Himalaya, which is present to the North of MBT and contains sedimentary rocks along with few outcrops of crystalline rocks; (3) the Main Central Thrust (MCT) is designated as the margin of the smaller and higher Himalayas. The higher Himalaya comprises a north-dipping pile of metamorphic rocks, and (4) the South Tibetan Detachment System (STDS) is the contact of the higher Himalaya and Tethys Himalaya, which includes sedimentary rocks (Gansser, 1964; Le Fort, 1975; Valdiya, 1980; Hodges, 2000; Banerjee & Bürgmann, 2002; Bhattacharya, 2008; Kumar et al., 2015b). The historical seismicity of this region during the period of 1935–2021 is explored and represented in Fig. 2.1. The extraordinary seismicity of this area clearly depicts that the Garhwal region is seismically active. Along with several smallmagnitude earthquakes, this area has also witnessed a few major earthquakes in the recent past. Chamoli and Uttarkashi earthquakes’ strong motion data, provided by PESMOS network (Mittal et al., 2012; Kumar et al., 2012), are utilized for the present work. These data are recorded at 11 stations within 103 km epicentral distance, and the geographical positions of the recording stations are reported in Table 2.1.

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Estimation and Validation of Arias Intensity Relation Using. . .

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Fig. 2.1 Seismicity during 1935–2021 of Uttarakhand Himalaya, India report by the bulletin of ISC (International Seismological Centre). The blue color star symbols represent the epicentre of the Uttarkashi and Chamoli earthquakes. (The figure is modified after Valdiya (1980) and Célérier et al. (2009))

2.3

Methodology

The Arias intensity maps established for the Garhwal region correspond to the 1991 Uttarkashi earthquake with magnitude Mw 6.8 and the 1999 Chamoli earthquake with magnitude Mw 6.6. In the present work, Arias intensity values are calculated in two ways (1) by using a waveform record and (2) from the empirical relation. The strong motion waveform recorded at different stations is utilized to calculate the Arias intensity value. Arias (1970) defined an instrumental intensity measure established on the integral over the time duration of the ground motion of the square of the acceleration as:

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Table 2.1 The geographical location of the stations used in the present work Sr. no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Stations name Bhatwari Uttarkashi Ghansali Barkot Rudraprayag Srinagar Purola Karnaprayag Tehri Kausani Almora Gopeshwar Joshimath Ukhimath Cinyalisaur

Latitude (Degree) 30.80 30.73 30.41 30.80 30.26 30.21 30.86 30.25 30.36 29.68 29.58 30.40 30.55 30.50 30.55

π I obs = 2g

Longitude (Degree) 78.60 78.45 78.65 78.21 78.98 78.76 78.08 79.23 78.05 79.71 79.65 79.33 79.56 79.10 78.33

t max

½aðt Þ]2 dt

ð2:1Þ

0

where Iobs is the Arias intensity from the observed record, tmax denotes the total period of the ground motion, g denotes the acceleration due to gravity and a(t) denotes acceleration of ground motion at time t. Arias intensity is expressed in the unit of m/sec. Wilson, 1993 proposed an empirical relation of Arias intensity (Ie), moment magnitude (Mw), stress drop (Δσ) and hypocentral distance (R) as: logðI e Þ = 4=3 logðΔσ Þ þ M - 2 logðRÞ - 6:66

ð2:2Þ

The average stress reduction connected with Himalayan earthquakes is about 60 bars (Kumar et al., 2008; Sharma et al., 2014), so the drop in stress is considered 60 bars for the present work. R ≤ 150 km is considered for this work. The Arias intensity values are computed at different recording stations using the observed record and from empirical relation as per Eqs. 2.1 and 2.2, respectively. These two procedures are adopted to compute Arias intensity values to validate the empirical relation (Eq. 2.2) for the present study region. After validation of this empirical relation, the Arias intensity maps are generated for the study region.

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2.4

19

Results and Discussion

The Arias intensity map is prepared for the Garhwal region and the intensity is estimated by using the empirical relation proposed by Wilson (1993). To validate this empirical relation for this study area, the Arias intensity is also computed by using the observed data of the 1991 Uttarkashi and 1999 Chamoli earthquakes. The acceleration records of both earthquakes are recorded at 9 and 7 stations and are utilized to compute the Arias intensity values at these stations. The Arias intensity (Ia) from observed records is computed by using the horizontal component. The comparison of Arias intensity obtained using empirical relation, and observed earthquake records are represented in Fig. 2.2. This figure reveals that Arias intensity obtained from the observed records does not vary so much from the Ia value obtained from the empirical relation and the resemblance of these values validates the empirical relation used in this work for the present study region. After validating the empirical relation proposed by Wilson (1993), the arias intensity map is prepared using this relation for the Uttarkashi and Chamoli earthquakes. For the map’s preparation, the study area is divited into 100 small grids having dimensions of 0.1° × 0.1° of each grid. The Arias intensity value is computed at each corner of every small grid corresponding to the epicentre of the Uttarkashi (30.78°N, 78.77°E) and Chamoli earthquakes (30.51°N, 79.40°E). The values obtained at each corner are further used to prepare the Arias intensity distribution map as shown in Fig. 2.3b, c. The maximum Arias intensity values for the Uttarkashi and Chamoli earthquakes are 3.2 m/s and 2.0 m/s, respectively. Several research groups suggest that Arias intensity value > 0.11 m/s is responsible for triggering a landslide (Keefer & Wilson, 1989; Harp & Wilson, 1995; Abdrakhmatov et al., 2003). Therefore, the region with Arias intensity value > 0.11 m/s is probable for coseismic landslides. Hence, in the present study region (Fig. 2.3b, c), the Arias intensity distribution maps reveal that 51% and 45% of the area exhibit > 0.11 m/s Arias intensity correspond to the Uttarkashi and Chamoli earthquakes, respectively, and thus prone to failure. Keefer and Wilson (1989) and Abdrakhmatov et al. (2003) proposed the threshold values of arias intensity for different types of slopes failure. They offered the threshold value for slumps, earth flows, and block slides as 0.32 m/s and for lateral spreads and flows as 0.54 m/s. The arias intensity map of Uttaakashi earthquake depicts that 23% and 16% of the area consist > 0.32 m/s and > 0.54 m/s

Fig. 2.2 The comparison of Arias intensity values obtained from empirical and observed data for the 1991 Uttarkashi and 1999 Chamoli earthquakes

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Fig. 2.3 (a) The blue color box shows the location of the study region for which Arias intensity maps are prepared. The Arias intensity map for (b) the Uttarkashi earthquake and (c) the Chamoli earthquake. The variation of Arias intensity values along the profile (d) AB and (e) CD. The symbol star denotes the location of the epicentres of the Uttarkashi and Chamoli earthquakes

Arias intensity. While the map of Chamoli earthquake suggests 21% and 15% of the area consist > 0.32 m/s and > 0.54 m/s Arias intensity. The arias intensity values are decreased as we move away from the earthquake’s epicentre, as represented in Fig. 2.3d, e. The present study region lies in the central seismic gap, and this region has the probability of happening of a major earthquake (Khattri, 1987). Therefore, the region’s Arias intensity maps are developed for future scenario earthquakes of magnitude 8.5 (Mw). Two cases are considered to establish the Arias intensity maps; in the first case, the scenario earthquake is taken to correspond to the epicentre of Uttarkashi earthquake. In another case, a scenario earthquake is considered at the epicentre of the Chamoli earthquake. The Arias intensity maps for future scenario earthquakes corresponding to the epicentre of Uttarkashi and Chamoli earthquakes are revealed in Fig. 2.4a, b, respectively.

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Fig. 2.4 The Arias intensity maps for future scenario earthquakes (Mw 8.5) correspond to the epicentre of the (a) Uttarkashi and (b) Chamoli earthquakes

2.5

Conclusions

In this research work, Arias intensity maps are prepared for the 1991 Uttarkashi earthquake (Mw 6.8) and 1999 Chamoli earthquake (Mw 6.6). The empirical relationship between Arias intensity and spectral parameters such as moment magnitude (Mw), stress drop, and hypocentral distance is utilized to prepare the Arias intensity map for the Garhwal Himalaya, India. The empirical relation is authenticated by employing the strong motion data of the Chamoli and Uttarkashi earthquakes recorded at different stations. The close resemblance of Arias intensity values obtained from the observed data and empirical relations provides the validation of the empirical relation for the present study region. The Arias intensity map correspond to future scenario earthquakes of magnitude 8.5 (Mw) and is also prepared for the Garhwal region. As the whole study region comprises Arias intensity value > 0.11 m/s, the complete study region is susceptible to co-seismic landslide corresponding to a scenario earthquake of 8.5 (Mw) magnitude. This study provides significant inputs that can be used for hazard mitigation due to an earthquake. Acknowledgement The authors are thankful to the Director, Wadia Institute of Himalayan Geology, Dehradun, India for his support, inspiration, and amenities. The authors sincerely acknowledge the strong motion data provided by PESMOS through the website www.pesmos.in. The International Seismological Centre (ISC) is acknowledged for providing an earthquakes bulletin through the site (www.isc.ac.uk). Authors Sandeep and Monika also acknowledge the Dept. of Geophysics, Banaras Hindu University, Varanasi.

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References Abdrakhmatov, K., Havenith, H. B., Delvaux, D., Jongmans, D., & Trefois, P. (2003). Probabilistic PGA and Arias intensity maps of Kyrgyzstan (Central Asia). Journal of Seismology, 7, 203–220. Ambraseys, N. N. (1974). Notes on engineering seismology. In: Solnes, J., (Ed.), Engineering seismology and earthquake engineering [NATO advanced study institute, Izmir, 1973]: Leiden, Noordhoff, pp.33–54. Arias, A. (1970). A measure of earthquake intensity. In R. J. Hansen (Ed.), Seismic design for nuclear power plants (pp. 438–483). MIT Press. Banerjee, P., & Bürgmann, R. (2002). Convergence across the northwest Himalaya from GPS measurements. Geophysical Research Letters, 29(13), 30–31. Bhattacharya, A. R. (2008). Basement rocks of the kumaun – Garhwal Himalaya: Implications for Himalayan tectonics, I(I), pp.1–10. Bilham, R. (2019). Himalayan earthquakes: A review of historical seismicity and early 21st century slip potential. Geological Society, London, Special Publications, 483(1), 423–482. Bilham, R., Bodin, P., & Jackson, M. (1995). Entertaining a great earthquake in western Nepal: Historic inactivity and geodetic tests for the present state of strain. Journal of Nepal Geological Society, 11(1), 73–78. Cabanas, L., Benito, B., & Herráiz, M. (1997). An approach to the measurement of the potential structural damage of earthquake ground motions. Earthquake Engineering & Structural Dynamics, 26(1), 79–92. Célérier, J., Harrison, T. M., Beyssac, O., Herman, F., Dunlap, W. J., & Webb, A. A. G. (2009). The Kumaun and Garwhal lesser Himalaya, India: Part 2: Thermal and deformation histories. Geological Society of America Bulletin, 121, 1281–1297. Evernden, J. F., Kohler, W. M., & Clow, G. D. (1981). Seismic intensities of earthquakes of conterminous United States their prediction and interpretation: U.S. Geological Survey Professional Paper 1223, 56 p. Gahalaut, V. K., & Kundu, B. (2012). Possible influence of subducting ridges on the Himalayan arc and on the ruptures of great and major Himalayan earthquakes. Gondwana Research, 21, 1080–1088. Gansser, A. (1964). Geology of the Himalayas (p. 289). Interscience. Harp, E. L., & Wilson, R. C. (1995). Shaking intensity thresholds for rock falls and slides: Evidence from 1987 Whittier narrows and Superstition Hills earthquake strong-motion records. Bulletin of the Seismological Society of America, 85, 1739–1757. Hodges, K. V. (2000). Tectonics of the Himalaya and southern Tibet from two perspectives. Geological Society of America Bulletin, 112(3), 324–350. Housner, G. W. (1965). Intensity of earthquake ground shaking near the causative fault: Proceedings of the third world congress of earthquake engineering, New Zealand, 1965, (Session III), 1, pp.94–111. Jade, S., Shrungeshwara, T. S., Kumar, K., Choudhury, P., Dumka, R. K., & Bhu, H. (2017). India plate angular velocity and contemporary deformation rates from continuous GPS measurements from 1996 to 2015. Scientific Reports, 7, 11439. Jibson, R. W. (2007). Regression models for estimating coseismic landslide displacement. Engineering Geology, 91(2), 209–218. Kayen, R. E., & Mitchell, J. K. (1997). Assessment of liquefaction potential during earthquakes by Arias intensity. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 123, 1162–1174. Keefer, D. K., & Wilson, R.C. (1989). Predicting earthquake-induced landslides, with emphasis on arid and semi-arid environments. In P. M. Sadler & D. M. Morton (Eds.), Landslides in a semiarid environment (Vol. 2(1), pp. 18–149), Inland Geological Society of Southern California Publications, Riverside, California.

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Khattri, K. N. (1987). Great earthquake seismicity gaps and potential for earthquake disaster along the Himalaya plate boundary. Tectonophysics, 138, 79–92. Kumar, A., Mittal, H., Sachdeva, R., & Kumar, A. (2012). Indian strong motion instrumentation network. Seismological Research Letter, 83(1), 59–66. Kumar, D., Sriram, V., Sarkar, I., & Teotia, S. S. (2008). An estimate of a scaling law of seismic spectrum for earthquakes in Himalaya. Indian Minerals, 61(3–4), 1–4. Kumar, P., Joshi, A., & Sandeep, K. A. (2015b). Three-dimensional attenuation structure in the region of Kumaon Himalaya, India based on inversion of strong motion data. Pure and Applied Geophysics, 172(2), 333–358. Kumar, P., Joshi, A., Sandeep, K. A., & Chadha, R. K. (2015a). Detailed attenuation characteristics of shear waves in Kumaon Himalaya, India using the inversion of strong motion data. Bulletin of the Seismological Society of America, 105(4), 1836–1851. Kumar, P., Monika, S., Kumar, S., Kumari, R., Kumar, D., & Kumar, N. (2021). Characterization of shear wave attenuation and site effects in the Garhwal Himalaya, India from inversion of strong motion records. Journal of Earth System Science, 130(186), 1–19. Kushwaha, P. K., Maurya, S. P., Rai, P., & Singh, N. P. (2021). Estimation of subsurface rock properties from seismic inversion and geo-statistical methods over F3-block, Netherland. Exploration Geophysics, 52(3), 258–272. Kushwaha, P. K., Maurya, S. P., Singh, N. P., & Rai, P. (2020). Use of maximum likelihood sparse spike inversion and probabilistic neural network for reservoir characterization: A study from F-3 block, The Netherlands. Journal of Petroleum Exploration and Production Technology, 10, 829–845. Le Fort, P. (1975). Himalayas: The collided range. Present knowledge of the continental arc. American Journal of Science, 275(A), 1–44. Lee, C. T., Huang, C. C., Lee, J. F., Pan, K. L., Lin, M. L., & Dong, J. J. (2008). Statistical approach to earthquake-induced landslide susceptibility. Engineering Geology, 100(1), 43–58. Mackie K., & Stojadinovic B. (2002). Optimal probabilistic seismic demand model for typical highway overpass bridges. In: Proceedings of 12th European conference on earthquake engineering, London, 9–13 September, The Netherlands: Elsevier Science Ltd. paper no. 467, pp. 9–13. Maurya, S. P., & Singh, N. P. (2020). Effect of Gaussian noise on seismic inversion methods. Journal of Indian Geophysical Union, 24(1), 7–26. Maurya, S. P., Singh, N. P., & Singh, K. H. (2020). Seismic inversion methods: A practical approach (Vol. 1). Springer. Mittal, H., Kumar, A., & Ramhmachhuani, R. (2012). Indian national strong motion instrumentation network and site characterization of its stations. International Journal of Geosciences, 3, 1151–1167. Monika, K. P., Sandeep, K. S., Joshi, A., & Devi, S. (2020). Spatial variability studies of attenuation characteristics of Qα and Qβ in Kumaon and Garhwal region of NW Himalaya. Natural Hazards, 103, 1219–1237. Sharma, S., Dasgupta, A., Kumar, A., Bharanidharan, B., Mittal, H., & Sachdeva, R. (2014). Earthquake activity in Kishtwar –Dharamshala region of north-west Himalaya. International Journal of Advanced Research, 2(8), 463–470. Valdiya, K. S. (1980). Geology of the Kumaun lesser Himalaya: Dehra Dun (p. 291). Wadia Institute of Himalayan Geology. Wilson, R. C., & Keefer, D. K. (1985). Predicting areal limits of earthquake-induced landsliding. In: Ziony, J. I. (Ed.) Evaluating earthquake hazards in the Los Angeles region—An earthscience perspective (pp. 317–345). US Geological Survey Professional Paper 1360. Wilson, R. C. (1993). Relation of Arias intensity to magnitude and distance in California (pp. 2331–1258). US Geological Survey.

Chapter 3

Exploring the Concept of Self-Similarity and High-Frequency Decay Kappa-Model and fmax-Model Using Strong-Motion Surface and Borehole Data of Japan: A Statistical Approach Rohtash Kumar, Raghav Singh, Amritansh Rai, Sandeep, S. P. Singh, S. P. Maurya, and Prashant Kumar Singh

3.1

Introduction

In the past decade, the Japan seismological network provided a breakthrough in various earthquake studies, especially earthquake source dynamics. However, the analysis of high-frequency features of the ground motion is still challenging. The acceleration spectra corresponding to the ω-square model (Aki, 1967; Brune, 1970, 1971; Kushwaha et al., 2019) raises with increasing frequency and become flat beyond corner frequency. Hanks (1982) noticed that there is an additional frequency called the maximum cut-off frequency ( fmax) characterized by sharp decay of amplitude. Anderson and Hough (1984) interpreted the spectral decay as exponential trend e‑πf κ, where ‘κ’ is kappa estimated in semi-log by linear regression. However, the source of high-frequency decay is still debatable. Hanks (1982) suggest the site condition are responsible for the decay. Papageorgiou and Aki (1983) relate the decay with the source. More recent studies of Tsai and Chen (2000), Purvance and Anderson (2003) and Kumar et al. (2014) suggest that the decay depends on both source and site characteristics. However, the complexity is still to be resolve. Various methods have been used by different scholars to estimate the ‘κ’. Also, different empirical relationships are developed such as shear wave 30 m velocity and ‘κ’ suggested (e.g., Silva et al., 1998; Edwards et al., 2011), zero distance kappa (κ 0) with bedrock depth and resonant frequency (Ktenidou et al., 2015). Van Houtte et al. (2011) estimated the κ using surface and borehole data of Japan and observed that

R. Kumar · R. Singh · A. Rai (✉) · Sandeep · S. P. Maurya · P. K. Singh Department of Geophysics, Institute of Science, Banaras Hindu University, Varanasi, India e-mail: [email protected] S. P. Singh Department of Atomic Energy, Mumbai, India © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 R. Kumar et al. (eds.), Recent Developments in Earthquake Seismology, https://doi.org/10.1007/978-3-031-47538-2_3

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the kappa value from borehole data is lower than the kappa value from surface data. They used the spectral inversion method and examined the kappa for source, propagation and site effect. Ktenidou et al. (2014) reviewed the ‘κ’ mainly focusing on kappa as site effect, and an empirical relationship between Vs30 and kappa was established. They have also shown the variation in site-dependent kappa in various studies and complied with them. Many researchers, e.g. Kawase and Matsuo (2004), Tsurugi et al. (2006, 2012, 2017), Wen and Chen (2012), Sato (2013), Tanaka et al. (2017) and so on, studied the spectral decay power function and fmax in the frequency range 5–30 Hz and concluded that fmax is independent of the seismic moment. Sato (2013) found no relationship between the average fmax with the seismic moment. However, Papageorgiou and Aki (1983) and Petukhin et al., 1999) observed that fmax decreases with the increasing seismic moment. Wen and Chen (2012) agree with Papageorgiou and Aki (1983) in his observation analyzing the Wenchuan earthquake (2008) and found fmax related to the source dynamics. The high-frequency spectral decay parameter ‘κ’ and fmax are very important as these are required in the prediction of strong ground motion (Boore, 1983, 2003), methods of empirical Green’s function (Irikura, 1986) and methods involving stochastic Green’s (Kamae et al., 1991). The goal of the present study is to enlighten the high-frequency spectral decay and evaluate these characteristics in the southwest Japan region. The most commonly used model in Japan is fmax while another kappa is used in other worldwide studies (Ktenidou et al., 2014). To evaluate the high-frequency characteristics, the ω2 model of Brune (1970, 1971) is used. The dependency of κ-model and fmax -model on epicentral distance and magnitude has been studied using statistical methods by analyzing the surface as well as borehole strong motion data of the Japan KIK-NET network.

3.2

Data Set

The Japan seismological network is consisting of K-NET (Kyoshin Network) and KiK-NET (Kiban Kyoshin Network) networks. The KiK-net network consists of pairs of seismographs installed on the ground surface as well as in a borehole with high sensitivity seismograph (Hi-NET). The pair of surface and borehole accelerometers are installed at approximately 700 locations in Japan. The Kyoshin Net (K-NET) seismological network of strong-motion seismometers provides the best quality of data set for analysis and resolving the various mysteries of the earth’s interior. The network consists of roughly 1,035 KNET95-type strong-motion accelerometers distributed all over Japan with 20m spacing. These three-component broadband accelerometers have a tolerance of 2000 Gals and a wide dynamic range. In the present study, the data recorded by KiK-NET in southwestern Japan is used for analysis. Both surface and borehole data have been utilized. The location of stations and earthquake epicentres are shown in Fig. 3.1.

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Fig. 3.1 Map showing KIK-NET sites and the epicentres of earthquakes used in the study

3.3 3.3.1

High-Frequency Spectral Decay Models fmax-Model

The Brune (1970) model is not adequate to elucidate the high-frequency attenuation of earthquake acceleration spectra. Deviation from the Brune (1970) model, Hanks (1982) introduced a frequency parameter ‘fmax’ above corner frequency. The phenomenon of high-frequency band constrains of the energy radiated from the earthquake was called ‘the crashing spectrum syndrome’. Hanks (1982) never omitted the upshot of source in the enlightenment of fmax but accredited the phenomenon

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primarily to localized site properties. The ‘fmax-model can be used to estimate corner frequency ( fc), seismic moment (M0), cutoff frequency ( fmax) and power coefficient of high-frequency decay (s), from the theoretical earthquake spectra. The theoretical acceleration spectra Af( f ) at a site based on the source spectra Sf( f ) wave propagation media and high-frequency decay factor P( f ) is given as: Af ðf Þ =

M 0 Rθ∅ FSPR 1 Sðf Þ exp X 4πρβ3

- πfX Qf β

Pðf Þ

ð3:1Þ

where, Rθφ is the radiation coefficient at azimuth ‘φ’ and ray take of angle ‘θ’ (here average value Rθφ is assumed 0.63 after Boore & Boatwright, 1984), ‘PR’ is the depletion factor accounting the energy partition into horizontal components (because of the vector sum of horizontal components, it is taken as a unit), ‘FS’ is a factor because of free surface amplification (taken as 2 after Bormann (2002)), ‘X’ is the hypocentral distance, ‘β’ is the velocity of S-wave and ‘Qf ’ is the S-wave quality factor. Boore (1983) defined P( f ) as a high cutoff Butterworth filter of ‘pth’ order as: 1

pð f Þ = 1þ

p

f

ð3:2Þ

f max

ω2 – source model of Brune (1970) defined by the Fourier Spectra of accelerogram as : Sð f Þ =

ð2πf Þ2 1þ

f fc

2

ð3:3Þ

The objective automated method of Andrews (1986) is used to assess the ‘M0’ and ‘fc’. Ingber and Rosen (1992) reannealing method is employed to evaluate the ‘fmax’ and ‘s’.

3.3.2

κ-model

Anderson and Hough (1984) articulated the parameter ‘κ’ to express the spectral decay characteristics of the seismic signal at high frequencies as: Aκ ðf Þ = As exp - πf κ

ðf > fE Þ

ð3:4Þ

The formula described above is accurate with the assumption that total effective attenuation i.e quality factor does not depend on the frequency. On the other hand,

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‘κ’ is interrelated with acceleration spectrum slope (λ) for a specific range of frequency above ‘fE’ (a particular frequency in log-linear space beyond which the decay of spectrum becomes linear), i.e.: κ= λ=

-λ π

Δ log Af Δf

ð3:5Þ ð3:6Þ

Anderson and Hough (1984) also observed a relationship between observed ‘κ’ and hypocentral distance. This relation consists of two parts namely slop (κx) defines the regional attenuation characteristics and intercept (κ0) describing the near-surface wave attenuation. The relation can be viewed as: κ = κ0 þ κx X

ð3:7Þ

The term ‘κ0’ corresponds to the observation site's geological characteristics. Anderson and Hough (1984) explain the ‘κ 0’ as an attenuation factor of vertically travelling S-wave through the near-surface geology and as a factor contributing to the increase of attenuation of predominantly horizontally propagating S-wave. The κx was originally introduced to visualize the earthquake source contribution. However, most recent studies correlate the κ x with wave propagation path and site. Neighbors et al. (2015) introduced the κ-distance-magnitude model. This model principally attempts to explore the simultaneous dependency of κ on magnitude and distance as: κðX, M, zÞ = κ ðX, M Þ þ κ 0 X,M

ð3:8Þ

in which κ0X, M is the distance and magnitude independent part of observed kappa. In the present study, all three models of kappa have been discussed.

3.4 3.4.1

Results and Discussion fmax-Model

The fmax-model has been analyzed using both surface and well earthquake data recorded by KiK-NET in southwestern Japan. The averaged Fourier spectra are used to estimate the spectral parameters i.e. Seismic moment (M0), corner frequency ( fc) and fmax. The obtained ‘M0’ values are comparable with the Global Centroid Moment Tensor solution. The quality factor relationship obtained by Tsurugi et al. (2000) is appropriate at least in the frequency range from 0.1 Hz to 50 Hz. The average observed and theoretical acceleration and displacement spectra of an

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Fig. 3.2 Average observed acceleration and displacement spectra along with the theoretical source model with fmax-model (solid line) and κ-model (dotted line)

earthquake that occurred SSE of Kurayoshi, Japan is illustrated in Fig. 3.2 with decent visual correlation accompanied by the values of M0, fc, fmax, p, κ, Moment magnitude (Mw), source radius (r) and stress drop (Δσ). The p is twice the power coefficient (s). The ‘fmax’ models of all the earthquakes have been estimated for both surface and borehole locations. Obtained fmax values range from 4.2 to 11.0 Hz and 5 to 11.0 Hz for surface and borehole data, respectively. The fmax-distance model in Fig. 3.3 depicts the variation of fmax-surface (fmax (s)) and fmax-borehole ( fmax(w)) with the epicentral distance. Figure 3.3 shows large scattering in fmax(s) values as compared with fmax(w) up to epicentral distance 150 km, which may be due to the dominance of near-surface heterogeneities. However, at a large distance, the values of fmax (s) are not scattered and approach the fmax(w) signifying the subjugation of the borehole depth effect on fmax under epicentral distance. The incessant diminution of both fmax(s) and fmax(w) can be correlated with wave propagation properties. Also, the average values of fmax(s) are lower than fmax(w) further confirming the contribution of path characteristics in fmax. The empirical relationships between epicentral distance (x) have developed for the study region as these relationships can be easily utilized in the different research works such as strong ground motion prediction equations (GMPEs), strong ground motion simulations. f max ðsÞ = 139:88x - 0:671

ð3:9Þ

f max ðwÞ = 134:83x - 0:689

ð3:10Þ

Some researchers accredited fmax as earthquake source characteristics (e.g., Hank, 1982; Anderson & Hough, 1984; Aki, 1988; Petukhin & Irikura, 2000; Kumar et. al.,

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Fig. 3.3 Plot showing the fmax-distance model on epicentral distance with an empirical model

2013b, 2015). Some investigators especially Kumar et. al. (2013b, 2015) attempt to indirectly correlate ‘fmax’ with source visualizing the fc and fmax variation with epicentral distance. This approach may be inappropriate as fc is the characteristics of the source and relative inspection of ‘fc’ and ‘fmax’ is far from the source theory. Therefore, we also scrutinized the fmax dependence on the source (Fig. 3.4) in the magnitude range 3.6≤Mw≤4.9. Both fmax(s) and fmax(w) are highly scattered and demonstrate almost no inclination toward Mw. The magnitude dependency of power coefficient (s) is shown in Fig. 3.5. The ‘s’ is almost persistent as a function of Mw. We also checked the comparability of the present fmax -models with the other available fmax -models in Japan (Table 3.1). Some researchers (Kawase & Matsuo, 2004; Wen & Chen, 2012; Sato, 2013) defined ‘fmax’ differently and estimated the ‘fmax’ using source spectra for a fixed value of ‘s’. On account of the various definition of ‘fmax’ models, these models cannot be directly compared; however, the results from those models are in a close match. The P( f ) from fmax(s) and fmax(w) models for all the earthquakes are shown in Fig. 3.6. Additionally, the results are statistically analyzed using a ‘t-test’. The p-value (probability of null hypothesis trueness) of dependent variable fmax(s) for the independent variable epicentral distance is 1.76 × 10‑6 and for Mw is 0.08. Similarly, the p-value for fmax(w) is 4.2 × 10‑9 and 0.068 for epicentral distance and Mw, respectively. The p-values of Mw for both surface and borehole data are greater than 0.05 suggesting the trueness of the null hypothesis, i.e. Mw is having negligible contribution in fmax value. The p-

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Fig. 3.4 Plot showing the dependence of fmax-model on earthquake magnitude

Fig. 3.5 Dependency of power coefficient (s) on seismic magnitude

values for epicentral distance indicate the strong dependence of the fmax-model on the epicenter. But borehole fmax-model is more dependent on the epicentral distance as compared with the surface fmax-model (Table. 3.2).

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Table 3.1 The fmax-models available in Japan region Author Tsurugi et al. (2020)

Earthquake name Intraplate crustal

Sato (2013)

Intraplate Interplate Outer rise Various inland

Kawase and Matsuo (2004) Satoh (2002)

Present study

Tottori earthquake (mainshock) Tottori earthquake (aftershocks) Intraplate (Surface) Intraplate (Borehole)

Magnitude (Mw) 5.9–7.1 3.3–5.8 5.4–7.0 5.9–6.5 5.8–7.5 4.5–7.3

fmax 6.5–9.9 8.8–20 9–14 8–15 10–14 5–20

High frequency decay coefficient (s) 0.78–1.60 0.62–2.59 2.0 2.0 2.0 1.0

7.3

6.0

0.6

3.4–5.5

2–20

0.6

3.6–4.9 3.6–4.9

4.2–11.0 5.0–11.0

0.75–2.90 0.7–2.70

Fig. 3.6 Surface and borehole P( f ) of fmax-model for all earthquakes used in the study

Table 3.2 Statistics of fmax-model with multivariate regression analysis (MVLR)

Coefficients Standard error t Stat P-value Lower 95% Upper 95%

fmax-model (Surface) Intercept epi (km) 14.274 -0.021 2.802 0.003 5.094 -5.69 1.12 × 10-05 1.76 × 10-06 8.591 -0.028 19.957 -0.013

Mw -1.134 0.635 -1.785 0.082 -2.422 0.153

fmax-model (Borehole) Intercept epi (km) 13.447 -0.0198 1.773 0.002 7.584 -7.820 8.23 × 10-09 4.2E × 10-09 9.844 -0.025 17.050 -0.014

Mw -0.950 0.415 -2.291 0.0682 -1.794 -0.107

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R. Kumar et al.

κ-Model Results

Acceleration time histories recorded at the surface and in the borehole are baseline corrected and rotated to have P, SH and Sv time histories. For each record, the arrival time of P- and S-wave are manually selected. Then S-wave windows were extracted based on the distance and magnitude with the lowest window of 5 s. Based on the pre-memory of the system, the noise windows are taken out. Noise and S-wave windows are tapered using a Hanning taper of 2.5% of window length and the amplitude is Fourier transformed. In the semi-log space, the acceleration spectra are examined to obtain the fx and fE i.e. decay is linear between these frequencies (Douglas et al., 2010 nomenclature followed) (Fig. 3.7). To avoid the intersection source effect, the ‘fc’ is packed with special care using displacement spectra. Tsai and Chen (2000) denounced Anderson and Hough (1984) for disregarding the importance of fE. Anderson and Humphrey (1991) proposed a new methodology to jointly determine the ‘fc’ and ‘κ’ without special attention to fE. In the present study, ‘κ’ has been estimated with special care of fx and fE. The basic procedure consists of manual picking of fx and fE with automatic slope determination. The derived value of kappa on surface κ(s) is 0.056-0.093 s while borehole kappa values are κ(w) 0.052 to 0.089 s. On average, the κ(s) is greater than κ(w) which may be attributed to the near-surface additional path travelled by the seismic wave from borehole depth to the surface station. We can now explore the dependence of κ(s) and κ(w) on epicentral distance after the computation of individual kappa. The concept of distance dependence was introduced by Anderson and Hough (1984) using the epicentral distance as an

Fig. 3.7 Plot showing FAS of direct shear wave on the semi-log scale with fe and fx with a best-fit line to estimate the slop (λ)

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Fig. 3.8 Dependency of κ-model on seismic magnitude (Mw)

independent variable. However, recent studies show no concurrence on the definition of distance as epicentral or hypocentral distance. For instance, hypocentral distances were used by Van Houtte et al. (2011) while epicentral distances were used by Douglas et al. (2010). The hypocentral distance is associated with wave propagation path from source to site. Hence, maybe better to consider epicentral distance as described by the attenuation characteristics of κ. Moreover, the rudimentary objective of the κ-distance model is to estimate the site-specific kappa (κ0) with extrapolation of ‘κR’ as a function of ‘R = 0’. In addition to the above fact, the use of epicentral distance is more continent as hypocentral distance cannot be zero because the depth of earthquake can never be zero. Also, if we replace epicentral distance with hypocentral distance then the analogy is misplaced (J. Anderson, personal comm., 2012). Hence, in the interest of better quantification and understanding of the kappa models, multivariate linear regression (MVLR) has been applied for analysis with epicentral distance. Before MVLR, to check the normal distribution of the data set, the Shapiro–Wilk test is performed. Now, epicentral distance and magnitude are taken as the independent variable with κ(s) and κ(w) as the dependent variable to perform the MVLR. However, the t-test indicates that the p-value for independent variable magnitude is 0.19944 and 0.304 corresponding dependent variable κ(s) and κ(w) respectively are much greater than 0.05. Therefore, there is no probability that the null hypothesis is true for both cases. Hence endorsing the fact that magnitude is not contributing to kappa values. The same is confirmed by Fig. 3.8, as there is no trend available and the values are not showing any correlation with magnitude. Therefore, we excluded magnitude for further MVLR analysis. The regression statistics of kappa is shown in Table 3.3. The MVLR analysis shows the values of κR(s) is 0.00013 S/Km with 95% confidence having a lower limit of 0.00011 S/Km and upper limit 0.00015 S/Km, and the value of κR(w) is 0.00014 S/Km with 95% confidence lower limit 0.00011 S/Km and upper limit 0.00016 S/Km. The p-value corresponding to epicentral distance after excluding the

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Table 3.3 Statistics of κ-model with multivariate regression analysis (MVLR) Parameters Coefficients Standard error t Stat P-value Lower 95% Upper 95%

κ-model (Surface) Intercept epi (km) 0.0475 0.00013 0.0087 1.15 × 10‑05 5.4596 11.3881 3.6 × 10-06 1.73 × 10-13 0.0298 0.00010 0.0652 0.00015

Mw 0.0026 0.0020 1.3071 0.1994 -0.0014 0.0066

κ-model (Borehole) Intercept epi (km) 0.0454 0.00014 0.0086 1.16 × 10-05 5.2481 11.5653 8.2 × 10-06 2.48 × 10-13 0.0278 0.00011 0.0630 0.00015

Mw 0.0020 0.0019 1.0327 0.3089 -0.0019 0.0059

magnitude from MVLR is 1.73 × 10‑13 and 2.48 × 10‑13 for κ(s) and κ(w) respectively representing that the kappa is strongly dependent on the epicentral distance. The probability value is higher in surface data as compared with borehole data, which may be due to the additional path from well depth to surface travelled by S-wave. Many researchers interpreted the κ 0 using different data sets and methodologies. Some correlate the κ 0 with average shear wave velocity in the upper 30 m low-velocity zone (Silva et al., 1998; Edwards et al., 2011). Ktenidou et al. (2015) analyze the Japan KIK-NET data and relate κ 0 with the bedrock depth and resonance frequency. We have estimated the κ 0 for both surface (κ 0(s)) and borehole (κ 0(w)) data. The κ0(s) is 0.0587 s with 95% confidence and a lower value of 0.0555 and upper value of 0.0619 s. Similarly, κ 0(w) is 0.0542 with 95% confidence with a lower value of 0.0509 and upper value of 0.0579 s. The average value of κ0(s) is greater than κ0(w). One possible explanation for this is the surface sites are softer than the borehole site. Additionally, κ0(s) include the influence of the low-velocity material having a thickness borehole to the surface. The results of some researchers (e.g. Oth et al., 2011; Van Houtte et al., 2011) analyzed the strong records of Japan and also pointed out that the borehole κ0 is smaller than the corresponding surface value. Furthermore, the range, of estimated ‘κ(s)’ is 0.056–0.093 s, is greater than ‘κ(w)’, which varies from 0.052 s to 0.089 s, confirming the effect of near-surface layer on kappa. The kappa values estimated in the present study are comparable with the other global studies (Table 3.4). Predicted values of κ(s) and κ(w) have also been estimated using MVLR. Residuals of predicted and observed kappa are shown in Fig. 3.9. It can be observed that the κ(s) residuals are having a greater value as compared with κ(w) residuals. Also, κ(s) residuals are highly scattered which can be interpreted as a result of the heterogeneities present in the near-surface wave propagation medium. This fact supports the studies showing the contribution of scattering in kappa value depending on the heterogeneity size (e.g. Edwards et al., 2015; Parolai et al., 2015). One highfrequency decay model can be converted as per requirement in a particular application (Fig. 3.10). Following empirical relationships between fmax-model and κ-model have been developed for Southwestern Japan:

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Table 3.4 Comparison of observed kappa values with other worldwide values estimated by various researchers Author Present study

Region Japan

Kumar et. al. (2020)

Northeast Himalaya region

Markušić et al. (2019) Kumar et al. (2018) Perron et al. (2017) Tz-shin Lai et al. (2016) Fu and Li (2016)

Croatia Western India Provence, France Taiwan

KR 0.00013 0.00014 (1.137 ± 0.65) × 10-5 (0.0436 ± 0.0013) × 10-5

Khor (avg)= 0.000184 kver(avg)= 0.000171 0.00004458 0.031 ± 0.008 0.029 ± 0.013 1.6 × 10-4 2.8 × 10-4 1.427 × 10-4 1.654 × 10-4

K0 0.0587 0.0542 (0.0467 ± 0.0011) (1.63 ± 0.80) 0.0275 0.0302 0.0208

Ktenidou et al. (2013) Sun et al. (2013)

Greece

0.00058

0.056 0.030 0.0227 ± 0.0065 0.0158 ± 0.0064 0.0217 ± 0.0069 0.0223 ± 0.0080 0.0377 0.0455 0.0150 0.0271 0.0268

Sichuan, China

Houtte et, al. (2011) Douglas et al. (2010)

Kiban-kyoshin, Japan Mainland France

2.8412 × 10-5 -2.0813 × 10-7 0.000191 0.000215 0.000175 0.000270

0.01357 0.01261 0.017 0.033 0.0207 0.0270

Longmenshan fault, Japan

Neighbors et. al. (2014)

Moule, Chile

5.991 × 10-5 ± 7.209 × 10-6 (for both)

Askan et al. (2014)

Northwest Turkey

Kh = 0.000132 Kv = 0.000188

Remark Surface Borehole For KH For Kv

KAS KDS Surface well KH KV

Sediments Hard site

Hard Soft Hard Soft

Horizontal Vertical Downhole Surface Rock Soil

f max ðsÞ = - 131:57κ ðsÞ þ 16:763

ð3:11Þ

f max ðwÞ = - 126:53κ ðwÞ þ 15:551

ð3:12Þ

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Fig. 3.9 Observed and predicted value of surface data kappa κ(s) and borehole data kappa κ(w) along with their residuals estimated using multivariate regression analysis (MVLR)

Fig. 3.10 Relationship between fmax-model and κ-model

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3.4.3

39

Stress Drops and Self-Similarity

The extensively used parameter stress drop (Δσ) cannot be measured directly by any available technique. The damaging high-frequency level of strong ground motion is controlled by Δσ (Hanks & McGuire, 1981). Many researchers (Kanamori & Anderson, 1975; Allmann & Shearer, 2009; Kumar et al. 2013a, 2015; Courboulex et al., 2016) report Δσ in different tectonic setups. It is related to stress released during earthquake rupture and relates the seismic moment with rupture dimension (Stein & Wysession, 2003): Δσ =

7M 0 2πf c 16 2:34β

3

ð3:13Þ

The concept of self-similarity exists only when the stress drop is constant for a particular region as ‘Δσ’ is the representation of rock strength to tolerate the various stress involved in the rupture process. In most of the worldwide studies with a wide magnitude range, the estimated ‘Δσ’ is 1-1000 bars (0.1 to 100 MPa) (Abercrombie, 1995; Allmann & Shearer, 2009). The variation can be related to the lithology and tectonic of the different regions as it has been observed that the interpolate tectonic regions have a lesser amount of ‘Δσ’ as compared to the intraplate regions (Kanamori & Anderson, 1975). Also, earthquakes that occurred in the subduction zone show a lower amount of stress as compared with other regions (Courboulex et al., 2016). Normal fault earthquakes are having lesser ‘Δσ’ than reverse fault earthquakes, with strike-slip having the largest stress drop (Cocco & Rovelli, 1989; Allmann & Shearer, 2009). Several studies (e.g. Dysart et al., 1988; García-García et al., 1996; Bilek & Lay, 1998; Wu et al., 1999; Allmann and Shearer, 2007; Tusa & Gresta, 2008; Süle, 2010; Kumar et al., 2015; Kumar et al., 2015) also showed that ‘Δσ’ increases with depth. In our study, we tried to explore the effect of some of the above factors on Δσ. The stress drop (Δσ (s)) estimated from surface data is 44.16-65.86 bars with an average value of 53.19 bars and borehole derived stress drop (Δσ (w)) is 46.38-68.13 bars with an average value of 54.16 bars. It can be observed from Fig. 3.11 that the trend of both ‘Δσ (s)’ and ‘Δσ (w)’ are almost constant. The small perturbation in both ‘Δσ (s)’ and ‘Δσ (w)’ can be attributed to the small errors in the estimation of corner frequency. Furthermore, the Δσ (s) is almost similar to ‘Δσ(w)’ neglecting any effect of depth on stress drop. The focal mechanism of all the analyzed earthquakes in the present study is not available but it has been noted that the available CMT solutions for all types of earthquakes that occurred in the region, ‘Δσ (s’) and ‘Δσ (w)’ are not scattered. Therefore, the type of faulting, i.e. normal, reverse/thrust and strike-slip, does not affect the value of ‘Δσ (s)’ and ‘Δσ(w)’. Our results also support the concept of self-similarity as ‘Δσ (s)’ and ‘Δσ (w)’ are almost constant.

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Fig. 3.11 Stress drop variation with seismic moment (M0) and earthquake source radius (r). (Red and black dots are corresponding to surface and borehole values, respectively)

3.5

Conclusion

In hazard seismology, the ‘κ’ and ‘fmax’ are the most commonly used and least understood parameters. To assess the seismic hazard at hard and soft rock sites, these are the basic parameters adjusting the host to the target. Although at the target site, it is typically difficult to evaluate the site-specific kappa (κ0) in low-to-moderate seismicity zones because traditional methods of acceleration spectra (Anderson & Hough, 1984) impose the requirement for high-magnitude events to achieve low fc and acceptable SNR up to high frequencies. In this study, the surface, as well as the borehole data set of the Japan KIK-NET seismological network, is analyzed to characterize the high-frequency decay using the model and κ-model. Both the Fmax-model and the κ-model are statistically analyzed using Shapiro–Wilk test, t-test and multivariate linear regression (MVLR). Stress drop (Δσ) is also analyzed to investigate the concept of selfsimilarity. The quality factor relationship derived by Tsurugi et al. (2000) for the study region is used to recompense the attenuation of the wavefield. Both fmax-source

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model and fmax-distance model have been examined using surface and borehole data. To explore the fmax-source model, the magnitude dependence of fmax has been examined and the scattering of data points show almost no relationship with the magnitude. Hence it is concluded that both fmax(s) and fmax(w) are not a characteristic of the earthquake source. This fact is further clarified by the t-test as the p-value of the null hypothesis is high, i.e. magnitude does not affect the MVLR if it is removed from the regression. The fmax-distance model has been examined for both surface and borehole data. Up to the epicentral distance of 150 km, fmax(s) scattered larger than the fmax(w), showing the impact of near-surface geology and heterogeneities on fmax(s). However, at a larger distance fmax(s) approaches fmax(w) as at a larger distance both similarly affected by the medium because the borehole depth is shallow. Further, the t-test p-value of the null hypothesis is very low for both fmax(s) and fmax(w) showing strong dependence on epicentral distance. Hence fmax is the characteristic of wave propagation media. The κ-magnitude and the κ-distance models are explored using the waveform of both surface and well accelerometers. The t-test performed on the κ-magnitude model shows that the p-value of the null hypothesis is very high signifying negligible contribution of magnitude in kappa value. This fact is further confirmed by the random variation in κ(s) and κ(w) with magnitude. The p-value for epicentral distance as an independent variable is extremely low representing the very high contribution of epicentral distance in kappa value. The average value of both κ 0(s) and κ0(w) indicates that the sites are hard. Moreover, κ 0(s) is greater than κ0(w) reflecting the effect of near-surface geology in the κ 0(s) values. This fact is also supported by the residuals of κ(s) and κ(w) as κ(s) residuals are more scattered than κ(w) residuals. Also, a negative correlation between the κ-model and fmax-model has been observed. The concept of self-similarity has also been enlightened with the breakdown of different reported factors affecting the stress drop. The average Δσ(s)’ and ‘Δσ(w)’ are 53.19 bars and 54.16 bars with almost constant variation in the seismic moment and source radius signifying the self-similarity of different magnitude events. The types of earthquakes, i.e. normal, reverse and strike-slip, are not show any significant contribution in ‘Δσ’. There is also no effect of focal depth on the estimation of ‘Δi’ has been observed. Also, the influence of borehole depths is not visible on ‘Δσ’. The small disparity in ‘Δσ(s)’ and ‘Δσ(w)’ is the result of small errors in the assessment of corner frequency. Therefore, the present study also supports self-similarity by discarding the other reported factors influencing the stress drop.

3.5.1

Data and Resources

The seismological data used in the present study is obtained from Japan's strongmotion seismological network KIK-NET operated by the National Research Institute for Earth Science and Disaster Prevention (NIED) (http://www.kyoshin .bosai.go. jp). The Generic Mapping Tools GMT 6.2.0 is used to plot the study area map.

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Acknowledgements The authors are very thankful to KIK-net, Japan for providing the free data as well as hypocentral parameters. The contribution of Generic Mapping Tools is highly appreciated. Funding and Conflict of Interest The authors declare that no funding has been received for this research and we do not have any conflict of interest regarding the present research work.

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Sun, X., Tao, X., Duan, S., & Liu, C. (2013). Kappa (k) derived from accelerograms recorded in the 2008 Wenchuan mainshock, Sichuan, China. Journal of Asian Earth Sciences, 73, 306–316. Tsai, C. C. P., & Chen, K. C. (2000). A model for the high-cut process of strong-motion accelerations in terms of distance, magnitude, and site condition: An example from the SMART 1 array, Lotung, Taiwan. Bulletin of the Seismological Society of America, 90(6), 1535–1542. Tsurugi, M., Kagawa, T., & Irikura, K. (2012). Study on high frequency cut-off characteristics of ground motions for intra-slab earthquakes occurred in Southwest Japan. 15th World Conference on Earthquake Engineering, 15WCEE. Tsurugi, M., Kagawa, T., & Irikura, K. (2017). Spectral decay characteristics fmax and κ for strong ground motion prediction. In 16th World conference on earthquake engineering, 16WCEE (No. 1232). Tsurugi, M., Kagawa, T., Okazaki, A., Hada, K., & Irikura, K. (2006). Study on a high-cut filter for strong ground motion prediction. Journal of Japan Association for Earthquake Engineering, 6(4), 94–112. Tsurugi, M., Tai, M., Kowada, A., Tatsumi, Y., & Irikura, K. (2000). Estimation of empirical site amplification effects using observed records. Proceedings of the 12th world conference on earthquake engineering, 1243 Tsurugi, M., Tanaka, R., Kagawa, T., & Irikura, K. (2020). High-frequency spectral decay characteristics of seismic records of inland crustal earthquakes in Japan: Evaluation of the f max and κ Models. Bulletin of the Seismological Society of America, 110(2), 452–470. Tusa, G., & Gresta, S. (2008). Frequency-dependent attenuation of P waves and estimation of earthquake source parameters in southeastern Sicily, Italy. Bulletin of the Seismological Society of America, 98(6), 2772–2794. Van Houtte, C., Drouet, S., & Cotton, F. (2011). Analysis of the origins of κ (kappa) to compute hard rock to rock adjustment factors for GMPEs. Bulletin of the Seismological Society of America, 101(6), 2926–2941. Wen, J., & Chen, X. (2012). Variations in f max along the ruptured fault during the M w 7.9 Wenchuan earthquake of 12 May 2008. Bulletin of the Seismological Society of America, 102(3), 991–998. Wu, Z. L., Chen, Y. T., & Mozaffari, P. (1999). Scaling of stress drop and high-frequency fall-off of source spectra. Acta Seismologica Sinica, 12(5), 507–515.

Chapter 4

Body Waves– and Surface Waves–Derived Moment Tensor Catalog for Garhwal-Kumaon Himalayas Rinku Mahanta, Vipul Silwal, and M. L. Sharma

4.1

Introduction

The seismic moment tensor (MT) is a 3X3 symmetric matrix, typically depicted as a beachball diagram that contains information regarding the geometry of an earthquake source (Isacks et al., 1968; Zhu & Zhao, 2016) . The estimation of MT allows us to determine the faulting characteristics including the strike, dip, and rake angle of a point source earthquake. It also allows the assessment of deformation patterns in the context of active tectonics. The Garhwal and Kumaon (G-K) region of the Himalayas, lies at latitudinal range of 29º–32° N and longitudinal range of 77°–81° E, is considered as a one of the highly seismically active zone situated in the Himalayan arc. These areas of northwestern Himalayas is situated in the western segment of central seismic gap (CSG) positioned between two major rupture zone – the Kangra earthquake (1905, M~7.8) and Bihar/Nepal earthquake (1934, M~8.3). The CSG consistently accumulates strain, giving rise to low to moderate earthquakes. Consequently, a significant amount of internal stress continuously accumulates in this region, that gives rise to the potential threat of great earthquakes (Khattri & Tyagi, 1983; Kayal, 2001; Mukhopadhyay et al., 2011; Paul et al., 2010). The Kumaon region experienced a significant earthquake, possibly in 1803, making it the latest recorded great seismic event in the area, with the last one believed to have occurred around 1255 (Bilham et al.,1995). Over the last three to four decades, the region has witnessed several moderate to major earthquakes, including notable events such as the Uttarkashi earthquake in 1991 (M-6.6) (Cotton et al., 1996), the Chamoli earthquake in 1999 R. Mahanta · V. Silwal (✉) Department of Earth Sciences, Indian Institute of Technology, Roorkee, India e-mail: [email protected] M. L. Sharma Department of Earthquake Engineering, Indian Institute of Technology, Roorkee, India © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 R. Kumar et al. (eds.), Recent Developments in Earthquake Seismology, https://doi.org/10.1007/978-3-031-47538-2_4

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(M-6.3) (Kayal et al., 2003), the Kharsali earthquake in 2007 (M-5.0) (Paul & Kumar, 2010), and the Rudraprayag earthquake in 2017 (M-5.7) (Tiwari et al., 2021). Due to the significant amount of seismic activity as well as complex tectonic nature of the area (Mahesh et al., 2015; Hajra et al, 2021), it is important to monitor the seismic parameters to effectively address potential seismic risks. In this study, we are presenting the seismic MT catalog of 16 events that occurred between the year 2000 and 2021 in G-K region having magnitude (M≥4.0). Different methodologies are employed for the routine estimation of seismic MTs, including high-frequency body wave approaches such as FPFIT (Oppenheimer et al., 1988) and HASH (Hardebeck & Shearer, 2008), as well as filtered waveform methods like cut-and-paste (CAP) (Zhu & Helmberger, 1996), Time Domain Moment Tensor (TDMT) (Dreger & Woods, 2002), Global Centroid Moment Tensor (GCMT) (Ekström et al., 2012) and W-phase (Duputel et al., 2012). We are using the CAP approach for MT estimation to compile the catalog for the G-K Himalayas. The prime characteristic of this approach is its utilization of both body and surface waves separately, employing the time shift between observed data and synthetics to get the most reliable MT solution with the minimum misfit. This study enhances our understanding of seismotectonics in the G-K region by providing a detailed seismic MT catalog for the recent decade, employing advanced methodologies such as CAP approach, contributing valuable insights into the tectonic processes and seismic behavior of the area.

4.2

Tectonic Settings

The Himalayan arc, formed by the convergence of the Indian and Eurasian plates, exhibits significant seismic activity due to the subduction of the Indian plate under the Eurasian plate (Verma et al., 1977). The arc divides into four litho-tectonic zones, overlapped by thrusts like Main Boundary Thrust (MBT), Main Frontal Thrust (MFT), Main Central Thrust (MCT) and South Tibetan Detachment (STD), forming the Main Himalayan Thrust (MHT). The interface between the Himalayan wedge and the descending Indian plate is marked by a decollement plane (Caldwell et al., 2013). Extensive research has focused on understanding the detailed tectonics and geology of the Himalayan arc, particularly the mid-crustal ramp between the Higher and Lower Himalayas (eg. Molner, 1990; Avouac, 2003; Bajaj & Sharma, 2019). The Indian plate is subducting beneath the Eurasian plate at a rate of approximately 20 mm per year, resulting in seismic activity (Ader et al., 2012). Notable historical earthquakes in the Himalayan arc, such as Kumaon (1803, M-7.7), Kathmandu (1833, M-7.7), Shillong (1897, M-8.1), Kangra (1905, M-7.8), Bihar/Nepal (1934, M-8.3), and Assam (1950, M-8.7) (Khattri, 1987; Bilham et al., 2001), have likely ruptured the seismogenic part of the MHT, accumulating stress in the interseismic period. Small to moderate earthquakes occur in the downdip part of the seismogenic MHT or the mid-crustal ramp (Molnar, 1990). The Himalayan arc

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displays spatial variation in seismicity, with seismic gaps indicating areas prone to large-magnitude earthquakes. The G-K Himalayan region, with a seismic gap of almost 700 years, falls under a high earthquake-prone zone. Geological studies suggest that accumulated stress along the MHT has not been fully released, posing a potential risk of great earthquakes (Bilham et al., 2001; Banerjee & Bürgmann, 2002; Berger et al., 2014).

4.3

Data

In this study, we focused on recent earthquakes in G-K Himalayan region, compiling information from International Seismological Center (ISC) covering the period 2010-2021 (Fig. 4.1 and Table 4.1). We analyzed some light to moderate

Fig. 4.1 The seismicity map of the G-K region of the Himalayan arc covering a period of 2010 to 2021. The color contrast signifies the focal depth of each event, while the size of each circle corresponds to the magnitudes of the earthquakes. The thick black lines in the map represents the active faults in the region (Dasgupta et al., 2000)

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Table 4.1 Event information of 16 earthquakes provided by ISC Event date 2021-09-11 2015-07-18 2019-12-13 2015-06-03 2011-03-14 2011-06-20 2017-02-06 2019-05-17 2017-12-28 2017-12-06 2021-05-23 2018-06-06 2012-11-27 2020-03-01 2012-02-09 2013-02-11

Event time 00:28:28.55 23:48:09.86 11:26:42.04 11:28:25.20 09:01:30.67 06:27:19.86 17:03:05.81 19:38:44.11 11:17:27.11 15:19:49.75 19:01:37.54 17:41:25.46 12:15:14.88 04:43:31.52 19:17:32.94 10:48:51.57

Latitude (N) 30.39 30.41 30.43 30.44 30.54 30.55 30.58 30.59 30.59 30.6 30.74 30.76 30.9 30.91 30.94 31

Longitude (E) 79.18 79.15 79.3 79.19 79.18 79.32 79.08 79.31 79.15 79.1 79.17 78.81 78.4 78.04 78.3 78.32

Depth (km) 10 23 0 10 24 26.6 14.6 16.9 30.5 12.8 0 24.1 10 0 24.8 6.3

Magnitude 4.4 4.3 4.3 4 4.8 4.8 5.6 4.4 4.6 5.1 4 4.4 4.3 4.1 5.1 4.6

earthquakes with magnitude (M≥4) near our seismic network of 18 stations, installed between 2010 and 2019. The Earthquake Engineering Department of the Indian Institute of Technology, Roorkee, continuously monitor the data. To uniquely identify a specific event, we designate it by its origin time in Coordinated Universal Time (UTC). For instance, if an event took place on January 1, 2020, at 12:00:00.00, we would label this event as 2020010112000000. Our final MT catalog includes 16 events, with earthquake locations and station distribution shown in Fig. 4.2.

4.3.1

Data Preparation

The seismic waveform data is a time series data consisting of North, East and Vertical components, which gives information about the travel time and amplitude of different seismic waves generated during an earthquake. Initially, our raw earthquake data consists of a single file containing three-component waveforms for all stations. Processing steps of the raw data includes: 1. Splitted raw data (Contains NEZ of components of each stations). 2. Trimming data to a required time window, 3. Addition of earthquake-related parameters into the SAC header of the data, 4. Removal of instrument response and 5. Rotation of seismic data. Results of processing on the waveforms are presented in Figure 4.3. All the detailed information and processing Python code are accessible on Zenodo (Mahanta and Silwal, 2024).

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Fig. 4.2 Illustrations of the locations of 18 broadband stations (depicted as blue inverted triangles) and 16 earthquake events (represented by circles) for which MT inversion is performed in this study. The variation in color signifies the focal depth of each event, while the size of the circles corresponds to the magnitudes of the earthquakes

4.4 4.4.1

Methodology CAP Approach

Zhao and Helmberger (1994) and Zhu and Helmberger (1996) proposed the ‘cut and paste’ method for MT estimations for earthquakes. This technique involves segmenting different components of synthetic seismograms and aligning with the corresponding portion of the observed data, allowing time shifts. CAP also identifies errors in the assumed seismic velocity model by using the time shifts between synthetics and observed waveforms at a specific station (Table 4.2). It employs different band-pass filters for surface and body waves. The rotated body and surface waves are split into five-time windows: (a) P wave vertical (PV), (b) P wave radial (PR), (c) Rayleigh wave vertical (SurfV), (d) Rayleigh wave radial (SurfR) and (e) Love wave transverse (SurfT) components. We can exclude or include any of these windows using standard waveform selection

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Fig. 4.3 The difference between raw waveform data (Upper set of three waveforms) and processed data (Lower set of three waveforms) after removal of instrument response and applying rotation. The processed data is used for the CAP method

criteria (Silwal & Tape, 2016). Considering the size of the earthquakes as well as the focal depth, different time shifts are allowed for each earthquake. For example, for a smaller and shallow event, the body wave is filtered between 1.5 to 4 s and allowed a maximum shift of ±2 s. Similarly for surface wave filter lies between 10 to 20 s, and maximum shift allowed is ±10 s. For a deeper and larger earthquake, these parameters should be different.

4.4.2

Preparing Synthetic Seismogram

The Green’s function acts as the impulse response of a layered medium, translating a received signal into Earth's response from a point source (Shapiro et al., 2005). We employ the Frequency-Wavenumber method, using double numerical integration, to extract Green’s functions (Zhu & Rivera, 2002). For a general double couple, nine files are generated at a specified depth and distance, with an extra three files if the isotropic component is included. Using these files, synthetics are generated by convolving a source time function with the Green’s function for a specific point.

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Table 4.2 Detail information of the location of 18 seismic stations used in this study Station name TRIY NIZM CHIN VINA BARS CHAN BHIR KHUR PRAT SIRA GIYA NEWT AYAR SRIK SURK RAJG SANK CHAK

Latitude (N) 30.65 30.36 30.41 30.57 30.84 30.31 30.05 30.58 30.46 30.13 30.76 30.38 30.3 30.61 30.41 30.84 31.07 30.73

Longitude (E) 78.98 79.47 78.74 78.66 78.62 78.62 79.05 78.49 78.48 78.63 78.42 78.43 78.43 78.3 78.29 78.24 78.19 77.84

Elevation (km) 2.19 1.6 1.95 1.64 2.1 2.24 1.97 1.73 2.13 1.42 2.11 1.91 2.11 1.62 2.75 1.91 1.95 2.29

Table 4.3 Velocity and resolution variation with depth after Mahesh et al. (2013). Vp and Vs are velocities of P and S waves, respectively. Qp and Qs denote the quality factors employed to quantify the attenuation of seismic waves Depth (km) 0.0 4.0 16.0 20.0

4.4.3

Vp (km/s) 5.60 5.90 6.00 6.40

Vs (km/s) 3.20 3.40 3.51 3.72

Vp/Vs 1.75 1.73 1.70 1.72

Qp 1000 1000 1000 1000

Qs 500 500 500 500

Model Used

For preparing the synthetics, we used the 1D velocity model estimated by Mahesh et al. (2013) (Table 4.3) for Garhwal-Kumaon Himalayas.

4.4.4

Grid Search Moment Tensor (MT) Inversion:

After getting the correct Green’s functions and processed observed data, we are ready for the inversion operation. In the process of grid search, we are looking for a minimum misfit function, Φ that maximally correlates the synthetics with the data.

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In the CAP approach, it can be seen how Φ is gathered from the slices of seismic filtered waveforms. Once the misfit function is established, we proceed towards getting the minimum misfit function by operating the grid search over the model parameters space. Our model parameters consist of five elements: magnitude of the earthquake m, focal depth z and orientation of the moment tensor: strike (κ), dip (θ) and rake (σ). We are considering that the earthquakes take place as the shear faulting without opening; so, our MTs are double couples. We isolated the origin time and epicentre as those from the ISC catalog. We are assigning some search range for our model parameters, such as depth (z): zISC-20 ≤ z ≤ zISC+20, where zISC is the depth provided by ISC catalog; magnitude (m): mISC-1 ≤ m ≤ mISC +1, here mISC is the ISC catalog magnitude; strike (κ): 0° ≤ κ < 360°; h = cosθ : 0 < h ≤ 1 where dip(θ): 0° ≤ θ ≤ 90° and rake(σ): -90° ≤ σ ≤ 90°. We are choosing h installed of dip (θ) to acquire uniformly distributed orientation by selecting κ, h and θ uniformity (e.g. Kagan, 1991; Tape & Tape, 2012; Silwal & Tape, 2016). Uniformly distributed double couple MT is provided by uniformly distributed orientations (Tape & Tape, 2015). Our unknown model vector for each of the earthquakes is: m = ðκ, σ, h, m, zÞT

ð4:1Þ

Our target is to search over this space of parameters to get the model vector mo = (κ o, σ o, ho, mo, zo), which reduces the misfit Φ. We allow Mo to be the corresponding M: M o = M ðκ o , σ o , ho , mo , zo Þ

ð4:2Þ

(Since seismic moment is also denoted by Mo, it should not be confused with the moment tensor (Mo) in our case) Mo can be found in two ways: by using random points or by using regular grid of points. In our study, we are using regular grid search. By using regular grid search over magnitude and depth, we estimate the minimum misfit function Φ at the MT. In the next stage, the analysis for MT has been done by fixing both depth(z = zo) and magnitude (m = m0); model parameters that will vary are the MT orientations, that is calculated by (κ, σ, and h).

4.4.4.1

Misfit Function

Let us consider the predicted time series as indicated by s(M) for a moment tensor M. It can be thought s(M) as a forward model which will input an MT and ground motion of the surface as the output. The fundamental physics is wave propagation through a simple layered medium. The dissimilarity between observed seismograms (‘data’) and modeled seismogram (‘synthetics’) is measured by our misfit function. There are three components of ground motion recorded by each station, which can be visualized by three

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seismograms. Let us consider u as a discrete time series of a component of observed ground velocity and at time tk the ground velocity becomes uk. The target is to calculate the M that reduces the difference between u and s(M). All the seismograms are broken into different time windows. Let p and q represent the time window index and station index respectively. For measuring the misfit between data and synthetics, we are using the L2 norm. The waveform difference of L2 norm inside a single time window is represented as: Φpq ðM Þ =

T

upq - spq ðM Þ Wpq upq –spq ðM Þ

1=2

ð4:3Þ

where Wpq is the weighting matrix which can be regarded as the inverse data covariance matrix (Aster et al., 2018). In our case, it is a diagonal square matrix having the same weight factor wpq towards the diagonal. It provides the flexibility of maintaining the weights of every time window. For each earthquake, a misfit function has been defined. Ns number of stations record each earthquake. As already described, each seismogram is split into a total of five windows (PV, PR, SurfV, SurfR, and SurfT). Considering L2 norm: ΦL2ðM Þ =

Ns

5

q=1

p=1

Φ2pq ðM Þ

ð4:4Þ

The time is shifted for each of the synthetic waveforms to match the data. Moreover, filter has been applied (identically) for data and synthetics over some specified bandpass. Also, the weighting of the waveforms is built-in by the stationsource distance that permits the remote stations to have influence as compared to the nearer stations (e.g. Zhu & Helmberger, 1996)

4.4.4.2

Scaling the Misfit Function

The scaled version of misfit of L2 norm is defined by: ΦðM Þ = ðk=uL2Þ ΦL2ðM Þ = ðk=uL2Þ

Ns

5

q=1

p=1

Φ2pq ðM Þ

ð4:5Þ

Here uL1 is characterized in terms of observed waveforms as: uL2 =

Ns

5

q=1

p=1

uTpq W pq upq

1 2

ð4:6Þ

Since the errors in the data are poorly known in most of the seismological studies, to overcome this problem, we need a scale factor. The constant k will be the same for all earthquakes. The best fitting of moment tensor (Mo) is not impacted by scaling of k/uL2.

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Results

We are presenting the result of MT estimation of one of the 16 events in Fig. 4.4. The event occurred on 11 September 2021; at a longitude 79.1781° and latitude 30.3941° in the Uttarakhand region. The result primarily shows the waveform fit between observed data (black) and synthetics (red). The maximum allowable time-shift of ±2 and ±10 s was used for body and surface waves, respectively, for correlattion between observed and synthetic waveforms. The fault plane that generated minimum misfit between observed and synthetic waveforms is our final inverted solution. In this example, inverted solution was obtained at fault plane 319o (strike), 27o (dip), and -65o(rake). Figure 4.5 Shows the grid search to obtain minimum misfit corresponding to the depth and magntitude. We searched over full space of orientations for each depth and magnitude to achieve the best fitting MT. For this earthquake, the best fitting solution is obtained at magnitude, Mw 4.1, and the hypocentral depth of 6 km; compared to the ISC catalog that has magnitude, Mw 4.4, and depth of 10 km. In the same way, the MT inversions were performed for other events. Different filters and time shifts are applied to different events in order to obtain the best waveforms fits for inverted solutions. Magnitude search and depth search, in corresponding ranges, was also performed for all events. The results of all 16 events are plotted in Fig. 4.6. Table 4.4 summarizes the fault-plane orientations of each event. Most of the earthquakes has shallow focal depth (≤70 km) except one event (147 km).

4.6

Discussion

MT solution is a standard mathematical notation for describing earthquake faulting process using point source assumption. Developing a systematic MT catalog has become routine work in seismology. Harvard maintains one of the most renowned MT catalog, Global Centroid Moment Tensors (GCMT) ( Ekström et al., 2012), however, this catalog is limited to intermediate to large magnitude events. The method (CAP) and techniques employed in our study for the G-K Himalayas were previously utilized by Silwal and Tape (2016) to estimate their MT catalog for 106 earthquakes in southern Alaska. Applying this approach, we obtained a high-resolution MT catalog for G-K region, containing 16 earthquakes. The key challenge in this study is inclusion of local datasets, instead of standard FDSN data. To process the local data, we incorporated preprocessing approach described in Mahanta and Silwal (2024). Hajra et al. (2021) conducted MT analysis above G-K region using the multistep inversion approach introduced by Cesca et al. (2010, 2013). Mahesh et al. (2015) explored fault plane solutions for 94 events in the region to understand crustal stress,

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Fig. 4.4 MT solutions and waveform comparisons for the event 2021091100282800. Columns represent P wave components (vertical and radial), Rayleigh wave components (vertical, radial, and transverse Love wave) respectively. Stations are ordered by increasing epicentral distance, with observed and synthetic waveforms in black and red, respectively. Body waves are filtered at 3–10 s and surface waves are filtered at 16–40 s. Numbers below each station indicate epicentral distance and azimuth. Three values beneath each waveform pair include cross-correlation time shift, percentage of misfit, and amplitude ratio. Header lines are as per Silwal (2015)

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Fig. 4.5 The depth and magnitude search to find out the minimum misfit over grid points. In this case, the optimum depth was found at 6 km and magnitude, Mw 4.1

Fig. 4.6 The beachball diagram representing MT catalog of 16 earthquakes is shown in this figure. The results shows as distribution of thrust, normal and strike-slip oriented mechanisms rather than a preferred thrust solution

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Table 4.4 Summary of all 16 fault-plane solutions obtained after performing MT estimation, as well as, depth and magnitude search Event name 2021091100282855 2015071823480986 2019121311264204 2015060311282520 2011031409013067 2011062006271986 2017020617030581 2019051719384411 2017122811172711 2017120615194975 2021052319013754 2018060617412546 2012112712151488 2020030104433152 2012020919173294 2013021110485157

Magnitude 4.1 4.3 3.8 3.8 4.3 4.2 5.5 3.7 4 4.5 4.1 4 4.4 3.5 4.5 4.2

Depth (km) 9 25 25 22 25 2 26 17 31 13 147 1 2 1 2 5

Strike 319 121 4 319 85 301 121 301 247 337 202 301 229 274 121 184

Dip 27 68 35 83 46 80 82 68 40 74 38 84 87 87 30 15

Slip -65 -15 24 20 83 87 -15 -2 -87 51 29 83 74 65 -87 -42

employing the MT inversion program INVARD (Ebel & Bonjer, 1990) with P and SH waves. Kanna et al. (2018) conducted a seismotectonic study on Western Himalayan-Ladakh-Karakoram, analyzing 19 earthquakes and determining MT using the ISOLA software (Sokos & Zahradnik, 2008). Similar estimations were also performed by Kumar et al. (2015). In our estimation, we employ the CAP approach (Zhao & Helmberger, 1994; Zhu & Helmberger, 1996) utilizing both body and surface waves for each earthquakes, distinguishing our approach from others. Similar methodologies have been implemented by different authors in various regions, such as He et al. (2015) for the Nepal earthquake (2015), Lei et al. (2019) for the South Sichuan Basin, Ma and Wu (2019) for the Huailen (Taiwan) earthquake (2018), and Zhou et al. (2019) for Hutbi, northwest China. These studies have demonstrated favorable outcomes using the CAP approach for MT estimation. Our study area lacks diversity in inversion methods, and introducing a novel approach to creating a MT catalog can be valuable for future research. This allows for comparisons with existing catalogs generated by different methodologies. Most recently, Kumar et al. (2023), used CAP approach for MT estimation of 2022 Dharchula earthquake in G-K region. In our MT catalog, we have documented 16 events featuring a combination of thrust, normal, and strike-slip mechanisms occurring in our region during the specified time period. For each event, a series of alterations were made to the weight

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file and inversion input parameters (Silwal & Tape, 2016) in order to obtain the opitimal solution. On basis of the waveforms fits obtained for these 16 events, we infer our solution be of high quality. The catalog created in this study will serve as a valuable foundation for future studies, particularly in full waveform-based tomographic studies. This study also provides frameworks for other relevant research topics as well. For instance, exploring the influence of incoporatin local, regional, and teleseismic data on the moment tensor solution. More work is require to investiage whether the MT solutions be improved by applying first-motion polarity constain, in addition to the waveform misfits. Further, we would like to add that we do not provide uncertainty measure for estimated MT solution, which is a valuable parameter to access the confidence in final solution. Further enhancements could lower the magnitude for which we can reliably obtain waveform based moment tensor solutions. Inclusion of 3D velocity model for preparation of synthetic waveform will be crucial in this regard.

4.7

Conclusion

This study presents a seismic moment tensor catalog for 16 earthquakes located in the Garhwal-Kumaon Himalayas region, using the Cut-and-paste approach. The selection of events was primarily location dependent and are in the vicinity of 18 broadband stations maintained by the IIT Roorkee. By employing both body and surface waves, the catalog reveals a distribution of thrust, normal, and strike-slip earthquake mechanisms. The observed variation in seismicity patterns suggests diverse stress accumulation pattern. The study highlights that crustal faulting in the region is not exclusively thrust-dominated, showing the presence of normal and strike-slip events too. This catalog, to be expanded with more earthquakes, will contribute to understanding deformation styles and long-term multi-disciplinary research in this seismically active area. The findings provide crucial input for seismic hazard assessment in the Garhwal-Kumaon region of the Himalayan arc. Acknowledgement We thank IIT Roorkee for provinding financial support and infrastructure for carrying out this work. The waveform data used in this study is obtained from the broadband seismometer network deployed in Garhwal Himalaya by the Earthquake Engineering Department, IIT Roorkee, and funded by Tehri Hydro Development Corporation India Ltd. (THDCIL). We thank Prof. S. C. Gupta and Dr. Arup Sen, for operations and management of seismic netrwork, and discussion regarding the metadata of locally saved data. We thank Navneet Srivastava for technical support. All the maps are drawn by the python version of Generic Mapping Tool (PyGMT) (Wessel et al., 2013), and inversion has been done by MTUQ (https://github.com/uafgeotools/mtuq), which uses Obspy (a Python) framework for processing seismological data (Beyreuther et al., 2010; Megies et al., 2011; Krischer et al., 2015).

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Chapter 5

Exploring GRACE and GPS and Absolute Gravity Data on the Relationship Between Hydrological Changes and Vertical Crustal Deformation in South India Ankit Singh, Rohtash Kumar, Amritansh Rai, Raghav Singh, and S. P. Singh

5.1

Introduction

During climatic cycles, changes in the mass of water, atmosphere, and non-tidal ocean disturb the Earth’s gravity field following Newton’s law of gravitation, and resulting loading effects on the Earth’s surface distort the lithosphere (He et al., 2017), which can be measured by GRACE. Further, the lithosphere can deform due to tectonic reasons as well. GPS can measure any change in lithospheric changes (He et al., 2017). Variations in atmosphere, hydrology, surface and ice/glacier mass loads cause elastic distortion of the solid Earth. Continuous geodetic data from CGPS stations and GRACE are used to record seasonal and secular mass variations in them. At inter-annual and seasonal time periods, hydrological mass fluctuations dominate all other sources of mass variations. GRACE’s primary scientific purpose is to explore this procedure, which is critical to understand water exchange inside the system, which includes the cryosphere (glaciers and large ice complexes), the seas, and the atmosphere (Davis et al., 2004; Maurya et al., 2019; Maurya, 2019). Water redistribution on the surface of the earth will result in a shift in weight or load on the Earth’s crust. On yearly timeframes, the crust will deform elastically, supported by the underlying mantle (Van dam et al., 2011). Extremely localized water-load variations will also affect the crust (Elo´segui et al., 2003). GRACE data should allow us to infer the elastic deformation associated with this changing load to the extent that gravity differences reported by GRACE are related to the hydrological

A. Singh · R. Kumar · A. Rai · R. Singh (✉) Department of Geophysics, Banaras Hindu University, Varanasi, India e-mail: [email protected] S. P. Singh Department of Atomic Energy, Mumbai, India © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 R. Kumar et al. (eds.), Recent Developments in Earthquake Seismology, https://doi.org/10.1007/978-3-031-47538-2_5

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cycle (Davis et al., 2004). Not only does GPS ground data show local tectonic deformation as materialistic deformation, but it also shows regional seasonal fluctuations owing to water loading cycle (Pan et al., 2018). In the GRACE data, we assume that tectonic signals are insignificant. We subtract the surface loading signals estimated by GRACE with climatic/hydrologic sources from the vertical velocity produced from non-stop and campaign-mode GPS data to extract the vertical crustal deformation indicating tectonic signals over the area (Pan et al., 2018). When the phases and amplitude of seasonal vertical deformation calculated from GPS and GRACE are reliable, we may conclude that hydrological factors are the primary source of periodic deformation in the area (Tiwari et al., 2014). Since March 2002, the GRACE mission has provided remarkable precision and resolution in the time variable gravity field (Tapley et al., 2004; Maurya and Singh, 2019a, b). GRACE employs a cutting-edge approach to monitor fluctuations in the gravity of the Earth by measuring the range of inter-satellite and range rate between two low-altitude and coplanar satellites using a K-band ranging KBR apparatus (Cazenave and Chen, 2010). In May 1997, the GRACE project was chosen as the second mission in the NASA Earth System Science Pathfinder (ESSP) Programme. NASA and the German Aerospace Centre collaborated on the Gravity Recovery GRACE (DLR). From its inauguration in March 2002 through the completion of its research assignment in October 2017, twin spacecraft made precise extents of the Earth’s gravitational field variances. GRACE Follow-Using (GRACE-FO) is a mission continuation that launched in May 2018 on almost identical hardware. GRACE satellite data is a valuable resource for researching climate geology and the Earth’s oceans. GRACE was a collaboration between the Centre for Space Research at the University of Texas in Austin, the German Aerospace Centre, Germany’s National Research Centre for Geosciences, Potsdam and NASA’s Jet Propulsion Laboratory. The NASA ESSP (Earth System Science Pathfinder) programme entrusted the overall mission administration to the Jet Propulsion Laboratory. At a near-polar inclination of 89°, the spacecraft were launched to a preliminary height of around 500 km. The satellites were detached by 220 km along their orbit path during normal operations. Every 30 days, this method was able to collect worldwide coverage. GRACE beyond its design life of 5 years, lasting 15 years until GRACE-2, was decommissioned on 27 October 27 2017. GRACE- FO, its replacement, was successfully launched on 22 May 22 2018. Satellite gravimetry, GRACE’s most important measurement, is not based on EM (electromagnetic) waves. As an alternative, the project employs a microwave ranging device to precisely detect variations in the distance and speed between two alike spacecraft orbiting 500 km (310 miles) above Earth in a polar orbit. Over a distance of 220 km, the ranging system can sense separation variations as tiny as 10 μm (about one-tenth of a human hair breadth). The twin GRACE satellites detect minute fluctuations in the gravitational pull of Earth as they orbit the planet 15 times each day. The first satellite is dragged slightly forward of the trailing satellite when it passes through a zone of slightly greater gravity, known as a gravity anomaly. As a result, the distance between the satellites grows. The first spacecraft then travels over the anomaly and slows down; in the meantime, the second spacecraft accelerates and

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decelerates over the same spot. Scientists can create a thorough picture of gravity anomalies of Erath by monitoring the continually varying distance between the two satellites and merging that data with accurate positional readings from GPS equipment. The pair of satellites (named “Tom” and “Jerry”) retain continuous two-way microwave-ranging communication in the K band. To calculate precise distance measurements, the frequency changes of the connection are compared. This is made possible by the onboard Ultra Stable Oscillator (USO), which creates the frequencies for the K-band ranging system. To be useful, the micrometre sensitivity of this measurement demands accurate estimations of each spacecraft’s position, velocity, and orientation. To reduce the influence of extraneous, non-gravitational forces (e.g., drag, solar radiation pressure), the vehicles employ sensitive Super STAR electrostatic accelerometers at their respective centres of mass. GPS sensors are used to identify the precise location of each satellite along the baseline between the satellites. The satellites use star cameras and magnetometers to establish their location. The GRACE vehicles also have optical corner reflectors to allow laser ranging from ground stations through the Centre of Mass Trim Assembly (MTA), which ensures that the centre of mass is properly corrected throughout the flight. GRACE’s monthly gravity anomaly maps are up to 1,000 times more precise than prior maps, significantly enhancing the accurateness of many approaches employed by hydrologists, oceanographers, geologists, glaciologists and other scientists to research climate-related phenomena. GRACE primarily identified changes in the global distribution of water. Ocean bottom pressure (the cumulative weight of the atmosphere and ocean waters) is as significant to oceanographers as atmospheric pressure is to meteorologists, and scientists utilise GRACE data to estimate it. Scientists can measure monthly variations in deep ocean currents by observing ocean pressure gradients, for example. Because huge ocean currents may also be approximated and validated by an ocean buoy network, GRACE’s poor resolution is acceptable in this study. Improved ways for employing GRACE data to characterise Earth’s gravitational field have recently been outlined by scientists. GRACE data are crucial in determining the source of sea level upsurge, whether it is due to mass being added to the sea (e.g. from melting glaciers) or changes in salinity or thermal expansion of heated water. The use of GRACE data to determine high-resolution static gravity fields has improved our knowledge of global ocean movement. Currents and fluctuations in Earth’s gravitational field cause hills and valleys on the surface of the ocean (ocean surface topography). GRACE allows for the separation of these two impacts, allowing for more accurate measurements of ocean streams and their impact on climate. GRACE also detects gravity field changes caused by geophysical phenomena. The steady rising of land masses originally low by ice sheets weight from the last ice age is the most prominent of these indications. GIA signals arise in gravity field measurements as secular trends that must be eliminated in order to correctly assess water variations and ice mass in an area. GRACE is also affected by variations in the gravitational field caused by earthquakes. GRACE data have enhanced the existing Earth gravitational field model, resulting in advancements in geodesy. Corrections to the equipotential surface, which is used to

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reference land heights, have been made possible by this enhanced model. This supplementary precise reference surface provides for more precise longitude and latitude values, as well as reduced inaccuracy in geodetic satellite orbit calculations. GRACE is affected by regional differences in atmospheric mass and high-frequency oscillations in the pressure of the ocean bottom. These changes are well recognised, and aliasing is avoided by removing them from monthly gravity readings utilizing forecast models. However, inaccuracies in these models have an impact on GRACE results. GRACE data may also help with fundamental physics. They attempted to quantify the relativistic frame-dragging effect by re-analysing data from the LAGEOS experiment. The present study aims to explore the GPS and GRACE data set to detect the impact of sessional variation groundwater on the ground deformation.

5.2

Study Area

The Indo-Gangetic Plains (IGP) is one of the world’s biggest fluvial plains, bordered on the north by the Himalaya and on the south by the Craton. The IGP is uneventfully flat with a wide range of surface soils from scorching dry Rajasthan in the west to per-humid West Bengal. The IGP is a “foredeep” depression between the Himalaya in the north and the Indian Peninsula to the south. The IGP is a massive uneven trough with a maximum thickness of around 10 km in the foothills to the north and a minimum thickness of a few metres near the craton to the south. The Indian Plate continues to move northward at a pace of 2–5 cm/year, and the solidity created across the plate guarantees that it is always beneath stress, providing the primary cause of strain in the cracked zones. Lucknow is a part of the IGP. Being drained by Himalayan rivers the region faces floods during monsoon. Lying in the tropical latitude it faces extreme heat as well. The region is extensively used for agriculture, and the farmers extensively depend upon the groundwater for irrigation. The region lies in the zone of effect of both south-western and south-eastern monsoon. The population of the region has been continuously on the rise. It has seen rapid urbanisation and hence the changing trends of water usage. With the exclusion of the Archaean metamorphic and igneous complex, the Deccan Traps are the most widespread geological formations on the Deccan Peninsula. Vesicular traps with closely linked and partially filled vesicles, inter-trapped sediments with principal porosities and huge traps with fracture porosities all play a key role in influencing groundwater possibilities. The Deccan peninsula has been considered a stable shield for a long time. No earthquakes or tremors of high magnitude were registered from any part of the peninsula in the past. The entire shield was regarded as aseismic by the early earth scientists. However, a devastating earthquake of magnitude about 6.5 to 7.0 on the Richter scale hit Koyna in 1967. This event terminated the early views and concepts. Hyderabad is a part of Deccan peninsular India. The region faces the southeastern monsoon. The region has hard rock geology being over the Deccan trap. The region is drained by a few small rivers. The city of Hyderabad depends largely on

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reservoirs for rain stored in the reservoirs. Hyderabad lies in the southern region of the Indian Peninsula, dominated by uncategorized Precambrian gneisses and granites known as “Pensul gneisses.” Granite underpins the region surrounding Hyderabad, which is a portion of a vast granitic batholith with revelations spanning over 5000 km*. Kanungo et al. report on its extensive structural research (1975). The granites are coarse to medium grained and come in two colors: pink granite and grey granite, dependent on the feldspar colour. Both of these kinds, which coexist, occupy a substantial portion of the land. Many sections of the Indian Shield saw a significant granitization-migmatization phase approximately 2.4 billion years ago (Divakara Rao et al., 1974). The Hyderabad batholith is also part of the Indian Shield’s granitization stage. Bangalore city is approximately 650 km² in size and is at a usual elevation of about 910 m above the sea level. It is located at 12.58° North latitude and 77.37° East longitude. Bangalore city has a population of about 6 million people, making it India’s fastest-growing and sixth-largest metropolis. This region also lies over the Deccan plateau and drained by small rivers and Kaveri running through proximity. The safety factor against liquefaction was utilized to create a liquefaction danger map. Bangalore is protected from liquefaction, according to research, except in a few places where the overburden is sandy silt and there is a shallow water table. The reactivated reverse/normal faults in the Bangalore region exhibit a dominating strikestrip movement, leading to recurrent rupturing at adjacent intervals. This may also be seen in the repeated earthquakes caused by the renewal of transcurrent faults (Valdiya, 1998). The majority of the Bangalore region is made up of Gneissic complexes, which were created by successive tectonic-thermal processes with massive influxes of sialic material between 3,400 and 3,000 million years ago, giving rise to a vast set of grey gneisses known as the “older gneiss complex.” Just like Lucknow, Hyderabad and Bangalore have also seen urbanisation and changing patterns of water usage and extraction. Devastating earthquakes have struck the Indian subcontinent in the past. The Indian plate is slamming into Asia at a pace of around 47 mm/year, which accounts for the high frequency and severity of the earthquakes. According to India’s geographical data, over 54% of the area is prone to earthquakes. According to United Nations and World bank researches, nearly 200 million Indian metropolitan inhabitants would be vulnerable to storms and earthquakes by 2050. In the most recent edition of the seismic zoning map of India, the earthquake-resistant design code of India [IS 1893 (Part 1) 2002] assigns four types of seismicity to India in terms of zone factors. In other words, the earthquake zoning map in India divides the nation into four seismic zones (Zones 2, 3, 4 and 5). Though Lucknow has never seen an earthquake yet, it falls in Earthquake Zone 3 and it comes under moderate hazard zone because it lies on the Faizabad faultline. Hyderabad is situated in an area prone to earthquakes measuring up to 5.0 on the Richter scale. However, any seismic activity on the city’s eastern side, which includes Godavari and Bandrachalam, which are in a zone where earthquakes measuring up to 5.7 on the Richter scale might occur, can have an impact. Hyderabad lies in the Zone 2 area. Bangalore lies in the Zone 2 area. Panjamani Anbazhagan, associate professor of civil engineering at IISc, headed a

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team of researchers that identified eight possible future earthquake zones in south India. Bangalore happens to be one of them. The Bengaluru-Mysuru area has had the most earthquake activity in Karnataka. Center for Space Research (CSR, University of Texas), JPL (Jet Propulsion Laboratory) and GFZ (Geo-Forschungs Zentrum Potsdam) announced handled monthly outcomes of GRACE data. In this study, we have used the level 4 mascon data for the given area of study. GRACE’s inter-satellite range measurements are fitted to mass concentration blocks (mascons), which are basically alternative type of gravity field basis function. Using “mascons” instead of the traditional spherical harmonic method, which was used for the first decade of GRACE/GRACE-FO measurements, provides a number of advantages. We can much more easily impose geophysical limitations using mascons. The RL06M.MSCNv02 surface mass change data are centred on Level-1 GRACE/GRACE-FO measurements analysed at JPL and have undergone the following processing: Because the original GRACE-C20 values have a higher uncertainty than the SLR-values, the C20 (degree 2, order 0), coefficients are substituted by solutions from Satellite Laser Ranging (Cheng et al., 2011). Sun et al. (2016) and Tiwari et al. (2009) approaches are used to estimate the degree-1 coefficients (Geocentre). Based on the ICE6G-D model from Peltier et al. (2018), a glacial isostatic adjustment (GIA) correction was implemented. We have used the processed GPS data from the Nevada Geodetic Laboratory (NGL) (Blewitt and Hammond, 2018). The NGL has been recording continuous GPS data in Lucknow since 2012. We have used the data for the time span 2012–2019 from NEVADA GEODETIC LABORATORY Lucknow. The GPS station in Lucknow is stationed at (26.91,80.95). We have used the GRACE data averaged over the zone bound by is given in Fig. 5.1 (26.75,80.75), (27.25,80.75), (26.25,81.25) and (27.25,81.25). The GPS station in Bangalore is stationed at (13.02,77.57). We have used the GRACE data averaged over the zone bound by (12.75,77.25), (13.25,77.25), (12.75,77.75) and (13.25,77.75). The GPS station in Hyderabad is stationed at (17.41,78.55). We have used the GRACE data averaged over the zone bound by (17.25,78.25), (17.75,78.25), (17.25,78.75) and (17.75,78.75).

5.3

Methodology

A Level-2 data set of GRACE comprises of Stokes coefficients (and associated errors) that reflect an expansion of the gravitational potential of Earth in spherical harmonics. Each data collection is the result of a one-month reduction of GRACE observations, which are essentially the range between co-orbiting satellites. On timeframes less than one month, corrections are performed to oceanic and atmospheric mass movements. The total mass change is accounted in terms of Equivalent Water Height, which could be responsible for the mass variation. If we were to use Level 2 data, then this EWH is calculated using the formula:

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Fig. 5.1 GPS stations at Lucknow, Hyderabad and Bangalore. (Courtesy NEVADA GEODETIC LABORATORY)

σ ðφ, θÞ =

αρe 3ρw

1

l

l=0 m=0

Pm l ðcos θÞ

2l þ 1 1 þ kl

m ΔSm l sinðmφÞ þ ΔC l cosðmφÞ ð5:1Þ

where ρe the average density of the Earth and ρw represents the density of water (1 g/ cm3). α denotes the equatorial radius, θ is the colatitude, while φ is the east longitude; and ΔSlm and ΔClm represent monthly Stokes coefficients. Plm(cosθ) denotes the fully normalized degree n and order Legendre function. The equivalent crustal adjustment related with the EWH can be computed by the method (He et al., 2017): Δhðφ, θÞ = α

1

l

l=1 m=0

Pm n ðcos θ Þ

h,l ½Slm sinðmφÞ þ Clm cosðmφÞ 1 þ k ,l

ð5:2Þ

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where Slm and Clm denote gravity field spherical harmonic coefficients. hl’ and kl’ are the accepted load Love numbers supplied by GRACE monthly data. Looking at the above two formulae carefully, we can see that the two are similar. The stoke’s coefficients and the spherical harmonic coefficients are related to each other by factor of density of earth and load love numbers. The impact of elastic loading on uplift rate owing to changes in continental water storage may be simulated as following (Kusche & Schrama, 2005; van der Wal et al., 2011): U 0lm V 0lm

where

U 0lm V 0lm

=

3ρw 1 h ρe 2l þ 1 l

ð5:3Þ

C lm Slm

denote spherical harmonic expansion coefficients of the elstic uplift

rate, ρw is water density (1000 kg m‑3), ρe denotes the Earth’s mean density (5517 kg m‑3), hl is the surface load Love numbers fo radial displacement and

C lm Slm

represent

the Stokes coefficients obtained from water thickness changes (Jiao et al., 2019). Jiao et al. (2019) demonstrated that the mass change (EWH) produced by grid surface deformation may be computed using the equation as follows (Sun et al., 2022): Δhwater ρwater = Δhgps ρcrust

ð5:4Þ

where Δhwater denotes the grid mass variation EWH, Δhgps represents GPS calculated average vertical displacement variation of grid and ρcrust denotes grid crustal density. Since we already got the EWH calculated from the Level 4 data, we can calculate the vertical crustal deformation from the EWH data by the method suggested by Sun et al. (2022). The TWS change for any region can also be obtained from the real-time analysis offered by the GRACE TELLUS interactive tool. They offer real-time analysis of preprocessed level 4 masscon data. We can obtain the analysis results in required format for any region on any point on the surface of the Earth

5.4 5.4.1

Results and Discussion GRACE and GPS Crustal Deformation Comparison

Referring to Figs. 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, we can see that the GRACE and GPS data show good correlation for Hyderabad and Bangalore. While the same comparison isn’t as well for Lucknow. While the GPS data shows sharp effects of the regional factors, the GRACE data shows averaged-out effects and hence is coarser. The pattern of the plot for GRACE and GPS shows the yearly oscillation and inter-annual variability, suggesting the hydrological effect of the monsoon type of climate manifesting in the form of crustal rise and subsidence. Seasonal and inter-

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Fig. 5.2 The plot showing vertical crustal deformation obtained from GRACE in Lucknow region

Fig. 5.3 Vertical crustal deformation obtained from GPS stationed at Lucknow

Fig. 5.4 Vertical crustal deformation obtained from GRACE data for Hyderabad region

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Fig. 5.5 Vertical crustal deformation obtained from GPS stationed at Hyderabad

Fig. 5.6 Vertical crustal deformation obtained from GRACE data for Bangalore region

annual hydrological fluctuations seem to predominate in the shield region of southern India, with inter-annual and seasonal vertical distortions anticipated. While the long-term trend for the Lucknow region suggests decline in water resources for the region (Singh & Raju, 2020). The long-term trend for Bangalore and Hyderabad indicates consistency in the crustal changes and TWS. Since South India is mostly dependent on monsoon and is devoid of major groundwater sources owing to its hard rock geology, so there is not much dependency on crustal deformation phenomenon over groundwater storage factors. Hence the GPS and GRACE signals fluctuate with

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Fig. 5.7 Vertical crustal deformation obtained from GPS stationed at Bangalore

the inter-seasonal monsoonal effects on a yearly basis. This is not the case with Lucknow, which belongs to the Indo-Gangetic plains and is facing a drastic decrease in groundwater resources (Singh & Raju, 2020). This is one of the reasons of the subsidence of the Indo-Gangetic Plains, which can be due to the over-extraction of groundwater resources for irrigation purposes. Though the patterns of the plots obtained by GRACE and GPS match up to greater extent, the range of the magnitude of vertical crustal deformation do not match very well. This could have been better if we were to calculate vertical crustal deformation using the equation suggested by Tapley et al. (2004). In this study, we used the formula suggested by Sun et al. (2021). If we can obtain EWH from the vertical deformation then we should be able to obtain vertical deformation using EWH. Under what circumstances we can use this simple relationship is yet to be known and should be an area of further study. For the moment, all we can say is that the patterns of the plot by GRACE and GPS match.

5.4.2

Terrestrial Water Storage

We analyzed the overall TWS (total water storage) variability for our study areas. We can see that the TWS has been continuously declining rapidly for the Lucknow region (Fig. 5.8). We can also see that for the initial years up to 2016, the pattern of graph remained similar while the magnitude continued decreasing. While after 2016, the pattern is varying and there is bias of randomness. This hints towards the changing patterns of water consumption and recharge. We can see that the overall TWS has been declining for the Hyderabad region as well (Fig. 5.9). Although the

Fig. 5.8 GRACE TWS analysis for Lucknow region

Fig. 5.9 GRACE TWS analysis for Hyderabad region

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Fig. 5.10 GRACE TWS analysis for Bangalore

severity is not as bad as Lucknow. The pattern of the graph is changing towards the end and hence hints towards the changing pattern of storage and consumption. We can see that the overall TWS trend is not declining for the Bangalore region (Fig. 5.10). This may be due to the fact that this analysis is done for a time span much shorter and non-simultaneous with those done for Lucknow and Hyderabad. Tending towards 2014, we can see an element of change in the pattern, though not as severe as that for Lucknow and Hyderabad.

5.5

Conclusion

The data from GRACE and GPS has been compared for all the given regions and the plots suggest good harmony among them. The magnitude of the crustal deformation for GRACE and GPS are not matching well but their range does suggest a comparability. The patterns of the plot of GRACE and GPS match well for Hyderabad and Bangalore for the given span of time but do not match well for Lucknow. This suggests that the crustal deformation as measured by the GPS for Hyderabad and Lucknow is majorly due to hydrological loading. The crustal deformation as

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measured by the GPS in Lucknow matches up to some extent with that obtained by GRACE in Lucknow. This suggests that the deformation measured by GPS can be corrected for the hydrological effect using GRACE. The TWS analysis study suggests subsidence in the Lucknow region while there is no such noticeable phenomenon for Hyderabad and Bangalore. The terrestrial water storage for Lucknow has been declining rapidly, for Hyderabad moderately and not declining for Bangalore.

References Blewitt, G., & Hammond, W. (2018). Harnessing the GPS data explosion for interdisciplinary science. Eos, 99. Cazenave, A., & Chen, J. (2010). Time-variable gravity from space and present-day mass redistribution in the Earth system. Earth and Planetary Science Letters, 298(3–4), 263–274. Cheng, M., Ries, J. C., & Tapley, B. D. (2011). Variations of the Earth’s figure axis from satellite laser ranging and GRACE. Journal of Geophysical Research: Solid Earth, 116(B1). Davis, J. L., Elósegui, P., Mitrovica, J. X., & Tamisiea, M. E. (2004). Climate-driven deformation of the solid Earth from GRACE and GPS. Geophysical Research Letters, 31(24), L24605. He, M., Shen, W., Pan, Y., Chen, R., Ding, H., & Guo, G. (2017). Temporal–spatial surface seasonal mass changes and vertical crustal deformation in south China block from GPS and GRACE measurements. Sensors, 18(1), 99. Jiao, G., Song, S., Ge, Y., Su, K., & Liu, Y. (2019). Assessment of BeiDou-3 and multi-GNSS precise point positioning performance. Sensors, 19(11), 2496. Kusche, J. E. J. O., & Schrama, E. J. O. (2005). Surface mass redistribution inversion from global GPS deformation and Gravity Recovery and Climate Experiment (GRACE) gravity data. Journal of Geophysical Research: Solid Earth, 110(B9). Maurya, S. P., & Singh, K. H. (2019a). Predicting porosity by multivariate regression and probabilistic neural network using model-based and coloured inversion as external attributes: a quantitative comparison. Journal of the Geological Society of India, 93(2), 207–212. Maurya, S. P., & Singh, N. P. (2019b). Characterising sand channel from seismic data using linear programming (l1-norm) sparse spike inversion technique: A case study from offshore¸ Canada. Exploration Geophysics, 50(4), 449–460. Maurya, S. P. (2019). Estimating elastic impedance from seismic inversion method. Current Science, 116(4), 628–635. Maurya, S. P., Singh, K. H., & Singh, N. P. (2019). Qualitative and quantitative comparison of geostatistical techniques of porosity prediction from the seismic and logging data: a case study from the Blackfoot Field, Alberta, Canada. Marine Geophysical Research, 40, 51–71. Pan, Y., Shen, W. B., Shum, C. K., & Chen, R. (2018). Spatially varying surface seasonal oscillations and 3-D crustal deformation of the Tibetan Plateau derived from GPS and GRACE data. Earth and Planetary Science Letters, 502, 12–22. Peltier, A., Villeneuve, N., Ferrazzini, V., Testud, S., Hassen Ali, T., Boissier, P., & Catherine, P. (2018). Changes in the long-term geophysical eruptive precursors at Piton de la Fournaise: Implications for the response management. Frontiers in Earth Science, 6, 104. Rao, V. D., Naqvi, S. M., Satyanarayana, K., & Hussain, S. M. (1974). Geochemistry and origin of the Peninsular gneisses of Karnataka, India. Geological Society of India, 15(3), 270–277. Singh, A., & Raju, A. (2020). Application of grace satellite data for assessment of groundwater resources in Central Ganga Alluvial Plain, Northern India. Environmental Concerns and Sustainable Development: Volume 1: Air, Water and Energy Resources, pp. 153–162. Sun, P., Guo, C., & Wei, D. (2022). GRACE Data explore moho change characteristics beneath the South America continent near the Chile Triple junction. Remote Sensing, 14(4), 924.

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Sun, K., Meng, G., Hong, S., Su, X., Huang, X., & Dong, Y. (2021). Interseismic movement along the Luhuo-Daofu section of the Xianshuihe Fault from InSAR and GPS observations. Chinese Journal of Geophysics, 64(7), 2278–2296. Sun, Y., Riva, R., & Ditmar, P. (2016). Optimizing estimates of annual variations and trends in geocenter motion and J2 from a combination of GRACE data and geophysical models. Journal of Geophysical Research: Solid Earth, 121(11), 8352–8370. Tapley, B. D., Bettadpur, S., Watkins, M., & Reigber, C. (2004). The gravity recovery and climate experiment: Mission overview and early results. Geophysical Research Letters, 31(9). Tiwari, V. M., Srinivas, N., & Singh, B. (2014). Hydrological changes and vertical crustal deformation in south India: Inference from GRACE, GPS and absolute gravity data. Physics of the Earth and Planetary Interiors, 231, 74–80. Tiwari, V. M., Wahr, J., & Swenson, S. (2009). Dwindling groundwater resources in northern India, from satellite gravity observations. Geophysical Research Letters, 36(18), L18401. Valdiya, K. S. (1998). Dynamic himalaya. Universities press. Van Dam, N. T., Sheppard, S. C., Forsyth, J. P. and Earleywine, M. (2011). Self-compassion is a better predictor than mindfulness of symptom severity and quality of life in mixed anxiety and depression. Journal of anxiety disorders, 25(1), 123–130.

Chapter 6

Moho Mapping of Northern Chile Region Using Receiver Function Analysis and HK Stacking Amritansh Rai, Rohtash Kumar, Dipankan Srivastava, Raghav Singh, Ankit Singh, and S. P. Maurya

6.1

Introduction

The Ps receiver function technique, which uses P-to-S converted seismic phases beneath a recording station, has made it possible to record the seismic discontinuity structure of the upper mantle and mantle conceivable. The Ps receiver function approach operates under the principle that direct S-wave energy from an earthquake always trails incoming direct P-wave energy. Consequently, any S-wave phases that are recorded in conjunction with the entering P wavefield are converted to P-to-S energy. P-to-S converted appearances arising from impedance discontinuities and subsurface velocity are emphasized by P-to-S receiver function analysis by signal deconvolution between the vertical component and horizontal seismograms. Through cross-component deconvolution, the receiver function can be isolated from the effects of instrument reaction and source function on the seismogram. This allows for a clearer representation of the impedance and velocity discontinuity structure of the crust and upper mantle along the lateral ray path. The presence of significant amplitude multiples caused by sharp velocity disparities in the Moho and deep sedimentary basins can lead to imaging outcomes that obscure deeper structures. Ps receiver functions have a significant drawback when it comes to imaging the higher mantle. The energy contained in Moho multiples, for example, may mask the lithospheric-asthenospheric boundary and other possible subcrustal discontinuities. The Sp receiver function technique differs from Ps receiver functions by aiming to distinguish continuous S arrivals from the S-to-P mode converted energy. Sp receiver functions offer a potential advantage as transformed P-wave energy travels faster than the arriving S wavefield. By using Sp receiver functions, higher mantle imaging can be achieved with minimal artifacts as they are relatively unaffected by A. Rai · R. Kumar · D. Srivastava (✉) · R. Singh · A. Singh · S. P. Maurya Department of Geophysics, Banaras Hindu University, Varanasi, India © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 R. Kumar et al. (eds.), Recent Developments in Earthquake Seismology, https://doi.org/10.1007/978-3-031-47538-2_6

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the interference of first-order multiples. The Sp receiver function method has utilized this feature to effectively create visual representations of the Moho, the boundary between the lithosphere and asthenosphere, and other presumed low-velocity regions in the upper mantle. In 1991, it was established that both actual and synthetic generated data show significant change in the amplitude variation and ambient energy levels during the time frame optimal for the detection of S-to-P converted phases (instantly before the S-wave appearance) in a comprehensive investigation of the S-to-P converted waves. This was mainly because of the interference from predecessors of the sS, ScS, and SKS phases. The existence of certain phases (namely, sPPPP and sPPP) were observed that have been regularly reflected off from the Earth’s surface over this particular time span. P-wave energy was also distinguished from S-to-P scattering from adjacent lithosphere heterogeneities between the source and receiver, with a ray path similar to the teleseismic phase SP. In the synthetic seismogram research, Bock (1994) recognized the existence of stages that have experienced many reflections of the Earth’s surface and arrive as precursors of S, SKS, and ScS waves. According to Bock, these precursors may coincide with higher mantle S-to-P converted phases and exhibit equal amplitudes. The hypothesis that all P-wave energy immediately preceding the arrival of S-wave was formed by mode conversion is shattered as multiple P-wave phases have been observed. The deconvolution process of the receiver function has the potential to amplify the interfering P-wave energy, leading to a receiver function that contains significant energy. However, this energy may not correspond accurately to the actual Sp receiver function phases. Utilizing receiver function analysis and HK stacking, we attempted to visualize the Moho structure in the Northern Chile Region in this study. We examine teleseismic earthquake information obtained from the International Federation of Digital Seismograph Networks (FDSN).

6.2

Seismotectonics of the Study Region

The subduction zone (68 mm/year) between the South American and Nazca plates goes across North-Central Chile (34°–25°S) and is still little known, particularly north of 30°S, due to a paucity of geophysical and geological studies. This region comes under tectonic and kinematic transition between Central Chile where plate convergence is totally accommodated by subduction (Métois et al., 2012), and North Chile, where plate convergence is accommodated by sub-Andean fold-and-thrust belt backarc shortening (Métois et al., 2013). The sub-Andean front declines in north-central Chile and a thrust series form the Sierras Pampeanas, which narrow south of 34°S. Assuming that a few of the thrusts are engaged structures with a medium present and past shallow seismicity, it is unknown whether this massive diffuse distortion zone allows a noteworthy portion of plate convergence motion, leading to an Andean sliver with motion different from the South American craton (Brooks et al., 2003; Métois et al., 2012; Vigny et al., 2009). If this sliver is present,

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then its motion throughout the interseismic phase would be challenging to quantify since the signal, which is just a few mm/year, may be hidden or altered by the coupling variations on the subduction boundary. The region of subduction in NorthCentral Chile similarly exhibits odd behavior, with the slab flattening at around 100 km deep from 32°S to 26°S (Tassara et al., 2006), and no volcanic motion is detected in this so-called “flat slab” region. The Juan-Fernandez ridge (JFR), Challenger fracture zone (CFZ), Copiap’o ridge (CoR), and Salar y Gom’ez ridge (S&GR) are four bathymetric structures (fracture and ridges zones) from south to north that are subducting within the area and which may play a key part in the subduction process (Métois et al., 2013). The Sierras Pampeanas’ many fronts are apparent in the dappled DEM and are denoted with the black dashed lines. The Nazca subducting plate bathymetric features are contoured in white lines (S&G R, CoR, CFZ, and JFR). Peak rupture regions of the instrumental (solid) and major historical (dashed) megathrust earthquakes since 1800 are shown as red-contoured ellipses (Lomnitz, 2004; Comte & Pardo, 1991). Green stars show the position of the principal shock in recognized seismic swarms (Holtkamp et al., 2011). A black star marks the hypocentre of the 1997 Punitaqui compressional intraslab event (Gardi et al., 2006; Vigny et al., 2009). Red stars indicate the epicenters of the 1977 Caucete and the 1894 San Juan earthquakes. Peninsulas and the coastal features are denoted by grey rectangles. Figure 6.1 depicts the three-plate model set up at the Northern and Southern extremities of the research zone. Only two megathrust earthquakes were experienced in North-Central Chile through the previous century: the 1906 Valparaiso earthquake (Mw 8.4; 32–34.5°S; Beck et al., 1998) and the 1922 Copiap’o earthquake (Mw 8.4; 26–30°S; Lomnitz, 2004). Since then, many additional significant earthquakes have happened: in 1943, a Mw 7.9 occurrence cracked south of La Serena; in 1985, a Mw 8.0 event cracked over in front of Valparaiso; and in 1946 and 1983, two Mw 7.8 earthquakes cracked the subduction boundary from 26°S to 27.5°S. Finally, other seismic swarms have happened in the region, including those near Caldera (27°S) in several years (1973, 1979, and 2006) near Tongoy (31°S) in 1997 (Holtkamp et al., 2011); and probably nearby La Serena (29°S) right now. The seismicity in the area around Valparaiso is complex, and the links between the events of 1985, 1906, and the 2010 Maule earthquake are uncertain. While the megathrust earthquakes of 2010 and 1906 are undeniably megathrust earthquakes with well-connected ruptures and little or no overlap, the lesser Valparaiso earthquake of 1985 is challenging to place in the sequence. The 1922 earthquake rupture zone appears to match well with the tightly linked Atacama stretch delineated by M’etois et al. (2012) at the northern end of our research region. This area has not ruptured since 1973, and there has been little background seismicity, which is akin to what was experienced before 2010 in the Maule area. As a result, it is believed that this location might be a developed seismic gap, with distortion accumulating at a constant rate of ~7 cm/yr concluded 90 years reaching the alike of 6 m of slip insufficiency supposing complete link throughout the entire segment surface.

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Fig. 6.1 Seismotectonic of Northern Chile region

Such a massive amount of slide, if free all at once concluded a 300-km-long length, would resemble an earthquake with a greater than 8 magnitude. A detailed determination of the segment borders, as well as the amount and distribution of coupling, is required to determine the seismic danger of this location. Métois et al. (2012, 2013) found considerable coupling differences laterally in the subduction zone of Chilean. A broad zone of poor coupling has been observed at 30°S (La Serena), dividing two strongly coupled segments. However, Determining the coupling distribution north of La Serena is a challenging task due to the lack of data beyond 30°S.

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6.2.1

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Atacama Fault System

The study area is situated in Atacama, bordered by Argentina to the east and the Pacific Ocean to the west. The Atacama Fault System (AFS) (Scheuber & Gonzalez, 1999; Cembrano et al., 2005) is the major crustal-scale, strike-slip fault system throughout the Central Andes fore arc (Fig. 6.1). The AFS comprises three distinct, curving sections running from north to south: Salar del Carmen, Paposo, and El Salado (Fig. 6.2). The AFS was formed in the Early Cretaceous to accommodate intra-arc sinistral and sinistral trans-tensional deformation when the axis of arc magmatism progressed eastwards (Scheuber et al., 1995; Scheuber & Gonzalez, 1999; Maurya et al., 2018). The mylonites are affected by brittle faults that exhibit comparable kinematics, and the ages of both ductile and brittle deformation vary along the strike (Brown et al.,

Fig. 6.2 Teleseismic Events for stations (a) AC05, (b) AC06, (c) AF01, (d) CO10. The seismic stations are located by triangles, while events are shown with dots on the map

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1993; Scheuber et al., 1995; Scheuber & Gonzalez, 1999). Syn-mylonitic hornblende and biotite from the Cerro Paranal Pluton’s outer shell provide 40Ar/39Ar and Rb-Sr ages ranging from 138 Ma to 125 Ma (Scheuber et al., 1995; Maurya & Singh, 2018).

6.3

Data

Teleseismic earthquakes recorded by four stations established by IRIS DMC in the Atacama, North Chile have been used (Fig 6.2). The teleseismic events from 2015 till 2022, of magnitudes > mw ~6.1 and high signal-to-noise ratio (SNR >5 & SNRH >5), are chosen for this study. In order to achieve a clear understanding of the upper mantle discontinuities and avoid any interference from diffraction at the coremantle boundary, the teleseismic waveforms analyzed were limited to those with a distance range of 30° to 90° from the epicenter. This allowed for a near-vertical incidence of the P wave, simplifying the wave field complexity. The near-surface velocities of Vp = 6.5 km/s and Vs = 3.6 km/s are used to divide the vertical and horizontal components of motion into incoming P, SV (radial), and SH (transverse) wave modes in order to avoid the impact of the free surface (Bostock, 1998).

6.4

Methodology

The receiver function approach is a very novel and strong technique for acquiring information about upper mantle and crust discontinuities under three-component seismic stations. Geophysical research is always aiming to explore and characterize the precise structure of the upper mantle and crust. Receiver functions show Earth’s structure beneath a station’s response through time series derived from threecomponent seismograms. The waveform separates mode-converted P-to-S waves that resonate in the structure underneath the seismometer. The P-wave from a distant source is attenuated at the crustal discontinuity or upper mantle barrier, ensuing in the conversion to an S wave. The vertical components of the teleseismic wave that strikes at (> 30°) are almost vertical to the receiver and rigorously determined by the earthquake origin. We may separate the S-wave produced regionally by using deconvolution of the vertical as well as horizontal components. In addition, the velocity and thickness of the layer are computed using the amplitude and travel time of these waves. Burdick and Langston (1977) developed the function used to illustrate the earth’s structure. The underlying discontinuities are restricted by simulating the amplitudes and times of these mode-converted phases and their consequences (Zhu & Kanamori, 2000). When a seismic event occurs, the seismic velocity structure impulse response underneath the seismic station serves as the receiver function. It is calculated by subtracting the seismic data from radial and vertical components. Deconvolution can

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be done in the time or frequency domain. When a moving seismic signal encounters a seismic velocity discontinuity at an oblique angle between two homogeneous strata, it separates into P-wave and SV-wave, with the latter arriving later at the station than the former. The angle of incidence of the initial P-wave determines the energy ratio in the P-wave to the transformed SV-wave. The smaller the ratio, the nearer the incident rays are to being perpendicular to the layer contact. If a 1-D model is used, it is easy to deduce that all P wave transformed energy will be stored in the receiver horizontal component. Earthquake signals from faraway happenings offer details about the source, signal path, and the lithospheric and crustal structures close the receiver. Investigating the S-waves triggered by refractions at a velocity discontinuity is a useful analytic method for obtaining details about the structure near the receiver.

6.4.1

Technique for Estimating Receiver Functions

The ground shifts inside the earth during an earthquake, and the hypo center is the location where the earthquake begins. The epicenter is a point that is projected above the hypocenter. The site where seismic waves are created is referred to as the source. Seismograms, which are real-time series data, are created from the produced waves in the seismograph. Three directions are used to order the information: east-west E, vertical Z, and north-south N. The recorded seismogram is rotated into a ZRT coordinate system to concentrate the energy on a particular component of the receiver. The transverse and radial components of the seismogram are deconvolved from the vertical component. Thus, the obtained time series is called as receiver function. A typical flowchart for the calculation of the receiver function is given in Fig. 6.3. Fig. 6.3 Typical “flow” chart of a receiver-function analysis. First, the seismogram is rotated to a suitable coordinate system and deconvolved to remove the source and path effect. The deconvolved output is the receiver function, which can be inverted to obtain velocity structure beneath the seismic station

Organize The Observations

Isolate The Receiver Response

Forward Model

Invert

Select The Best Solution

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Rotation

Seismographs record the motion of the earth in three directions, as defined by the ZNE coordinate system: north-south (N ), vertical (Z ), and east-west (E). Through an orthogonal transformation system, all of these elements were translated to the local wave coordinate classification by a transformation angle, which is known as back azimuth (ɛ). ɛ is the projection of the original recorded seismogram’s Z component to the north component. In general, there are two types of rotation systems: 2-D and 3-D. In this study, we used a 2-D rotation system with a constant Z component from the recorded coordinate scheme to the direction of an earthquake. The equation for transforming from the ENZ to the RTZ wave coordinate scheme is as follows and is depicted in Figs. 6.4, 6.5: R T Z

=

cos θ

sin θ

0

E

- sin θ 0

cos θ 0

0 1

N Z

ð6:1Þ

This matrix above represents the orthogonal transformation between two-dimensional systems, where θ = (3π/2 ‑ ɛ), which represents the rotational angle of the orthogonal transformation, and ɛ denotes the back azimuth angle.

6.4.1.2

Deconvolution

The source, route, lithospheric structure, and crustal structure near the receiver are all recorded when an earthquake signal is received from distance occurrences Phases of the impulse response transformed at impedance boundaries are obtained via deconvolution of the source time function. To exclude the source impact and ray Fig. 6.4 Seismograph recording three-component (radial, transverse, and vertical) seismic wave

Pro

Souce

po ga

tio

nD

ire

ctio

n

Receiver Z R T

N Horizontal Plane (Map View)

E

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Fig. 6.5 Rotation of the original three-component seismogram to new RTZ coordinate system

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T

North

West

BAZ Z East

R

South Source

path, the T and R component seismograms are deconvolved with the P signal on the Z component. Let’s assume that the recorded real signal arrived from a distant source and is represented in the frequency domain as the radial component E(w), together with all of the signal that travels through the instrument response I(w), the route T(w), and the response to the local velocity discontinuity caused by crust anisotropy F(w). The signal captured in the radial direction (from the source to the receiver) and vertical direction (Z ) is supplied by two fundamental equations. If w denotes the frequency domain, then: R ðwÞ = E ðwÞT ðwÞI ðwÞF ðwÞ

ð6:2Þ

Z ðwÞ = E ðwÞT ðwÞI ðwÞ

ð6:3Þ

The inverse Fourier transform of the velocity contrast function F(w) yields the receiver function in the time domain: F ðwÞ = RðwÞ=Z ðwÞ

ð6:4Þ

The deconvolution in the time domain is represented by Eq. 6.4. If F(t) is the receiver function acting as the velocity attenuation function in the direction of the entering seismic waves, then it may be written as follows: F ðt Þ = F - 1 ½F ðwÞ

ð6:5Þ

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A time domain deconvolution corresponds to the partition in the frequency domain. In the frequency domain, calculating F(w) is a deconvolution issue. Deconvolution can be done in either the time domain or the frequency domain. As a result, computing the Receiver Function is a deconvolution task. There are two very public deconvolution techniques: (a) Spectral Domain Deconvolution with Water Level (b) Iterative Time Domain Receiver Function Analysis (a) Spectral Domain Deconvolution with Water Level All of the seismogram’s components must be converted to the frequency domain for this technique to work. Because the denominator and numerator can both be real or imaginary, multiplication with the conjugate component with the denominator yields a real number for the denominator. In Eq. 6.5, we can simply apply the following basic strategy: RðwÞ = H ðwÞ=V ðwÞ

ð6:6Þ

RðwÞ = H ðwÞV c ðwÞ=V ðwÞV c ðwÞ

ð6:7Þ

where Vc (w) is a V(w) complex conjugate. The overall result will be quite high if the denominator is comparatively small compared to the numerator, hence this issue can be answered using the water level deconvolution method described by (Wiggins & Clayton, 1976) when dividing by a constant value, which is known as Water Level Value. Although this method is quick and easy, it causes lumps in the seismogram that are unrelated to the velocity constraint (Fig. 6.6). The less the water level value we can utilize the improved because the water level filter can create receiver function falsifications. 0.0001, 0.001, 0.01, and 0.1 are common quantities to investigate, but don’t be scared to experiment with different numbers (Ligorrfa & Ammon, 1999). This method works best with data that have a high signal-to-noise (SNR) ratio.

Fig. 6.6 Illustration of the water-level deconvolution from (Ligorrfa & Ammon, 1999)

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(b) Iterative Time Domain Receiver Function Analysis The iterative deconvolution technique is based on minimizing the difference between the observed horizontal seismogram and the predicted signal created by the convolution of an iteratively modernized spike train with the vertical component seismogram in the receiver-function approximation (Ligorrfa & Ammon, 1999). Ligorrfa and Ammon’s (1999) iterative in-time approach adopts that the receiver function is a superposition of multiple impulses with an unrestricted frequency range, but that Gaussian shape impulses are used. These Gaussian forms are formed by mixing the vertical and radial components and picking the co-related value’s initial arrival with the greatest amplitude. To detect the extra delays in spikes and amplitudes, the radial component is removed from the convolution of currentmeasured receiver functions with the vertical component. The technique is continued until the required best misfit is reached. Even if the recorded seismogram has a poor SNR, this approach works. The locations of the pulses in the receiver function show where the crust separates from the source or receiver and reveal velocity attenuation across the earth’s structure. The result of the deconvolution technique on a rotating seismogram is known as the receiver function, and it describes the Earth’s reaction near the seismic station.

6.4.2

H-K Stacking

The depth of the Moho discontinuity should be computed after finding the peak in the receiver function waveform that indicates Moho conversion. Only the delay time between the mode-converted S wave and the P wave is provided by the receiver function. The Vp/Vs ratio (K ) is needed to convert the delay time to depth. If no such knowledge exists, K and H can be constrained using the arrival timings of the multiples. Tps arrival times can be the same for different K and H value pairings. Similarly, any Tppps arrival time is valid. However, for particular Tps and Tppps values, K and H have just one solution. Utilizing the H-K stack Method, the average crustal thickness of H and K below the seismic station is determined from Ps mode converted phases and their first-order impacts PpPs and PpSs +PsPs (Zhu & Kanamori, 2000). The SNR will be improved by employing the stacking method of teleseismic events because mutual properties of the signals will be enhanced via productive interference and the random noise will be canceed out through damaging interference. The travel times and converted phase amplitudes Ps and their numerous seeming on radial receiver functions components are determined by the Moho depth and the ratio of Vp/Vs so that the receiver functions are stacked between various stations at different estimated time intervals of various phases Ps, PpPs, and PpSs+PsPs. The Vp/Vs ratio is connected to the Poisson’s ratio (σ) by the relationship = 0.5 × [1 – 1/(k2 – 1)], where k is the Vp/Vs value. Poisson’s ratio is a crucial parameter for describing the physical properties of

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the earth’s crustal rocks (Christensen, 1996). At each station, the radial receiver function amplitudes are stacked as follows: SðH, k Þ = W 1 Rðt 1 Þ þ W 2 Rðt 2 Þ þ W 3 R ðt 3 Þ

ð6:8Þ

where R(t) is the radial receiver function and t1, t2, and t3 are the projected arrival times of Ps, PpSs, and PpSs + PsPs (or PpPs). The weighting factors Wi ( i = 1, 2, 3) meet W1 + W2 + W3 = 1. Also, because both phase modes PpSs and PsPs have a negative polarity, we attach a negative sign to it in the summing, necessitating W1 ≥ W2 + W3 (Tkalčić et al., 2011).

6.5 6.5.1

Results Receiver Function Analysis

Discrete single-event seismograms are analyzed utilizing the receiver function approach, which deconvolves the SH and SV components and recovers receiver side S velocity configuration using the P component as a source wavelet estimate. To prevent interference from seasonal noise patterns, our approach employs an enhanced Wiener spectral deconvolution. The regularization parameter is determined based on the covariant noise spectrum between the vertical and horizontal components. (Audet, 2015). Receiver functions are filtered using a second-order Butterworth filter, where the cutoff frequencies are set at 0.05 to 0.5 Hz. After that, the receiver functions are stacked into 10 back azimuths. The primary waves can be seen at zero time. The crustal phases are interpreted in terms of delay times. The positive peaks in the waveforms are mainly due to high impedance contrast across the discontinuity and vice-versa. The station AC04 (28.20°S; 71.07°W) is located in Huasco Province, Atacama, Chile. Visual inspection of the radial receiver function in Fig 6.7 at this station indicates negative phases around 2 s, which may be due to the presence of LVZ. The positive peaks at 6 s and 12 s are interpreted as Moho Ps phase and Pps phase, respectively. The faint negative peak at 19 s may be due to the Pss (PsPs) phase. The station AC05 (28.83°S, 70.27°W) is located in Alto del Carmen, Atacama, Chile. Receiver functions are calculated as shown above. From Fig 6.8, the positive peak at 6.2 s is interpreted as the Moho Ps phase. The negative pulse around 9 s could signify a slightly deeper boundary with a descending decline in the seismic velocity pattern. The positive amplitude around 17 s may represent the Pps phase. Time lag on Ps phase arrival at different back azimuths may indicate a dipping Moho. The station AC07 (27.12°S, 70.86°W) is located in Caldera, Atacama, Chile. This station has been active since the year 2019 so not many receiver functions are obtained due to a lack of events and the conditions meeting the criteria stated earlier. However, the stacked receiver function is very good as can be seen in Fig. 6.9. A

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Fig. 6.7 Receiver functions for station AC04 shown over 30 s. The (left) radial and (right) transverse components, sorted by back azimuth of incoming wave field within 10° bins. Slowness information is averaged out. The top traces show the receiver functions further averaged over all back azimuth and slowness values. Negative polarity arrivals are dominant at early record. Faint positive peak can be seen around 6 s which is coming from Moho discontinuity

Fig. 6.8 Receiver functions for station AC05 shown over 30 s. Here positive peak is dominant at 7 s which is consistent with Ps conversions at Moho

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Fig. 6.9 Receiver Functions over Station AC07 for 30 s. Figure format is same as earlier. Strong peak is observed at 5 s which is identified as Moho Ps phase. PpPs phase is observed at 15 s and PsPs phase is observed around 20 s

strong positive peak at 5 s is interpreted as the Moho Ps phase. A low positive peak around 15 s and faint negative phases at 20 s can be interpreted as Pps phase and Pss phase, respectively. The station CO10 is located in Choros, La Higuera, Coquimbo, Chile. Its elevation from the mean sea level is 35 m. From the receiver function in Fig 6.10, it can be said that a faint positive peak at ~5 s is due to Moho discontinuity. A positive peak around 12 s is due to the PpPs phase i.e., Ps multiples. A negative peak around 17 s may be due to the PsPs phase.

6.5.2

Result: H-K Analysis

Thus, obtained receiver functions are stacked utilizing the product of all phase stacks (Fig. 6.11). This product-type stacking is independent of the choice of weights given to the phases. The corresponding point in the maximum intensity region gives the Moho depth (H ) and Vp/Vs value (K ). 6.5 km/s is chosen as the Vp for calculating the stacks. The stacks were computed for different values of Vp but no significant changes were observed. With the help of the obtained Vp/Vs value, Poisson’s ratio can be computed. The Moho depth and Poisson’s ratio for each station are tabulated here.

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Fig. 6.10 Receiver Function over Station CO10 for 30 s. Figure format is same as before. The seismogram is dominated by negative phase arrivals. Faint positive peak is observed around 5 s. Strong positive peak is observed at 12 s

a

b

Stack 2.0

2.0

1.9

1.9

1.8

1.8

1.6 20

1.6 20

25

30 35 40 Thickness (km)

45

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Stack 2.1

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35 40 45 Thickness (km)

50

Stack

2.4

CO10

2.3 2.2 Vp/Vs

1.9 1.8

2.1 2.0 1.9

1.7

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1.6 20

25

d AC05

2.0 Vp/Vs

AC07

1.7

1.7

c

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2.1

AC04

Vp/Vs

Vp/Vs

2.1

25

30 35 40 Thickness (km)

45

50

1.7 20

25

30

35 40 Thickness (km)

45

50

Fig. 6.11 H-k stacking results for Vp/Vs (k) and crustal thickness (H ) of all stations used in the study (a) AC04, (b) AC07, (c) AC05, (d) CO1

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Discussion

The study area is the Atacama region which is situated in Northern Chile. The Atacama basin is a bulging morphological irregularity in the Central Andean forearc (Schurr & Rietbrock, 2004). Obtained receiver functions at stations AC04 & AC05 tell that the region could have shallow LVL. The variations in Moho phase arrival at different back azimuths specify prevalent directional structure i.e., either anisotropy or dipping interface. If there had been an isotropic structure, then there should be no signal at the transverse receiver functions. Thus, transverse receiver functions represent rock anisotropy, structural heterogeneity, or both (Cassidy, 1992; Levin & Park, 1997; Savage, 1998; Frederiksen & Bostock, 2000; Niu & Liu, 2011). Receiver functions obtained from an event with varying back azimuths capture the anisotropic layer’s characteristics differently, contingent upon the ray path angle relative to the anisotropy orientation. (Porter et al., 2011). The dipping layer and anisotropy can be distinguished with the help of amplitude and delay times on the tangential record section. A subsiding layer, specifically, leads to a zero-lag arrival with a change in polarity on the tangential record section. This phenomenon, not observed in the anisotropic case, is evident at station AC04 as well, where a zero-lag arrival with a polarity reversal is present. So, there is a dipping layer beneath this station.

6.7

Conclusion

In this study, Rfpy software is utilized to compute the receiver functions. The Package utilizes the IRIS station database and downloads the teleseismic waveforms for epicentral distances between 30° and 90°. The waveforms are pre-processed for calculating the receiver functions. First, waveforms were rotated to the ZRT coordinate system. After that wiener deconvolution is applied to remove the source and path effect. The resultant waveform is the receiver function. Receiver functions over AC04 and AC05 show a potential region of low-velocity layer at a shallower depth. Furthermore, the anisotropy or inclined Moho is deduced by analyzing the time delays of the Moho Ps phase across various back azimuths. Moreover, Moho depth and Poisson’s ratio were derived by inverting the receiver functions using H-K stacking techniques of Zhu and Kanamori (2000). A higher Moho depth of 46 km is obtained below AC07 station, which is located in Caldera, Atacama. Corresponding to this, Poisson’s ratio of 0.24 is achieved. A high poisson ratio is acquired below the CO10 station, which is located in Coquimbo. Corresponding to this, a Moho depth of 25 km is obtained. The acquired P-wave receiver functions could be used to deduce the S-wave velocity structure beneath each station through inversion. This would help to improve the crustal imaging of the area. In addition, harmonic decompositions of the receiver functions could be done to study the anisotropy behavior. CCP stacking of receiver functions will give more knowledge about the seismicity of the area (Table 6.1).

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Table 6.1 Moho Depth and Possion’s ratio for all the stations

Station AC04 AC05 AC07 CO10

Moho depth (KM) 26 31 46 25

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Poisson’s ratio 0.23 0.30 0.24 0.35

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Ligorrfa, J. P., & Ammon, C. J. (1999). Iterative deconvolution and receiver-function estimation. In Bulletin of the Seismological Society of America, 89. Lomnitz, C. (2004). Major earthquakes of Chile: A historical survey, 1535-1960. Seismological Research Letters, 75(B3), 368–378. Maurya, S. P., Singh, K. H., Kumar, A., & Singh, N. P. (2018). Reservoir characterization using post-stack seismic inversion techniques based on real coded genetic algorithm. Journal of Geophysics, 39(2). Maurya, S. P., & Singh, N. P. (2018). Application of LP and ML sparse spike inversion with probabilistic neural network to classify reservoir facies distribution-A case study from the Blackfoot field, Canada. Journal of Applied Geophysics, 159, 511–521. Métois, M., Socquet, A., & Vigny, C. (2012). Interseismic coupling, segmentation and mechanical behavior of the central Chile subduction zone. Journal of Geophysical Research: Solid Earth, 117(3). Métois, M., Vigny, C., Socquet, A., Delorme, A., Morvan, S., Ortega, I., & Valderas-Bermejo, C. M. (2013). GPS-derived interseismic coupling on the subduction and seismic hazards in the Atacama region, Chile. Geophysical Journal International, 196(2), 644–655. Niu, F., & Li, J. (2011). Component azimuths of the CEArray stations estimated from P-wave particle motion. Earthquake Science, 24, 3–13. Owens, T. J., Zandt, G., & Taylor, S. R. (1984). Seismic evidence for an ancient rift beneath the Cumberland Plateau, Tennessee: A detailed analysis of broadband teleseismic P waveforms. Journal of Geophysical Research: Solid Earth, 89(B9), 7783–7795. Pardo, M., Comte, D., & Monfret, T. (2002). Seismotectonic and stress distribution in the central Chile subduction zone. Journal of South American Earth Sciences, 15(1), 11–22. Porter, R., Zandt, G., & McQuarrie, N. (2011). Pervasive lower-crustal seismic anisotropy in Southern California: Evidence for underplated schists and active tectonics. Lithosphere, 3(3), 201–220. Savage, M. K. (1998). Lower crustal anisotropy or dipping boundaries? Effects on receiver functions and a case study in New Zealand. Journal of Geophysical Research: Solid Earth, 103(B7), 15069–15087. Scheuber, E., & Gonzalez, G. (1999). Tectonics of the Jurassic-Early Cretaceous magmatic arc of the north Chilean Coastal Cordillera (22°–26°S): A story of crustal deformation along a convergent plate boundary. Tectonics, 18(5), 895–910. Scheuber, E., Hammerschmidt, K., & Friedrichsen, H. (1995). 40Ar/39Ar and Rb-Sr analyses from ductile shear zones from the Atacama Fault Zone, northern Chile: The age of deformation. Tectonophysics, 250(1-3), 61–87. Schurr, B., & Rietbrock, A. (2004). Deep seismic structure of the Atacama basin, Northern Chile. Geophysical Research Letters, 31(12). Tassara, A., Götze, H. J., Schmidt, S., & Hackney, R. (2006). Three-dimensional density model of the Nazca plate and the Andean continental margin. Journal of Geophysical Research: Solid Earth, 111(B9). Tiwari, A. K., Maurya, S. P., & Singh, N. P. (2018). TEM response of a large loop source over the multilayer earth models. International Journal of Geophysics, 2018. Tkalčić, H., Chen, Y., Liu, R., Zhibin, H., Sun, L., & Chan, W. (2011). Multistep modelling of teleseismic receiver functions combined with constraints from seismic tomography: Crustal structure beneath southeast China. Geophysical Journal International, 187(1), 303–326. Vigny, C., Rudloff, A., Ruegg, J.-C., Madariaga, R., Campos, J., & Alvarez, M. (2009). Upper plate deformation measured by GPS in the Coquimbo Gap, Chile. Physics of the Earth and Planetary Interiors, 175(2), 86–95. Wiggins, R. A., & Clayton, R. W. (1976). Source shape estimation and deconvolution of teleseismic bodywaves. Geophysical Journal of the Royal Astronomical Society, 47(1), 151–177. Zhao, L. S., & Frohlich, C. (1996). Teleseismic body waveforms and receiver structures beneath seismic stations. Geophysical Journal International, 124(2), 525–540. Zhu, L., & Kanamori, H. (2000). Moho depth variation in southern California from teleseismic receiver functions. Journal of Geophysical Research: Solid Earth, 105(B2), 2969–2980.

Chapter 7

Coulomb Stress Change of the 2012 Indian Ocean Doublet Earthquake Pankhudi Thakur, Rohtash Kumar, Ranjit Das, Amritansh Rai, Raghav Singh, Ankit Singh, and S. P. Maurya

7.1

Introduction

On April 11, 2012, a powerful earthquake with a magnitude of 8.6 on the moment magnitude scale (Mw) occurred at a depth of 45.6 km. The epicenter was situated at the northwest intersection point of the Indian, Australian, and Sunda tectonic plates, approximately 500 km west of the seismic event that took place on December 26, 2004. Another earthquake measuring Mw 8.2 happened on the same day, delayed by about two hours, 120 kilometers from the primary event. Known as a doublet earthquake, such a pair of earthquakes with comparable sizes and mechanisms struck relatively close together in time and space (Kagan & Jackson, 1999; Delescluse et al., 2012). The USGS refers to the Mw 8.6 earthquake as the Indian Ocean earthquake, and from this point forward, we will use the same terminology. Both of these earthquakes had NNE and SSW directions of occurrence and were strikeslip events (Maurya, 2019; Tiwari et al., 2018; Maurya & Singh, 2018, 2019a). The focal mechanisms of the two earthquakes that occurred on April 11, 2012, with magnitudes of 8.6 and 8.2, exhibit congruence. This similarity implies that either a left lateral movement along a fault oriented in a north-northeast (NNE) direction or a right lateral shift along a fault aligned in a south-southwest (SSW) direction could have potentially triggered each of these earthquakes. This observation is based on information provided by the United States Geological Survey (USGS). These earthquakes produced a lot of strong aftershocks, with 465 Mw > 4.0 events occurring near the mainshock in 33 days. The areas SW of the mainshock and the P. Thakur · R. Kumar · A. Rai · R. Singh · A. Singh · S. P. Maurya (✉) Department of Geophysics, Banaras Hindu University, Varanasi, India e-mail: [email protected] R. Das Department of Computer Science and System Engineering, Universidad Católica del Norte, Antofagasta, Chile © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 R. Kumar et al. (eds.), Recent Developments in Earthquake Seismology, https://doi.org/10.1007/978-3-031-47538-2_7

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central fracture are where the aftershocks tend to cluster the most. Due to the local stress brought on by the mainshock, several events occurred, the largest of which measured Mw 8.2. There have been multiple earthquakes in the region previously. One of the most significant earthquakes on record struck Sumatra on December 26, 2004, Impacting a wide expanse spanning from the northern perimeter of Sumatra Island to the offshore vicinity of the Andaman Islands. This event ruptured a segment of the trench that extended about 1200 km, as reported by various sources including DeDontney et al. (2012), Srivastava et al. (2013), and Qiu et al. (2019). Another major earthquake, measuring Mw 8.7 on the Richter scale, occurred off the western coast of northern Sumatra on March 28, 2005. Examining the continuing changes in the Earth’s crust and the potential risks of earthquakes along neighboring parts of the subduction zone was essential due to the destructive impacts of both the prior and current seismic events. The distribution of aftershocks and their decay patterns, the immediate alteration in Coulomb stress within the vicinity, and these aspects, in particular, assume importance and make it easier to understand the seismic hazard in this area.

7.2

Geodynamics Setting

Geologist Hamilton (1979) played a crucial role in redefining the Indonesia/Sumatra region’s significance within global plate tectonics. It was only following the massive Mw 9.2 Sumatra earthquake on December 26, 2004, along with the subsequent devastating tsunami, that the Sumatra area of Indonesia garnered substantial recognition and attention. As described by McCaffrey in 1992 and 2009, this area serves as a prime illustration of slip partitioning. In this phenomenon, the motion occurring between two tectonic plates that converge at an angle is distributed among several parallel faults. The ongoing vibrant seismic activity within this area can be attributed to the convergence of the Indian, Australian, and Sunda plates, each traveling at distinct rates (45 mm/yr. and 52 mm/yr. relative to ITRF05), leading to a continuous display of significant seismic events. As outlined by Curray (2005) and Curray et al. (1979), the interaction between the advancing Indian and Australian plates results in the development of a strike-slip fault arrangement along the Burma plate. This configuration emerges as the subplate ascends over the subducted Indian plate. Additionally, a distinctive feature of this area is the presence of folded and uplifted segments. The Indian Ocean earthquake, along with its ensuing aftershocks, is located approximately 250 km to the northwest of the point where the Indian, Australian, and Sumatra plates intersect on the Indian plate. At a rate close to 52 millimeters per year, the Australia plate is undergoing subduction beneath the Sunda plate to the south of Sumatra along the Sunda Trench. This subduction process occurs nearly perpendicular to the trench, as documented by (Bock et al., 2003). Figure 7.1 shows the depiction of the Sumatran fault and the subduction zone within the area. Utilizing geodetic, seismological, rheological, and

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Fig. 7.1 The Sumatran fault, subduction zone, and minor faults in the Indian Ocean Earthquake

structural data, it is feasible to address the essential inquiries regarding the probabilistic earthquake risks within this region. This study will benefit from the capacity to deduce fault friction at depth through GPS measurements conducted on the Earth’s surface. This rationale prompted the initiation of GPS investigations in central Sumatra in 1989, entailing measurements taken at various prominent locations (Bock et al., 1990; Prawirodirdjo et al., 1997). A comprehensive geodetic GPS network, exemplified by the Sumatran GPS Array (SuGAr) under the guidance of Subarya et al. (2006), has been meticulously overseeing and observing this area following the occurrence of the 2004 Sumatra earthquake.

7.3

Coulomb Failure Modelling

Chinnery (1963) was the first to illustrate how an earthquake diminishes the average shear stress along the fault that experienced slippage. About 20 years after this discovery, it was discovered that off-fault aftershock lobes correlated with slight

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increases in shear and Coulomb stress (Das & Scholz, 1981). (Stein & Lisowski, 1983). The most basic representation of the Coulomb failure stress change is expressed as follows. Δσ f = Δτ þ μ ðΔσ n þ ΔPÞ

ð7:1Þ

In this context, the symbol μ denotes the friction coefficient (varying between 0 and 1), Δσn represents the alteration in normal stress, P signifies the change in pore pressure within the fault zone, and Δτ corresponds to the change in shear stress along the fault. The concept of Reduced effective friction coefficient (King et al., 1994) is commonly employed to depict how P tends to counterbalance n in Eq. (7.1), and it is formulated as follows: Δσ f = Δτ þ μ0 Δσ n

ð7:2Þ

The loading or unloading of a fault toward brittle failure may be inferred from an increase or decrease in Coulomb stress change on the fault. A region’s net stress accumulation does, however, always decrease as a whole as a result of an earthquake. In relation to stress alteration patterns, specific areas proximate to a given earthquake encounter an elevation in stress levels. In the region encompassing the rupture plane and expanding into two or more adjacent areas, where subsequent significant seismic events might experience delays, the primary factor driving this occurrence is the alteration of Coulomb stress. To model the Earth’s medium in this research, we employed the Coulomb3.3 version (Stein et al., 1996), assuming a uniform isotropic elastic half-space. This entails disregarding influences stemming from a layered Earth or a three-dimensional heterogeneous structure. Errors resulting from such an approximation are typically estimated to be less than 10% (Savage, 1987). Because the oceanic crust typically has a coefficient of friction between 0.6 and 0.8, we assumed it to be 0.7 (Byerlee, 1978). With a 0.5-degree grid spacing, we calculated the co-seismic displacements at each grid point. The dimensions of both fault geometries are smaller compared to the calculations proposed by Aki and Richards (1980) and endorsed by Wells and Coppersmith (1994). Specifically, the surface rupture length and width often exhibit lesser values than those observed for sub-surface rupture dimensions. The model anticipates an increase in stress of around 5 bars in the northeastern and southwestern areas of the lobes (at the fault’s endpoints along its axis), accompanied by a decrease in stress of about 4 bars in the zone of lateral lobes perpendicular to the fault axis (Fig. 7.2).

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Fig. 7.2 The Coulomb stress changes (bar) in the transverse and lateral directions of the fault

7.4

Results and Discussion

The Indian Ocean doublet earthquake emerges as the largest strike-slip fault seismic event ever recorded through instrumental recording giving the characteristics of subduction zone earthquakes. The strike-slip faults show how important the plate driving forces are relative to one another (Andrade & Rajendran, 2011). Both earthquakes may cause co-seismic displacement and Coulomb stress changes because their moment magnitudes (Mw 8.6 and 8.2) are of the same order. The static Coulomb stress is simulated by our model as increasing by nearly 5 bars and decreasing by nearly 4 bars. When compared to the Sumatra earthquake of 2004, this change—between 15 and 20 bar—is much smaller (McCloskey et al., 2005; Cattin et al., 2009). Approximately two hours later, an Mw 8.2 aftershock (opposite to the doublet event) occurred within the area where Coulomb stress had escalated.

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Fig. 7.3 Horizontal displacement vectors due to the main Sumatran fault

The displacements in the horizontal and vertical directions are shown in Figs. 7.3 and 7.4, respectively. Another notable instance is the 6.5 Mw Big Bear earthquake, which took place on June 28, 1992, merely three hours following the Landers earthquake (Liu et al., 2003). This event transpired in a region where the Coulomb stress had risen by 3 bars. We found that the region of increased Coulomb stress has seen 65% of aftershocks. The aftershocks typically happened close to the mainshock location. It has been suggested that a large asperity may be connected to a fault zone. Numerous events with sparsely spaced small asperities could result from the rupture of the fault zone. In this situation, the driving force behind the rupture’s spread might not be strong enough to penetrate a wider area. While the asperities themselves are resistant to breakage, the weaker zones around them are. Smaller events (aftershocks) are likely to rupture such regions (Igarashi et al., 2003; Matsuzawa et al., 2004; Wiseman and Bürgmann, 2012).

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Fig. 7.4 Vertical displacement (colors and contours) due to the main Sumatran fault

Research demonstrated that even a slight alteration, such as introducing a Coulomb stress change of merely 1 bar to a nearby critically stressed fault, has the potential to trigger a significant earthquake or subsequent aftershocks (King et al., 1994). For remote triggering to occur, both static stress changes and dynamic stress/ strain changes are essential, particularly when they exceed the thresholds of 500 kPa in stress or 10^-6 in strain, as emphasized by Miyazawa (2011). According to Prejean et al. (2004), the Denali fault earthquake of Mw 7.9 in 2002 provided sufficient proof that earthquakes could be dynamically triggered up to 3660 km away in western North America. Dynamic stress is more effective for triggering than static stress the greater the distance (Miyazawa, 2011). Only post-seismic relaxations of stresses are likely to cause aftershocks to extend beyond 2–3 rupture lengths (Reddy et al., 2013).

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According to observations made by Helmstetter and Sornette (2003), modified Omori law and Gutenberg-Richter law are among the well-constrained equations that the aftershock sequences tend to follow and have predictable patterns. However, it is important to keep in mind that each event has a stochastic nature. The parameters within the equations associated with the mentioned principles facilitate the computation of the probability of aftershocks concerning their magnitude, position, and occurrence time. In this context, we analyzed the aftershocks of a modified rendition of Omori’s law, revealing a departure from the norm through heightened postseismic activity. According to the seismotectonic map of the study area, the aftershock distribution is primarily within the Indian plate and is most dangerously distant from plate boundaries. Furthermore, the two most recent seismic events within the Indian Ocean (measuring Mw 8.6 and 8.2) exhibit strike-slip characteristics, unlike the preceding earthquakes in Sumatra on December 26, 2004, and Nias on March 28, 2005, which displayed thrust fault mechanisms. This discrepancy suggests the potential for the Indian Ocean earthquakes to be intraplate. The distribution of aftershocks indicates that the earthquake in the Indian Ocean might potentially indicate the adjustment of the Earth’s crust within the Indian plate in response to the 2004 Sumatra and 2005 Nias seismic events. The seismic activities in the Indian Ocean are likely connected to the driving forces exerted by the Australian and Sunda plates on the Indian plate. This linkage is rooted in the influence of plate-driving forces on regulating the local stress conditions encountered by a specific tectonic plate.

7.5

Conclusion

Based on the Coulomb stress change pattern, aftershocks took place within the ruptured area where the Coulomb stress rose by 4–5 bars. Additionally, a separate group of aftershocks emerged in a location distant from the ruptured area, where the Coulomb stress decreased by 1 bar. The main cause of the aftershocks that took place in the region of reduced stress appears to be a remotely triggered mechanism brought on by changes in static and/or dynamic stress after the main shock. Therefore, the stress change (calculated following the Coulomb failure criteria) brought on by the mainshock (Mw 8.6) is likely what caused the Sumatra aftershock (Mw 8.2) to occur. For a clearer understanding of the aftershock occurrence, it is imperative to consider factors such as the regional stress field, viscoelastic relaxation, and rheological properties. The interaction between transient stress over space and time, along with modifications in Coulomb stress, holds the capacity to facilitate the occurrence of subsequent earthquakes and amplify seismic hazards within the area.

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References Aki, K., & Richards, P. G. (1980). Quantitative seismology, theory and methods. W.H. Freeman. Andrade, V., & Rajendran, K. (2011). Intraplate response to the Great (2004) Sumatra–Andaman earthquake: A study from the Andaman segment. Bulletin of the Seismological Society of America, 101(2), 506–514. Bock, Y., McCaffrey, R., Rais, J., Puntodewo, S. S. O., & Murata, I. (1990). Geodetic studies of oblique plate convergence in Sumatra. EOS Transactions American Geophysical Union, 71(857), I990. Bock, Y. E. H. U. D. A., Prawirodirdjo, L., Genrich, J. F., Stevens, C. W., McCaffrey, R., Subarya, C., Puntodewo, S. S. O., & Calais, E. (2003). Crustal motion in Indonesia from global positioning system measurements. Journal of Geophysical Research: Solid Earth, 108(B8), 2367. Byerlee, J. (1978). Friction of rocks. In Rock friction and earthquake prediction (pp. 615–626). Cattin, R., Chamot-Rooke, N., Pubellier, M., Rabaute, A., Delescluse, M., Vigny, C., Fleitout, L., & Dubernet, P. (2009). Stress change and effective friction coefficient along the SumatraAndaman-Sagaing fault system after the 26 December 2004 (Mw= 9.2) and the 28 March 2005 (Mw= 8.7) earthquakes. Geochemistry, Geophysics, Geosystems, 10(3), 1–21. Chinnery, M. A. (1963). The stress changes that accompany strike-slip faulting. Bulletin of the Seismological Society of America, 53(5), 921–932. Curray, J. R. (2005). Tectonics and history of the Andaman Sea region. Journal of Asian Earth Sciences, 25(1), 187–232. Curray, J. R., Moore, D. G., Lawver, L. A., Emmel, F. J., Raitt, R. W., Henry, M., & Kieckhefer, R. (1979). Tectonics of the Andaman Sea and Burma: Convergent margins. Das, S., & Scholz, C. H. (1981). Off-fault aftershock clusters caused by shear stress increase? Bulletin of the Seismological Society of America, 71(5), 1669–1675. DeDontney, N., Rice, J. R., & Dmowska, R. (2012). Finite element modeling of branched ruptures including off-fault plasticity. Bulletin of the Seismological Society of America, 102(2), 541–562. Delescluse, M., Chamot-Rooke, N., Cattin, R., Fleitout, L., Trubienko, O., & Vigny, C. (2012). April 2012 intra-oceanic seismicity off Sumatra boosted by the Banda-Aceh megathrust. Nature, 490(7419), 240–244. Hamilton, W. B. (1979). Tectonics of the Indonesian region (Vol. 1078). US Government Printing Office. Helmstetter, A., & Sornette, D. (2003). Båth’s law derived from the Gutenberg-Richter law and from aftershock properties. Geophysical Research Letters, 30(20). Igarashi, T., Matsuzawa, T., & Hasegawa, A. (2003). Repeating earthquakes and interplate aseismic slip in the northeastern Japan subduction zone. Journal of Geophysical Research: Solid Earth, 108(B5). Kagan, Y. Y., & Jackson, D. D. (1999). Worldwide doublets of large shallow earthquakes. Bulletin of the Seismological Society of America, 89(5), 1147–1155. King, G. C., Stein, R. S., & Lin, J. (1994). Static stress changes and the triggering of earthquakes. Bulletin of the Seismological Society of America, 84(3), 935–953. Liu, J., Sieh, K., & Hauksson, E. (2003). A structural interpretation of the aftershock “cloud” of the 1992 M w 7.3 landers earthquake. Bulletin of the Seismological Society of America, 93(3), 1333–1344. Matsuzawa, T., Takeo, M., Ide, S., Iio, Y., Ito, H., Imanishi, K., & Horiuchi, S. (2004). S-wave energy estimation of small-earthquakes in the western Nagano region, Japan. Geophysical Research Letters, 31(3). Maurya, S. P. (2019). Estimating elastic impedance from seismic inversion method. Current Science, 116(4), 628–635. Maurya, S. P., & Singh, N. P. (2018). Application of LP and ML sparse spike inversion with probabilistic neural network to classify reservoir facies distribution-a case study from the Blackfoot field, Canada. Journal of Applied Geophysics, 159, 511–521.

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Maurya, S. P., & Singh, K. H. (2019a). Predicting porosity by multivariate regression and probabilistic neural network using model-based and coloured inversion as external attributes: A quantitative comparison. Journal of the Geological Society of India, 93(2), 207–212. Maurya, S. P., & Singh, N. P. (2019b). Characterising sand channel from seismic data using linear programming (l1-norm) sparse spike inversion technique: A case study from offshore, Canada. Exploration Geophysics, 50(4), 449–460. McCloskey, J., Nalbant, S. S., & Steacy, S. (2005). Earthquake risk from co-seismic stress. Nature, 434(7031), 291–291. Miyazawa, M. (2011). Propagation of an earthquake triggering front from the 2011 Tohoku-Oki earthquake. Geophysical Research Letters, 38(23). Prawirodirdjo, L., Bocl, Y., McCaffrey, R., Genrich, J., Calais, E., Stevens, C., Puntodewo, S. S. O., Subarya, C., Rais, J., Zwick, P., & Fauzi, R. M. (1997). Geodetic observations of interseismic strain segmentation at the Sumatra subduction zone. Geophysical Research Letters, 24(21), 2601–2604. Prejean, S. G., Hill, D. P., Brodsky, E. E., Hough, S. E., Johnston, M. J. S., Malone, S. D., Oppenheimer, D. H., Pitt, A. M., & Richards-Dinger, K. B. (2004). Remotely triggered seismicity on the United States west coast following the M w 7.9 Denali fault earthquake. Bulletin of the Seismological Society of America, 94(6B), S348–S359. Qiu, Q., Feng, L., Hermawan, I., & Hill, E. M. (2019). Coseismic and postseismic slip of the 2005 Mw 8.6 Nias-Simeulue earthquake: Spatial overlap and localized viscoelastic flow. Journal of Geophysical Research: Solid Earth, 124(7), 7445–7460. Reddy, C. D., Sunil, P. S., Bürgmann, R., Chandrasekhar, D. V., & Kato, T. (2013). Postseismic relaxation due to Bhuj earthquake on January 26, 2001: Possible mechanisms and processes. Natural Hazards, 65, 1119–1134. Savage, J. C. (1987). Effect of crustal layering upon dislocation modeling. Journal of Geophysical Research: Solid Earth, 92(B10), 10595–10600. Srivastava, H. N., Bansal, B. K., & Verma, M. (2013). Largest earthquake in Himalaya: An appraisal. Journal of the Geological Society of India, 82, 15–22. Stein, R. S., & Lisowski, M. (1983). The 1979 Homestead Valley earthquake sequence, California: Control of aftershocks and postseismic deformation. Journal of Geophysical Research: Solid Earth, 88(B8), 6477–6490. Stein, R. S., Dieterich, J. H., & Barka, A. A. (1996). Role of stress triggering in earthquake migration on the north Anatolian fault. Physics and Chemistry of the Earth, 21(4), 225–230. Subarya, C., Chlieh, M., Prawirodirdjo, L., Avouac, J. P., Bock, Y., Sieh, K., Meltzner, A. J., Natawidjaja, D. H., & McCaffrey, R. (2006). Plate-boundary deformation associated with the great Sumatra–Andaman earthquake. Nature, 440(7080), 46–51. Tiwari, A. K., Maurya, S. P., and Singh, N. P. (2018). TEM response of a large loop source over the multilayer earth models. International Journal of Geophysics. Wells, D. L., & Coppersmith, K. J. (1994). New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement. Bulletin of the Seismological Society of America, 84(4), 974–1002. Wiseman, K., & Bürgmann, R. (2012). Stress triggering of the great Indian Ocean strike-slip earthquakes in a diffuse plate boundary zone. Geophysical Research Letters, 39(22).

Chapter 8

Earthquake Source Dynamics and High-Frequency Decal Characteristics of Japanese Arc Region Ankit Singh, Rohtash Kumar, and Amritansh Rai

8.1

Introduction

Assessing the size or magnitude of an earthquake presents a two-fold challenge: The first aspect involves understanding the processes occurring in the immediate vicinity of the seismic source, while the second relates to how seismic waves are altered during their propagation from the source to the observation location. While gaining insights into the underlying physics of the seismic source necessitates observations made at distances far from the epicenter, the variation in the substance that the waves travel through introduces variability into the earthquake wave pattern, albeit with a certain level of predictability. The determination of earthquake magnitudes using P-waves and S-waves indicates an approximation pertaining to the mean energy output of radiation for these the corresponding seismic body waves occurring at the given frequencies chosen for magnitude calculation (Duda, 1978; Joyner & Boore, 1982; Maurya & Singh, 2019; Kushwaha et al., 2019; Maurya et al., 2019a, b). The earthquake source parameters can be broadly categorized into two main groups (Duda, 1978). The first class is called kinematic parameters, such as fault length, fault width, area of fault plane, direction of faulting, and earthquake volume. The second class is called dynamic parameters, such as earthquake energy, seismic energy, seismic efficiency, duration of faulting, rise time, rupture velocity, earthquake magnitudes, stress drop, effective mass, seismic moment, coherence length, and coherence time. Within earthquake source models, the acceleration spectrum exhibits a rise as frequency increases, leveling off beyond the corner frequency. Hanks (1982) noted the presence of an additional frequency known as the upper limit frequency fmax, beyond which the amplitudes of acceleration spectral components decline suddenly A. Singh (✉) · R. Kumar · A. Rai Banaras Hindu University, Varanasi, Uttar Pradesh, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 R. Kumar et al. (eds.), Recent Developments in Earthquake Seismology, https://doi.org/10.1007/978-3-031-47538-2_8

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and unexpectedly. A sharp reduction in amplitudes occurs at the cut-off frequency fmax, prompting a debate about its origin. Yokoi and Irikura (1991) and Kumar et al. (2013, 2014) attribute this occurrence to the characteristics of the seismic source itself. On the other hand, Tsai and Chen (2000) developed a predictive model incorporating variables like earthquake magnitude, site properties, and distance. Their model highlights the high-cut phenomenon is influenced by both site conditions and the characteristics of the source. Their findings additionally indicate that separation plays a comparatively minor role as a governing factor in the high-cut processes. A comparative study on fc and fmax by Kumar found that both have the same behavior to seismic moment and hence they are dependent on the earthquake source. Conversely, these factors are observed to be unrelated to both the distance from the epicenter and the characteristics of the recording sites.

8.2

Methodology

After the temporal records have been adjusted in orientation to isolate the ground motion of the SH component, adjustments are made to the spectrum to account for instrument response and the attenuation caused by propagation effects following the procedure mentioned by Kumar et al., 2012. The acceleration time histories of SH component of the seismogram and its displacement spectrum obtained after taking fast Fourier transform are depicted in Figs. 8.1 and 8.2, respectively. This research integrates Brune’s model, which incorporates decay beyond the corner frequency, along with the incorporation of a factor for reducing high-frequency components. The observed acceleration spectrum is proposed by Boore (1983) effectively aligned using a Butterworth high-cut filter, which proves its efficiency for frequencies exceeding fmax. AðR, f Þ =

ð2πf Þ2 Ω0 1 þ ðf =f c Þ2 1 þ ðf =f max ÞN

1=2

Fig. 8.1 Acceleration time history of the SH component of the seismogram

ð8:1Þ

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Fig. 8.2 Displacement spectrum of the seismogram

DðR, f Þ =

Ω0 1 þ ðf =f c Þ

2

1 þ ðf =f max ÞN

1=2

ð8:2Þ

To carry out the specified source model analysis and compute the spectral parameters, the software tool EQK SRC PARA was utilized (Kumar et al., 2012). This process involved determining the low-frequency displacement spectral level (Ω0), high-cut frequency ( fmax), and corner frequency ( fc). The source radius (r), stress drop (ΔΩ), and seismic moment (M0) of earthquakes were estimated using the mean values of spectral characteristics obtained from various locations. In accordance with Keilis-Borok (1960), M0 is derived from the Ω0 value using the following calculation: M0 =

4πρβ3 RΩ0 Rθφ Sa

ð8:3Þ

In this context, ρ stands for the average density (specifically 2670 kg/m3), β represents the s-wave velocity within the source region (measuring 3200 m/s), R indicates the distance from the earthquake’s point of origin, R (θ, φ) denotes the

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average radiation pattern (with a value of 0.63), and Sa represents the amplification at the free surface (with a magnitude of 2). Hanks and Kanamori (1979) determined the moment magnitude using the approach outlined as: Mw =

2 log M 0 - 10:73 3

ð8:4Þ

According to Brune (1970, 1971), the estimation of source radius and stress drop involves the following procedure: source radius, r =

2:34β 2πf c

ð8:5Þ

stress drop, ΔΩ =

7M 0 16r 3

ð8:6Þ

In this ongoing study, the research centered on source characteristics such as source size, stress drop, and seismic moment, in addition to another quantifiable spectral parameter, referred to as fc and fmax. The relationship between these parameters and their connection with the source was explored using a dataset comprising 10 instances. A total of 10 local earthquakes, each with a magnitude of 3.8 or higher, were examined. These earthquakes were recorded by the Strong Motion Seismograph Networks (kik) in Japan [https://www.kyoshin.bosai.go.jp/ ]. The objective of this examination was to deduce the attributes of the frequent reduction in intensity observed in the earthquake spectrum, as well as to establish source parameters for earthquakes transpiring in this particular area.

8.3

Geology and Geo-Tectonics

The Japanese arc has a long geologic history compared to other western Pacific arcs. Ophiolites, along with their connected deep-water sedimentary formations, believed to originate from the fragmentation of the Proterozoic supercontinent, represent the earliest geological formations, with their origins tracing back to the Cambrian and Ordovician epochs. The majority of the underlying rocks consist of accretionary prisms formed during the Jurassic to Paleogene periods, predating the emergence in the middle Miocene epoch of the Sea of Japan (Taira 1989). Arc magmatism has been the dominant geological process starting from the middle Miocene (Sato, 1994, Yamaji & Yoshida, 1998). The current tectonic framework was completely established, and the present-day landscape took shape during the Quaternary period. Following the late Miocene epoch, two distinct fold-thrust belts emerged along the Japan Sea boundary: In the SW region of Japan, the Sanin fold-thrust belt (Nakamura, 1983) and the fold-thrust belt adjacent to the northern margin of the Japan Sea (Itoh & Nagasaki, 1996) are notable features. A study conducted by

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Fig. 8.3 The topographic map of Japan showing the major fault lines, plate boundaries and coastlines

Tokuyama et al. (1992) disclosed that in the northern part of Japan, the fold-thrust belt located along the Japan Sea margin, the formation of thrusts involving oceanic basement contributes to the emplacement of ophiolite structures. The primary constituents of the underlying rock formations are accretionary prisms, which may be found on the basement geology map from the Jurassic to the Paleogene (Maruyama et al., 1997). The topographic map and major boundaries, including faults, are depicted in Fig. 8.3, and the gradual enlargement of the crust from the Asian landmass toward the ocean is widely acknowledged. The positioning of granitic rocks, such as granodiorites, occurred subsequent to the formation of the Earth’s crust. The Japanese arc system within the central part of the crust’s thickness ranges from around 30 to 40 km, with variations in thickness influenced by specific tectonic conditions (Ogawa et al., 1994). In the Hidaka Mountains of Hokkaido, the crust’s

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thickness measures roughly 30–50 km, likely representing the greatest thickness among the crusts in Hokkaido. As per Arita et al. (1998), collision tectonics lead to crustal delamination in the southern Hidaka region. The thickness of the crust in NE Honshu measures around 30–35 km, while in SW Japan, it ranges from approximately 35–40 km. The top level of the crust is where intra-arc seismicity is focused. Seismicity decreases below 10–20 km in NE Honshu and below 12–25 km in SW Honshu (Okubo & Matsunaga, 1994; Ito et al., 1999). The elevated heat flow observed in NE Honshu, leading to a more limited brittle-ductile transition zone, might account for the contrast difference in the depth of seismic activities within the crust between the two arcs. A significant portion of its initial history relies on speculative assumptions. The following progression of the arc’s development became closely intertwined with the formation of the Pacific (Panthalassa) ocean basin and the eventual closure of the Tethys Seaway (Fig. 8.3). At the confluence of the Tethys Seaway and the Pacific Ocean due to the accretion of eastern Asia, the Japanese arc system originated (Taira, 2001). There were no major continent–continent collisions during the arc’s growth. Instead, the primary mechanisms of basement rock development were subduction and accretion of diverse oceanic elements, as well as episodic emplacement of metamorphic bands. The tectonic evolution of the arc has entered a new phase, characterized by the development of a back-arc basin and the subsequent initiation of early back-arc subduction starting from the Neogene epoch, If the process of back-arc subduction persists, the Japanese arc will transform into a configuration characterized by dual subduction. If the Japanese arc collides with Asia, it is probable that a geological structure resembling the Taiwan-type orogenic wedge would arise, followed by the establishment of a substantial fold-thrust belt in the back-arc, similar to the Cordilleran orogenic belt observed in the Americas.

8.4

Results and Discussion

A collection of graphs has been created to investigate the characteristics of computed source parameters and the relationships that exist between these parameters. The subsequent discussion delves into the interpretation of these graphical representations: Corner frequency should typically decrease as source size increases since it is negatively correlated with source size for earthquakes. Figure 8.4 illustrates the changes in corner frequency ( fc) in relation to seismic moment (M0). For the M0 smaller than 5*1019 dyne-cm the scatter appears. The decrease in corner frequency with an increase in the seismic moment for earthquakes strongly validates the inverse correlation between the size of the earthquake source and the corner frequency. The plot also supports the work by Kumar et al. (2012) that the dependence of fc on M0 decreases with the decrease in M0 (or smaller earthquakes).

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Fig. 8.4 Variation of M0 with fc for EW, NS and UD channels of seismometers. Left side of the panel represents data from surface seismometers. Right side of panel represents data from well seismometers

Fig. 8.5 Variation of fmax with Mw for EW, NS and UD channels of seismometers. Left side of the panel represents data from surface seismometers. Right side of panel represents data from well seismometers

The question of whether the fmax seen in an earthquake’s acceleration spectrum is due to attenuation caused by subsurface geological features below the recording site or reflects the source characteristics is one that is still being actively debated. The plot of fmax with Mw shows the decrease in fmax with an increasing value of Mw (Fig. 8.5). Although there is some dispersion in the dataset, it appears from the figure that the declining trend for fmax with rising seismic moment magnitude is nearly identical to that for fc with seismic moment. Thus, it can be inferred that fmax exhibits a comparable reliance on seismic source size, just like fc. Overall, the trend is linear for the plot. This supports well the fact that the fmax is linearly dependent on the magnitude of the earthquake and varies inversely with it. This observation has shown that the source process is responsible for both fc. and fmax. Tsai and Chen (2000) have documented analogous findings. They developed a regression model that was adjusted based on the earthquake’s location, distance, and magnitude. They discovered that both the source effects and the site effects regulate the high-cut process ( fmax). They concluded that the least important factor in determining the fmax is distance as well. Purvance and Anderson (2003) investigated the high-cut decline, characterized by the j factor, across earthquakes spanning magnitudes from 3.0 to 8.0. As outlined in the study, the impact of propagation path factors on the decline in high-frequency components is minimal, as this phenomenon is primarily determined by the properties of the seismic source (depicted in Figs. 8.6 and 8.7).

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Fig. 8.6 The plot of fmax against epicentre for the surface data

Fig. 8.7 The plot of fmax against epicentre for the well data

Kappa is a one-parameter estimator of a seismogram’s spectral amplitude decline with frequency. High values (>40 ms) show that high-frequency energy has been eliminated, whilst low values (5 ms) show very little attenuation of high-frequency energy. When employed in seismic designs, kappa is frequently taken as a site word (Kilb et al., 2012). The estimated value of kappa for the Japan region from surface stations lies between 0.02 and 0.06 and from well stations lies between 0.019 and 0.035 sec (Table 8.1).

Station name CHIBA

EDOSAKI

HITACHINAKA

KASUMIGAURA

NARITA

NISHIGO

SHIMOSA

SOSA

UJIIE

YAITA

1

2

3

4

5

6

7

8

9

10

EW = 0.0360 NS = 0.0443 UD = 0.0215 EW = 0.0479 NS = 0.0560 UD = 0.0431 EW = 0.0338 NS = 0.0364 UD = 0.0293 EW = 0.0311 NS = 0.0289 UD = 0.0246

EW = 0.0194 NS = 0.0202 UD = 0.0201 EW = 0.0378 NS = 0.0356 UD = 0.0315 EW = 0.0327 NS = 0.0321 UD = 0.0201 EW = 0.0282 NS = 0.0255 UD = 0.0273

Average value of kappa at different station of japan having constant magnitude 4 Average value of kappa Average value of kappa SURFACE WELL EW = 0.04725NS = 0.0310 EW = 0.0380 NS = 0.0395 UD = 0.0461 UD = 0.0381 EW = 0.0483 NS = 0.0421 EW = 0.0231 NS = 0.0203 UD = 0.0291 UD = 0.0182 EW = 0.0255 EW = 0.0176 NS = 0.0217 UD = 0.0435 NS = 0.0146 UD = 0.0126 EW = 0.0388 NS = 0.0442 EW = 0.0271 NS = 0.0210 UD = 0.0350 UD = 0.0230 EW = 0.0400 EW = 0.0173 NS = 0.0280 UD = 0.0200 NS = 0.0185 UD = 0.0176 EW = 0.0669 NS = 0.0632 EW = 0.0210 NS = 0.0218 UD = 0.0425 UD = 0.0231

Table 8.1 Obtained kappa value for all stations of surface as well as for wells Average value of kappa at different station of japan having constant magnitude 3.8 Average value of kappa Average value of kappa SURFACE WELL EW = 0.0581 EW = 0.0576 NS = 0.0554 UD = 0.0417 NS = 0.0567 UD = 0.0400 EW = 0.0393 NS = 0.0398 EW = 0.0199 NS = 0.0203 UD = 0.0299 UD = 0.0200 EW = 0.0526 NS = 0.0569 EW = 0.0213 NS = 0.0216 UD = 0.0607 UD = 0.0206 EW = 0.0369 EW = 0.0263 NS = 0.0394 UD = 0.0309 NS = 0.0291 UD = 0.0272 EW = 0.0476 NS = 0.0451 EW = 0.0235 NS = 0.0280 UD = 0.0328 UD = 0.0243 EW = 0.0546 EW = 0.0277 NS = 0.0527 UD = 0.0377 NS = 0.0333 UD = 0.027 EW = 0.0409 NS = 0.0502 EW = 0.0272 NS = 0.0234 UD = 0.0263 UD = 0.0234 EW = 0.0548 EW = 0.0404 NS = 0.0500 UD = 0.0332 NS = 0.0366 UD = 0.0336 EW = 0.0428 NS = 0.0414 EW = 0.0365 NS = 0.0364 UD = 0.0311 UD = 0.0268 EW = 0.0328 EW = 0.0418 NS = 0.0324 UD = 0.0342 NS = 0.0376 UD = 0.0387

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Using sensors positioned in a borehole reaching a depth of 1800 meters along the Nojima fault in central Japan, Hiramatsu et al. (2002) examined the scaling rule between microearthquake corner frequency and seismic moment (-1.3ML1.3). Data were collected for this study using two distinct sampling rates: 100 Hz and 10 kHz. The source parameters deduced from the higher sampling rate data showcased a correlation of M0 fc - 3, thereby validating a constant stress drop pattern. Conversely, estimations obtained from the lower sampling rate data displayed a relationship of M0 fc - 4. These results underscore the assertion that the absence of high-frequency elements in the 100 Hz sampled data resulted in inaccurate determinations of fc and M0 values.

8.5

Conclusion

The estimated value of kappa for the Japan region from surface stations lies between 0.02-0.06 and from well stations lies between 0.019 and 0.035. It is in good accordance with the values that have been found in areas with similar rock formations as in Japan. The value of kappa varies from 0.02 to 0.06 for the same magnitude of an earthquake this shows that kappa is not source dependent. Total 10 sites, each site having 20 data of surface and well of magnitude equal to 3.8 or greater than 3.8 from Japan (Kik), have been estimated and interpreted. As indicated in Table 8.1, it is evident that the maximum frequency is contingent upon the earthquake’s magnitude. With an increase in magnitude, the maximum frequency shows a decrease. This result is in good accordance with the other studies of the dependence of magnitude and maximum frequency. In our study, the relation between M0 and fc is estimated, and the result varies from M0 α f -3.05 to M0 α f -2.732. For the same magnitude of event at all epicenter, fmax has more or less the same values. So, we can conclude that fmax is linearly dependent on epicentral distances. The fmax estimated from these local earthquakes agrees with Aki’s global observations (1988). By examining the relative connection between fc and fmax, the study investigated how fmax correlates with source characteristics, depth of occurrence, epicentral distance, and site. The patterns and trends are evident in the diagrams, illustrating the associations between fmax and fc with fmax and M0 were consistent.

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References Aki, K. (1967). Scaling law of seismic spectrum. Journal of Geophysical Research, 72(4), 1217–1231. Arita, K., Ikawa, T., Ito, T., Yamamoto, A., Saito, M., Nishida, Y., Satoh, H., Kimura, G., Watanabe, T., Ikawa, T., & Kuroda, T. (1998). Crustal structure and tectonics of the Hidaka Collision Zone, Hokkaido (Japan), revealed by vibroseis seismic reflection and gravity surveys. Tectonophysics, 290(3–4), 197–210. Boore, D. M. (1983). Stochastic simulation of high-frequency ground motions based on seismological models of the radiated spectra. Bulletin of the Seismological Society of America, 73(6A), 1865–1894. Brune, J. N. (1970). Tectonic stress and the spectra of seismic shear waves from earthquakes. Journal of Geophysical Research, 75(26), 4997–5009. Brune, J. N. (1971). Seismic sources, fault plane studies and tectonics. Eos, Transactions American Geophysical Union, 52(5), IUGG–178. Duda, J. S. (1978). Physical significance of the earthquake magnitude- the present state of interpretation of the concept. Tectonophysics, 119–130. Elsevier Scientific Publishing Company. Hanks, T. C., & Kanamori, H. (1979). A moment magnitude scale. Journal of Geophysical Research: Solid Earth, 84(B5), 2348–2350. Hanks, T. C. (1982). fmax. Bulletin of the Seismological Society of America, 72, 1867–1879. Hiramatsu, Y., Yamanaka, H., Tadokoro, K., Nishigami, K. Y., & Ohmi, S. (2002). Scaling law between corner frequency and seismic moment of microearthquakes: Is the breakdown of the cube law a nature of earthquakes? Geophysical Research Letters, 29(8), 52–51. Ito, M., Nishikawa, T., & Sugimoto, H. (1999). Tectonic control of high-frequency depositional sequences with durations shorter than Milankovitch cyclicity: An example from the Pleistocene Paleo-Tokyo Bay, Japan. Geology, 27(8), 763–766. Itoh, Y., & Nagasaki, Y. (1996). Crustal shortening of Southwest Japan in the late Miocene. Island Arc, 5(3), 337–353. Joyner, W. B., & Boore, D. M. (1982). Estimation of response-spectral values as functions of magnitude, distance, and site conditions. US Geological Survey. Keilis-Borok, V. I. (1960). Investigation of the mechanism of earthquakes. Soviet Research in Geophysics (English Transl.), 4, 29. Kilb, D., Biasi, G., Anderson, J., Brune, J., Peng, Z., & Vernon, F. L. (2012). A comparison of spectral parameter kappa from small and moderate earthquakes using southern California ANZA seismic network data. Bulletin of the Seismological Society of America, 102(1), 284–300. Kumar, A., Kumar, A., Gupta, S. C., Mittal, H., & Kumar, R. (2013). Source parameters and fmax in Kameng region of Arunachal lesser Himalaya. Journal of Asian Earth Sciences, 70, 35–44. Kumar, A., Kumar, A., Mittal, H., Kumar, A., & Bhardwaj, R. (2012). Software to estimate earthquake spectral and source parameters. International Journal of Geosciences, 3(5), 1142–1149. Kumar, A., Mittal, H., Kumar, R., & Ghangas, V. (2014). High frequency cut-off of observed earthquake spectrum and source parameters of local earthquakes in Himachal Himalaya. International Journal of Science and Research, 3(7), 1642–1651. Kushwaha, P. K., Maurya, S. P., Singh, N. P., & Rai, P. (2019). Estimating subsurface petrophysical properties from raw and conditioned seismic reflection data: A comparative study. The Journal of Indian Geophysical Union, 23, 285–306. Maruyama, S., Isozaki, Y., Kimura, G., & Terabayashi, M. (1997). Paleogeographic maps of the Japanese Islands: Plate tectonic synthesis from 750 Ma to the present. Island Arc, 6(1), 121–142.

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Maurya, S. P., & Singh, N. P. (2019). Estimating reservoir zone from seismic reflection data using maximum-likelihood sparse spike inversion technique: A case study from the Blackfoot field (Alberta, Canada). Journal of Petroleum Exploration and Production Technology, 9, 1907–1918. Maurya, S. P., Singh, K. H., & Singh, N. P. (2019a). Qualitative and quantitative comparison of geostatistical techniques of porosity prediction from the seismic and logging data: A case study from the Blackfoot field, Alberta, Canada. Marine Geophysical Research, 40, 51–71. Maurya, S. P., Singh, N. P., & Singh, K. H. (2019b). Use of genetic algorithm in reservoir characterisation from seismic data: A case study. Journal of Earth System Science, 128, 1–15. Nakamura, K. (1983). Possible nascent trench along the eastern Japan Sea at the convergent boundary between Eurasian and North American Plates. Bulletin of Earthquake Research Institute, University of Tokyo, 58, 711–722. Ogawa, Y., Nishida, Y., & Makino, M. (1994). A collision boundary imaged by magnetotellurics, Hidaka Mountains, Central Hokkaido, Japan. Journal of Geophysical Research: Solid Earth, 99(B11), 22373–22388. Okubo, Y., & Matsunaga, T. (1994). Curie point depth in Northeast Japan and its correlation with regional thermal structure and seismicity. Journal of Geophysical Research: Solid Earth, 99(B11), 22363–22371. Purvance, M. D., & Anderson, J. G. (2003). A comprehensive study of the observed spectral decay in strong-motion accelerations recorded in Guerrero, Mexico. Bulletin of the Seismological Society of America, 93(2), 600–611. Sato, H. (1994). The relationship between late Cenozoic tectonic events and stress field and basin development in northeast Japan. Journal of Geophysical Research: Solid Earth, 99(B11), 22261–22274. Taira, A. (1989). Accretion tectonics and evolution of Japan. The Evolution of the Pacific Ocean Margin, 100–123. Taira, A. (2001). Tectonic evolution of the Japanese Island arc system. Annual Review of Earth and Planetary Sciences, 29(1), 109–134. Tokuyama, H., Kuramoto, S. I., Soh, W., Miyashita, S., Byrne, T., & Tanaka, T. (1992). Initiation of ophiolite emplacement: A modern example from Okushiri ridge, Northeast Japan arc. Marine Geology, 103(1–3), 323–334. Tsai, C.-C. P., & Chen, K. C. (2000). A model for the high-cut process of strong-motion accelerations in terms of distance, magnitude, and site condition: An example from the SMART 1 array, Lotung, Taiwan. Bulletin of the Seismological Society of America, 90(6), 1535–1542. Yamaji, A., & Yoshida, T. (1998). Multiple tectonic events in the Miocene Japan arc: The Heike microplate hypothesis: Journal of Mineralogy, Petrology, and Economic Geology, 93, 389–408. Yokoi, T., and Irikura, K. (1991). Meaning of source controlled fmax in empirical Green’s function technique based on a T2 -scaling law. Annuals of Disaster Prevention Research Institute, Kyoto University 34 B-1, pp. 177–189.

Chapter 9

Lapse-Time Dependence of Coda Quality Factor Within the Lithosphere of Northern Ecuador Amritansh Rai, Rohtash Kumar, Ankit Singh, Raghav Singh, Indrajit Das, and S. P. Maurya

9.1

Introduction

Seismic attenuation normally refers to the decrease in amplitude of seismic waves with increasing distance from the source, depending on the elastic and anelastic properties of the medium. Generally, intrinsic absorption (Qi-1), in which the seismic energy dissipates owing to the conversion of kinematic energy into heat, is used to explain attenuation caused by the anelastic characteristics of media (Knopoff, 1964). Anelastic characteristics are influenced by the thermoelastic effect, internal friction, grain boundaries, defects in the grain and sliding processes across fractures. The energy of seismic waves is redistributed by attenuation owing to scattering (Qsc-1), an elastic process, as a result of the incident wave’s reflection, refraction and conversion to other waves. Seismic waves scatter due to inhomogeneities non the medium of transmission, resulting in continuous wave trains known as coda waves that follow the direct P and S waves (Kushwaha et al., 2020, 2021; Maurya et al., 2020, b). One of the most used methods for estimation of seismic wave attenuation is based on the decay rate analysis of the coda wave envelope. The coda, which is the backscattered wave that originates from the many randomly distributed heterogeneities in the earth, is the tail of an earthquake that is observed at a close distance (Aki, 1969; Herraiz, 1987; Rautian & Khalturin, 1978; Maurya & Singh, 2020). Numerous studies have been conducted globally on the Q value of coda waves, also known

A. Rai · R. Kumar · A. Singh · R. Singh · S. P. Maurya (✉) Department of Geophysics, Banaras Hindu University, Varanasi, India e-mail: [email protected] I. Das Department of Computer Science and system Engineering, Universidad Católica del Norte, Antofagasta, Chile © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 R. Kumar et al. (eds.), Recent Developments in Earthquake Seismology, https://doi.org/10.1007/978-3-031-47538-2_9

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as Qc (Aki & Chouet, 1975). When compared to stable areas, seismically active zones are shown to have Low-Q values. The attenuation may be caused by the inherent effects of the medium’s anelastic behaviour or by the scattering phenomena linked to the inhomogeneities that are present. Consequently, the study found that Qc provides information on both intrinsic attenuation and scattering. Within an elastic medium, the seismic wave loses its mechanical energy for each wave that passes through the medium and is transformed into heat by a phenomenon that cannot be reversed. Different phenomena are to be blamed for this loss. Absorption or intrinsic attenuation covers all the phenomena that are responsible for the loss. Aki (1980) explains how amplitude is lost owing to the heterogeneities distributed in the medium through which seismic wave travels. Kikuchi (1981) investigated the effect of cavities and fissures on scattering. The greatest method to explain the dispersal is referring to the medium that is laterally homogenous in the sense that it allows the tracking of moving wavefronts. In such a medium, the propagation is described by geometrical approaches because whenever a seismic wave interacts with any heterogeneity, it gets refracted and reflected. The single backscattering model, as introduced by Aki and Chouet in 1975, is used to calculate coda-wave attenuation through local seismic event data. This model is built on the principle that scattering is a relatively weak process. By combining inherent attenuation and scattering effects, the overall wave attenuation can be determined by analyzing coda decay. While Tsujiura in 1978 and Aki in 1980 argued that scattering attenuation holds more significance compared to intrinsic attenuation, Frankel and Wennerberg in 1987 contradicted this notion, asserting that intrinsic attenuation plays a more prominent role in coda-wave attenuation. In this study, the single station analysis of coda wave quality factor was obtained for the first time in Ecuador following the single backscattering model.

9.2

Geology and Seismological History of Study Area

Ecuador is situated in the northwestern expanse of the South American tectonic plate. Its location lies to the eastern side of the demarcation established by the Colombia-Ecuador trench. This trench serves as the demarcation line for the convergence occurring between the Nazca plate and the South American plate. For visual reference, please consult Fig. 9.1. Within this tectonic context, Ecuador experiences the impact of three notable categories of earthquakes: first, subduction earthquakes; second, shallow upper-plate earthquakes; and to a lesser degree, earthquakes associated with volcanic activity. These volcano-related seismic events typically exert more localized effects on the region. The coastal regions experience shallower subduction earthquakes, while deeper events (reaching depths of up to 300 km) are distributed throughout the country. The study area where the station and most of the events used in this study are located is confined between the Ecuador-Colombia Trench and the Llanos Fault

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Fig. 9.1 Tectonic setup of the study area showing all the important fault systems along with station (blue triangle) and events (white circles) used in this study (NPDB: North Panama Deforming Belt; ECT: Ecuador-Colombia Trench; LFS: Llanos Fault System; RFS: Romeral Fault System; SMBF: Santa Marta-Bucaramanga Fault; BF: Boconó Fault)

System. Another fault system that is present in the vicinity is the Romeral fault system, running almost parallel to the Ecuador-Colombia trench. Shallow upper-plate earthquakes in Ecuador are concentrated primarily beneath the coastal plain and the Sub-Andean zone, with an additional occurrence under the Andean cordillera north of approximately 2.5° S latitude. The seismic activity in Ecuador is notably frequent and significant, with a considerable number of earthquakes measuring ≥5.0 in magnitude. Throughout the current century, Ecuador has

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encountered 16 earthquakes registering a magnitude of ≥7. Notably, the country witnessed a momentous event in 1906 – an 8.6 magnitude earthquake that stands as the fifth-largest recorded quake in global seismic history. This occurrence took place offshore. According to assessments by the United States Geological Survey, there exists a considerable likelihood of another major earthquake, similar to the 1906 incident, transpiring off the coast of Ecuador before the year 2000 (Nishenko, 1989). Over recent decades, these earthquakes have led to a substantial loss of life, with casualties totaling around 60,000, predominantly concentrated in Quito, situated within the Interandean valley. Of the 23 seismic events perceived in Quito with an intensity of VI or greater since 1541, seven events reached intensities of VII or higher in the years 1587, 1627, 1698, 1755, 1797, 1859 and 1868 (Yepes & Del Pino, 1990). In the same region, several notable earthquakes have taken place, including a magnitude 7.6 event on 19 January 1958 and a magnitude 7.7 event on 12 December 1979, as documented by Pararas Carayannis in 1980, drawing from the US Geological Survey [USGS] and the Global Earthquake Model catalogues (please refer to Data and Resources). Within the central segment of this area, additional megathrust earthquakes associated with subduction have occurred: a magnitude 7.1 earthquake on 3 May 1896, a magnitude 7.4 event on 1 June 1907, a magnitude 7.9 event on 14 May 1942, a magnitude 7.4 event on 16 January 1956 and a magnitude 7.1 event on 4 August 1998, as reported by Beck et al. in 1998 and Yepes et al. in 2016. Analyzing the relatively short seismic history over the past 120 years suggests an approximately 20-year recurrence period for events with magnitudes greater than 7.0 in the central sector. On another note, recent studies involving paleoseismic analysis at the Jaramijo site indicate evidence of a powerful subduction earthquake with a magnitude of around 8. This event occurred approximately 1170 ± 30 years ago and was accompanied by a tsunami with a run-up height ranging from 3 to 5 meters, according to research conducted by Chunga et al. in 2018.

9.3

Data Set Used for Analysis

The coda waves, S wave and P wave arrivals from 49 local earthquakes were used for analysis of Qc for the Ecuador area. The data set of 49 earthquakes was extracted during the period from January 2021 to June 2022 from one station OTAV of a small seismological network IU operated in Ecuador. The network was deployed for a short duration to determine the local seismicity.

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9.4

125

Method and Data Analysis for Estimation of Qc

A method for estimating Qc using the single backscattering model was introduced by Aki and Chouet in 1975. This model is based on the concept that coda waves at frequencies below approximately 1 Hz are formed from surface waves that undergo backscattering, while at frequencies exceeding about 10 Hz, they are formed from body waves that experience backscattering. This scattering occurs within an unconfined, uniform and isotropic medium due to the presence of scatterers randomly distributed across the surface in two dimensions. The model assumes that scattering is a relatively feeble phenomenon, causing emitted waves to experience only minor dispersion prior to reaching the receiver. Consequently, the medium is assumed to disallow alterations in velocity or the occurrence of multiple scattering. According to this model, for a narrow bandwidth signal centred at frequency f and at lapse time t, the coda-wave amplitude A ( f,t) is described as: Aðf , t Þ = Sðf Þt - α exp

- πft Qc

ð9:1Þ

where α represents the geometrical spreading factor (taken as 1 for body waves), S(f) denotes the source function at frequency f and is considered constant, and Qc represents the quality factor that represents the average attenuation characteristics of the medium. After rearranging the terms in Equation (9.1) and taking the natural log, the above expression can be shown as follows: InðAðf , t Þ, t Þ = InðSðf ÞÞ -

πft Qc

ð9:2Þ

The following linear form is used to rewrite the previous equation: InðAðf , t Þt Þ = C - bt

ð9:3Þ

Plotting the envelope of ln A ( f, t) +βlnt as a function of t at a given central frequency after band-pass filtering the signal gives a straight line with slope = -πfQ(f); and hence, Q (f) can be determined. For Coda-Q estimation, a MATLAB programme Coda-Q (Kumar et al., 2015) that combines the aforementioned analytic procedures with Eqs. (9.1) and (9.2) has been written. Before analysis, the raw data are filtered several times. First of all, choosing the start time of the coda window correctly aids in eradicating any S-wave contamination. Multiplying the S-wave travel time by two yields the start time for the coda duration (Rautian & Khalturin, 1978). To get reliable Qc estimations, the length of the coda window must now be carefully selected. There is no limitation on the length of the window itself, although Havskov and Ottemoller (2003, 2005) used a lapse time window limit of 20 seconds. Three different time windows – the 30 s, 40 s and 50 s – are utilised in the current study. Waveforms having a signal-to-noise

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ratio (SNR) of at least three are chosen for the investigation. SNR is calculated as the ratio of the noise window immediately prior to the signal to the last component window coda part. To get accurate values of Qc, another criterion is then applied to the filtered data. Only values that satisfy this new criterion have a logarithmic correlation coefficient between coda wave amplitude and lapse time (Eq. 9.3) larger than 0.7. A band-pass Butterworth filter is now used to filter the data from the previous step at several frequency bands, including 1–2 Hz, 2–4 HZ, 4–8 Hz, 8–12 Hz, 12–24 Hz, and 16–32 Hz. The resulting Qc values for each frequency band have been allocated to the central frequency of each corresponding frequency band. An event that occurred on 27 March 2022 was recorded at station OTAV and used for coda Q evaluation and is shown in Fig. 9.2. The illustrations of (a) P wave and S wave arrival time coupled with earthquake origin time, (b) and (c) band-pass filtered seismogram at different frequency bands, and ln (A( f,t),t) versus lapse time are shown in Figs. 9.3, 9.4, 9.5 and 9.6. Additionally, the Qc value at each central frequency and the correlation coefficient for each linear fitting are mentioned.

9.5

Results and Discussion

The coda waves part of the seismogram of 10, 20, 30, 40, 50 and 60 sec duration lapse time from 49 local earthquakes have been analysed at seven frequency bands employing the single back-scattering model. Results obtained on the estimation of Qc, based on the above analysis, are discussed. Table 9.1 shows the average of estimated Qc at OTAV station in the region using six lapse time windows at seven frequency bands. The average Qc value varies from 82.307, 92.377, 11.525, 20.564, 100.866 and 216.607 at 1.5 Hz to 551.808, 757.295, 794.390, 947.052, 1888.833 and 3474.825 at 24 Hz for lapse time windows of 10, 20,30, 40, 50 and 60 sec, respectively. The obtained values are in accordance with the global average of Qc values documented by various researchers (Ambeh & Lynch, 1993 in Dominica; Mak et al., 2004 in Hong Kong; Ma’hood and Hamzehloo, 2009 in Bam region, Iran and Barros et al., 2011 in Amazon craton, Brazil). The Qc value in general increases with increase in frequency as well as with lapse time window. A power law of the form Qc = Q0f n for the OTAV station and each lapse time window pair is obtained from the estimated Qc -values and are plotted as a function of frequency as shown in Fig. 9.7. The penetration depth of coda wave associated with each lapse time can be calculated using the method introduced by Pulli (1984). The values of Q0 increases with the lapse time in general, suggesting the decrease in heterogeneity in with depth except for the lapse time 30 sec and 40 secs curves (Fig. 9.7). The reason for sudden decrease in Q0 value at these two lapse times can be attributed to the presence of a heterogenous and highly dissipating media at this depth (roughly 50–60 km). This decrease in the Q0 value can also be a suggestive of relatively deep boundary between crust and mantle (Moho) and coincide with nearly the same depth

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Fig. 9.2 An example of the seismogram recorded at OTAV (a) marked P, S and coda arrivals. A time window of 10.24 sec is shown in green shades (b) and (c) Seismogram with coda windows filtered at central frequencies of 1 Hz–2 Hz and 4 Hz–8 Hz along with estimated Qc

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Fig. 9.3 Seismogram with coda windows filtered at central frequencies of 4 Hz–8 Hz

Fig. 9.4 Seismogram with coda windows filtered at central frequencies of 8 Hz–16 Hz

documented by Granja (2013). Also, the relatively low Q0 values (0.6) support the tectonic of the region as it is located near the Romeral fault system between the Ecuador-Colombia Trench and the Llanos Fault System. It has been observed by various researchers that the value of ‘n’ is higher in the seismically highly active region as compared to other regions (Hiramatsu et al., 2000; Hoshiba, 1993; Jin & Aki, 2005; Sato et al., 2012).

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Fig. 9.5 Seismogram with coda windows filtered at central frequencies of 12 Hz–24 Hz

Fig. 9.6 Seismogram with coda windows filtered at central frequencies of 16 Hz–32 Hz

9.6

Conclusion

Coda waves emerge as a result of the irregularities within the Earth’s medium, serving as indicators of the extent of medium heterogeneity. The rate of decay in coda amplitudes over time and the intensity of coda wave excitation are critical factors in comprehending the attributes of attenuation and the potency of scattering within the Earth’s subsurface.

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Table 9.1 Average quality factor at different lapse times and frequencies for OTAV station Frequency 1.5 3 6 9 12 18 24

Q10 82.307 160.404 186.271 225.208 283.984 427.736 551.808

Q20 92.377 247.584 371.517 492.650 473.521 596.664 757.295

Q 30 11.525 199.263 311.769 407.481 569.209 676.301 794.390

Q40 20.564 242.213 464.351 673.183 719.023 821.457 947.052

Q50 100.866 258.071 577.326 689.900 939.328 1429.644 1888.833

Q60 216.607 345.335 497.892 885.302 2324.865 3060.642 3474.825

Fig. 9.7 Plots of frequency-dependent Qc at lapse time of 10 s, 20 s, 30 s, 40 s, 50 s and 60 s

In this research, the study focuses on estimating Coda-Q values within the Ecuador region of South America. The coda waves of 49 local earthquakes recorded by one digital seismometer have been analysed using three lapse time windows (10 sec, 20 sec, 30 sec, 40 sec, 50 sec and 50 sec) at seven frequency bands with a central frequency varying from 1.5 Hz to 24.0 Hz. The variation in Qc, for the lapse time window of 10 secs is 82.307 to 216.607 at 1.5 Hz and 581.808 to 3474.825 at 24 Hz. Also, there is a variation in average Qc with frequency (Fig. 9.8). So, it is clear that Qc is a function of frequency and increases with frequency in Ecuador.

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Fig. 9.8 Plot showing variation in Qavg for all lapse times versus frequency

The Q0 (coda-q at 1 Hz) value increases with the lapse time window length while there is no correlation has been observed in the degree of frequency dependence (n) with increasing window length. The variation can be interpreted as that in the study region, the scattering effect decreases with depth, which may be due to the decrease in heterogeneities of the medium with increasing depth, and also, the depth of Moho at 55–60 kms can be interpreted by the decrease in Q0 value at time-lapse 20 secs and 30 secs. The high values for frequency exponent (n > 0.6) suggest that the study area is tectonically active. Acknowledgements The authors are grateful to Prof. H. R. Wason for providing the data. The authors are also thankful to Jaypee Ventures Pvt. Ltd., Noida for funding the project under which data are collected.

References Aki, K. (1969). Analysis of the seismic coda of local earthquakes as scattered waves. Journal of Geophysical Research, 74(2), 615–631. Aki, K. (1980). Attenuation of shear-waves in the lithosphere for frequencies from 0.05 to 25 Hz. Physics of the Earth and Planetary Interiors, 21(1), 50–60. Aki, K., & Chouet, B. (1975). Origin of coda waves: Source, attenuation, and scattering effects. Journal of Geophysical Research, 80(23), 3322–3342. Ambeh, W. B., & Lynch, L. L. (1993). Coda Q in the eastern Caribbean, West Indies. Geophysical Journal International, 112(3), 507–516. Havskov, J., & Ottemoller, L. (2003). SEISAN: The earthquake analysis Softwares for windows, Solaris and Linux, version 8.0. Institute of Solid Earth Physics, University of Bergen, .

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Havskov, J., & Ottemoller, L. (2005). SEISAN (version 8.1): The earthquake analysis software for windows, Solaris, Linux, and mac OSX version 8.0. pp 254. Hiramatsu, Y., Hayashi, N., Furumoto, M., & Katao, H. (2000). Temporal changes in coda Q1 and b value due to the static stress change associated with the 1995 Hyogo-ken Nanbu earthquake. Journal of Geophysical Research: Solid Earth, 105(B3), 6141–6151. Hoshiba, M. (1993). Separation of scattering attenuation and intrinsic absorption in Japan using the multiple lapse time window analysis of full seismogram envelope. Journal of Geophysical Research: Solid Earth, 98(B9), 15809–15824. Jin, A., & Aki, K. (2005). High-resolution maps of coda Q in Japan and their interpretation by the brittle-ductile interaction hypothesis. Earth, Planets and Space, 57, 403–409. Kikuchi, M. (1981). Dispersion and attenuation of elastic waves due to multiple scattering from cracks. Physics of the Earth and Planetary Interiors, 27(2), 100–105. Knopoff, L. (1964). Q. Reviews of Geophysics, 2, 625–660. Kumar, A., Kumar, R., Ghangas, V., & Sharma, B. (2015). MATLAB codes (CodaQ) for estimation of attenuation characteristics of coda waves. International Journal of Advanced Research, 3(9), 1078–1083. Kushwaha, P. K., Maurya, S. P., Rai, P., & Singh, N. P. (2021). Estimation of subsurface rock properties from seismic inversion and geo-statistical methods over F3-block, Netherland. Exploration Geophysics, 52(3), 258–272. Kushwaha, P. K., Maurya, S. P., Singh, N. P., & Rai, P. (2020). Use of maximum likelihood sparse spike inversion and probabilistic neural network for reservoir characterization: A study from F-3 block, The Netherlands. Journal of Petroleum Exploration and Production Technology, 10, 829–845. Ma’hood, M., & Hamzehloo, H. (2009). Estimation of coda wave attenuation in East Central Iran. Journal of Seismology, 13(1), 125–139. Mak, S., Chan, L. S., Chandler, A. M., & Koo, R. C. H. (2004). Coda Q estimates in the Hong Kong region. Journal of Asian Earth Sciences, 24(1), 127–136. Maurya, S. P., & Singh, N. P. (2020). Effect of Gaussian noise on seismic inversion methods. The Journal of Indian Geophysical Union, 24(1), 7–26. Maurya, S. P., Singh, N. P., & Singh, K. H. (2020a). Seismic inversion methods: A practical approach (Vol. 1). Springer. Maurya, S. P., Singh, N. P., & Tiwari, A. K. (2020b). Forward and inverse modeling of large loop TEM data over multi-layer earth models. Advances in modeling and interpretation in near surface geophysics (pp. 121–153). Springer, Cham. Nishenko, S. P. (1989). Hazards and predictions. In The encyclopedia of solid earth geophysics (pp. 260–268). Van Nostrand Reinhold. Pulli, J. J. (1984). Attenuation of coda waves in New England. Bulletin of the Seismological Society of America, 74(4), 1149–1166. Rautian, T. G., & Khalturin, V. I. (1978). The use of the coda for the determination of the earthquake source spectrum. Bulletin of the Seismological Society of America, 68, 923–948. Sato, H., Fehler, M. C., & Maeda, T. (2012). Seismic wave propagation and scattering in the heterogeneous earth. Springer Science & Business Media.

Chapter 10

Coda Q Estimates of the Bilaspur Region of Himachal Lesser Himalaya Vandana, S. C. Gupta, Ashwani Kumar, and Himanshu Mittal

10.1

Introduction

Seismic wave amplitudes diminish as they propagate from their sources due to factors such as wavefront expansion and energy absorption through interactions at heterogeneities, like rock interfaces with varying properties, as well as scattering by smaller-scale heterogeneities. Material characteristics influence energy absorption. Coda waves are seismic shear waves resulting from these heterogeneities, indicating the medium’s heterogeneous nature. The quality factor Q is a dimensionless parameter describing the efficiency of seismic energy transmission (Knopoff, 1964), combining seismic wave scattering and intrinsic attenuation. Understanding seismic wave attenuation is essential for earthquake source estimation, ground motion simulation, nuclear explosion monitoring (Mayeda et al., 2003; Mittal, 2011; Maurya et al., 2020, 2023; Sandhu et al., 2020; Kushwaha et al., 2021; Richa et al., 2022), seismic hazard assessment (Abercrombie, 1997; Kumar et al., 2013, 2014, 2015; Sharma et al., 2015; Vandana et al., 2016; Mittal et al., 2016; Mishra and Vandana, 2019), and inferring tectonic characteristics (Aki, 1980). Seismic wave attenuation can be studied using P wave (Qα), S wave (Qβ), Coda waves (Qc), and Lg waves (QLg) at local or regional distances. The coda wave results from backscattered body waves from crustal heterogeneities, observed as a decaying tail on a seismogram at short distances (Aki, 1969; Aki and Chouet, 1975; Rautian and Khalturin, 1978). Coda waves follow primary and secondary waves. The onset of coda wave is twice the S-wave travel time (Rautian and Khalturin, 1978). Various methods, like those by Aki and Chouet (1975), Rautian and Khalturin (1978), Del Pezzo et al. (1983), and Rovelli (1984), estimate Vandana (✉) · H. Mittal National Center for Seismology, Ministry of Earth Sciences, New Delhi, India S. C. Gupta · A. Kumar Department of Earthquake Engineering, Indian Institute of Technology, Roorkee, India © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 R. Kumar et al. (eds.), Recent Developments in Earthquake Seismology, https://doi.org/10.1007/978-3-031-47538-2_10

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Q from coda waves. A single backscattering model (Aki, 1969; Aki & Chouet, 1975; Sato, 1977; Gupta & Kumar, 2002) neglects scattering-induced energy loss. Alternatively, the multiple scattering model views energy diffusion (Kopnichev, 1977; Gao, 1983; Frankel & Wennerberg, 1987; Zeng et al. 1991; Gupta et al., 1995, 1998; Vandana et al., 2015; Mishra and Vandana, 2019). The Kol Dam is located in the Lesser Himachal Himalaya in Bilaspur, Himachal Pradesh. According to IS: 1893-(Part l) 2002, the area falls in seismic zone V. Tectonic structures of various sizes have been mapped nearby. This study applies Aki and Chouet’s single backscattering model (1975) to explore coda wave attenuation characteristics. The dataset comprises 94 local earthquakes from the Kol Dam area in the Himachal Lesser Himalaya. Researchers have investigated coda-Q frequency and lapse time relationship.

10.2

Geologic Characteristics and Seismic Tectonics of the Lesser Himalayan Region in Himachal

The Himalayas are understood to have formed due to the collision between the Indian and Eurasian plates, based on the theory of global tectonics (Le Fort, 1975; Seeber et al., 1981; Khattri, 1987). The Himalayas consist of four main tectonic and geographic divisions from south to north: the Outer Himalaya (Siwalik), Lesser Himalaya, Great Himalaya, and Tethyan Himalaya or Tibet Himalaya (Himadri). These divisions are further divided into the regions of Kashmir, Himachal, Kumaun, Nepal, Sikkim, Bhutan, and Arunachal from west to east. The Indus-Tsangpo Suture Zone defines the northern boundary of the Indian plate. The Trans-Himardi fault marks the separation between the Tethyan Himalaya and the Great Himalaya. The MBT separates the Lesser Himalaya from the Outer Himalaya (Siwaliks), while the MCT delineates the separation between the Lesser Himalaya and the Great Himalaya. The Himalaya Frontal Thrust divides the Outer Himalayas from the Indo-Gangetic Plains. The study area is situated in the Himachal Lesser Himalaya, forming the northern part of the Himalayan orogenic belt within this broad tectonic framework. This region is characterized by significant tectonic features such as the MCT, MBT, Drang Thrust, JawalaMukhi Thrust, and Brasar Thrust, as depicted in Fig. 10.1. The Drang Thrust and MBT are particularly relevant to the dam’s location. The MBT separates the Sub-Himalayan and Lesser Himalayan regions and serves as the northern boundary of the Siwalik belt. The Main Frontal Thrust (MFT) marks the southern limit of the Frontal Belt, with only a few locations displaying surface expressions of this thrust. Various subsidiary thrusts, including the JawalaMukhi Thrust and Drang Thrust, cross the belt between the MBT and MFT. Neotectonic activity has been observed in certain locations, including the MBT and western JawalaMukhi Thrust (e.g., Srikantia & Bhargava, 1998). According to the seismic zoning map of India (BIS: 1893–2002, Part I: General Provisions and Buildings), the region falls under seismic zone V, where several moderate to large earthquakes have

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Fig. 10.1 Map shows the tectonic features along with instrumental stations located in the study region

occurred in the past century. Notable events include the Kangra earthquake of April 4, 1905 (M = 8.0), the Chamba earthquake of 22 June 1945 (M = 6.5), the Kinnaur earthquake of January 19, 1975 (M = 6.2), the Dharamshala earthquake of April 26, 1986 (M = 5.5), and the Uttarkashi earthquake of October 20, 1991 (M = 6.7), all occurring in close proximity to the study area.

10.3

Methodology

The quality factor (Q) of the Bilaspur region is calculated in this study using a single backscattering model developed by Aki and Chouet (1975). This concept interprets the coda waves as backscattered body waves produced by randomly distributed heterogeneities in the upper mantle and crust of the earth. For a narrow bandwidth signal centered at frequency f and at lapse time t, the size of scatters regarded to be higher than the wavelength and with no velocity change A( f, t) is defined as:

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Aðf , t Þ = Sðf Þt - α exp

- πft Qc

ð10:1Þ

where S( f ) stands for source function at frequency f; α stands for geometrical spreading parameter, which is taken to be “0.5” and “1” for surface waves and body waves, respectively; and Qc is coda waves quality factor. Equation (10.1) is expressed as: InðAðf , t Þ, t Þ = InðSðf ÞÞ -

πft Qc

ð10:2Þ

The slope of a least-squares straight-line fit between ln(A( f,t)) versus time t yields an estimate of Qc value. The aforementioned relations are valid for lapse times more than twice the S-wave travel time, according to Rautian and Khalturin (1978). The power law describes the frequency-dependent relationship of coda-Q: Qc ð f Þ = Q 0 f n

ð10:3Þ

Where n denotes the degree of frequency dependence of Qc and Q0 is the value of Qc at 1 Hz. We may use straightforward linear regression to estimate n and Q0 using the logarithm of Eq. (10.3).

10.4

Dataset and Analysis

The Bilaspur area within the Himachal Lesser Himalaya accommodates a local seismological network featuring five recording stations: Bandla (BAND), Jamthal (JAMT), Neri (NERI), Nihri (NIHR), and Sikandra (SKND). Table 10.1 presents Table 10.1 Site characteristics and epicentral locations of the recording stations SI. no.

Station name

Station code

1 2 3 4 5

Bandla Jamthal Neri Nihri Sikandra

BAND JAMT NERI NIHR SKND

Location Lat(N) 31–19.98 31–23.94 31–12.66 31–23.70 31–33.30

Long(E) 76–46.20 76–51.89 77–00.08 77–01.38 76–48.84

Rock types

Elevation (m)

Mode of operation

Sandstone Quartzite Phyllites Quartzite Slates

1367 824 1071 2129 1537

Analog Analog Analog Analog Digital

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information about these stations, encompassing their names, codes, geographic coordinates, elevations, underlying rock composition at the seismometer locations, and operational techniques. The data concerning nearby earthquakes were collected using two distinct sensor types. The initial kind of equipment included MEQ-800 analog microearthquake recorders. On these analog recorders, the outputs from the L-4C and S-7000 short-period vertical component seismometers were captured. Recording was done on smoked paper. Digital clocks were integrated into the analog recorders to mark time on the records. The digital timekeepers were synchronized with Indian Standard Time (IST) to ensure precise timekeeping. The second instrument type is a digital seismograph comprising a broadband seismometer (KS-2000) manufactured by Teledyne Geotech, USA, and a 24-bit data collection system. A sampling rate of 100 samples per second was utilized for the digital data. Data samples were aligned with IST or UTC using GPS synchronization. The network recorded 94 earthquakes between May 2008 and April 2011, featuring focal depths ranging from 0.4 to 41.3 km, constituting the dataset for this study. Vertical components were utilized in the present investigation. With the aid of conversion tools integrated within the SEISAN software, data collected from all stations were transformed into Seisan format (Havskov & Ottemoller, 2003). The HYPOCENTER program was employed to estimate the hypocenter parameters for these events (Lienert et al., 1986; Lienert & Havskov, 1995). The estimated hypocenter parameters for these events possess standard errors ≤0.50 s for origin time (RMS), ≤ 5.0 km for epicenter (ERH), and ≤ 5.0 km for focal depth (ERZ). The determination of coda-Q was executed through a MATLAB program. Using Aki and Chouet’s single backscattering model developed in 1975, coda Q is estimated. The procedures follow SEISAN’s CODAQ subroutine guidelines (Havskov & Ottemoller, 2003). To ensure accurate Qc values, waveforms with signal-to-noise ratios (SNRs) greater than 5 are selected for analysis, with a requirement of a correlation coefficient exceeding 0.7. Origin time and coda arrival time are calculated based on P and S wave arrival times. Applying various frequency bands listed in Table 10.2, a Butterworth filter is employed to band-pass filter the seismogram. The study employs individual 30-second lapse time intervals. Coda waves are rectified for geometric spreading prior to considering them as a component. To incorporate geometric spreading (with α = 1 for local earthquakes), amplitudes are scaled by ‘tα’. The root mean square (RMS) values of coda amplitudes are computed within a Table 10.2 Various central frequencies with low-cut and high-cut frequency bands are used for filtering

Low cut-off (Hz) 1.00 2.00 4.00 6.00 8.00 12.00 16.00

Central frequency ( f ) (Hz) 1.50 3.00 6.00 9.00 12.00 18.00 24.00

High cut-off (Hz) 2.00 4.00 8.00 12.00 16.00 24.00 32.00

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moving 2-second window with a 1-second step, enabling the envelope of the analyzed signal to be estimated. Subsequently, the natural logarithm of RMS amplitudes is calculated and plotted against time. For the given central frequency ( fc), a linear equation is fitted, with the slope yielding coda-Q, as shown in (Fig. 10.2).

10.5

Results and Discussions

A seismological network comprising 4 analog seismographs and one digital seismograph has been deployed to monitor the earthquake activity around the Kol dam located in Himachal Lesser Himalaya. In the current study, a dataset of 94 located earthquakes recorded on a digital station in Sikandra (SKND) station has been utilized to observe the attenuation of seismic waves using the coda waves. In order to analyze the frequency-dependent attenuation of coda waves, the recorded waveforms were filtered at 7 center frequencies. In order to prevent direct and forward scattering waves, the beginning of coda waves (tcoda) has been calculated to have a travel duration that is double that of shear waves (t0) (Rautian & Khalturin, 1978). For the estimate of Q values, only waveforms with a signal-to-noise ratio more than 5 and a correlation coefficient greater than 0.7 have been taken into account. Havskov et al. (1989) and Haskov and Ottemoller (2001) made the observations and recommendations that waveform data with S/N below 5 has a negative impact on estimations. The frequency-dependent behavior of Q estimations has been determined using a total of 458 Q values. The Q values for the various distance ranges at various central frequencies ( fc) are displayed in Table 10.3. According to the epicentral distances, the 94 earthquakes were grouped into three categories: local range (R < 30 km), medium-range (30 ≤ R < 60 km), and distant range (>60 km). Each of the three distance ranges as well as the total set of data were found to have a Q-f relation, as shown in Table 10.3. A total of 170 Q values have been recorded for earthquakes that occurred in the nearby range; the focal depths and magnitude of these tremors range from 1.45 km to 23.4 km and ML = 0.15–2.26, respectively. The results of the Q-f relation were Q0 = 103 and n = 1.10. The Q values in the near range cover an area of 7261 square kilometers. 206 Q values have been obtained in the middle range and are shown in Table 10.4. These events have magnitudes (ML=0.45–2.8) and took place at focal depths ranging from 0.45 km to 41.3 km. The regression analysis yielded Q0 and n of 105 and 1.14, respectively. The Q values in the middle range encompass 12,750 square km. A total of 82 Q values in the remote range are derived from earthquakes (ML = 1.4–3.03) with depths ranging from 0.96 km to 33.8 km. The regression analysis yielded Q0 and n of 119 and 1.16, respectively. To illustrate earthquakes with various depth ranges, the considered earthquakes have been displayed in Fig. 10.3 alongside circles with radii of 30 km and 60 km in relation to the digital

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Fig. 10.2 Plot of the event recorded at SKND station on July 5, 2009. (a) Unfiltered data-trace with coda window, (b) to (e) bandpass filtered displacement amplitudes of coda window at 1–2 Hz, 4–8 Hz, 8–16 Hz, and 16–32 Hz, respectively, and the RMS amplitude values multiplied with lapse time along with the best square fits of selected coda window at central frequencies of 1.5, 6, 12 and 24 Hz, respectively. The Qc is determined from the slope of the best square line. Abbreviations are P: P-wave arrival time; S: S-wave arrival time

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Table 10.3 Q values calculated in different distance ranges, where N is the number of data points and SD is the standard deviation

fc (Hz) 1.50 3.00 6.00 9.00 12.00 18.00 24.00 Total

Near range (60 km) Avg Q SD 153 32 551 141 975 193 1635 465 2269 582 3195 997 4445 1755

N 4 5 10 15 17 16 15 82

All combined Avg Q SD 155 48 377 137 885 268 1436 454 1846 616 2692 968 3781 1404

N 47 45 59 75 78 78 76 458

station (SKND). Figure 10.3 shows that there is little variance in Q values relative to epicentral distance. The three sets of data, when statistically analyzed, produced Q0 scores between 103 and 119. The obtained Q and n values for the three distance ranges show an increase with distance, which illustrates that seismic wave scattering is more pronounced close to the earthquake sources. The results of a similar regression analysis performed on the combined set of data points were Q0= 105 and n = 1.14. The latter is generally indicative of the overall Q0 value for the region as a whole, which has a 21,899 sq. km spatial extent. Comparing Q values at different distance ranges within a 30-second time window reveals the depth- and distance-dependent nature depicted in Fig. 10.4. Figure 10.5 shows the comparison of Qc calculated in the current study with the various studies in various Indian regions. It is clear from Fig. 10.5 that the Qc for the Bilaspur area of Himachal Lesser Himalaya is comparable to NW Himalaya (Kumar et al., 2005).

10.6

Conclusion

The Aki and Chouet (1975) single backscattered model was employed to evaluate the frequency-dependent coda quality factor (Qc (f)= Q0f n) in the Bilaspur region of the Himachal Lesser Himalaya. The study computed “Q0” and “n” using a 30-second time window and seven central frequencies spanning 1.5 to 24 Hz at near (R30 km), intermediate (30R60 km), and far (>60 km) distances. Analysis of coda waves across frequencies ranging from 1.5 to 24 Hz revealed varying Qc values within the 30-second time window, ranging from 155 at 1.5 Hz to 3781 at 24 Hz. This emphasizes the frequency-dependent nature of Qc, which increases with higher frequency. A Q-f relationship of Qc=105f 1.14 was determined for the entire region. The estimated Qc value near Bilaspur within the Himachal Himalayan region

Station SKND

Distance range (km) R < 30 30 ≤ R < 60 R > 60

Average distance 21.70 42.45 76.34

Average depth 12.91 12.95 15.96

Average lapse time 31.50 43.14 63.13

Average s-wave velocity 3.30 3.30 3.30

D1 = vt/ 2 51.98 71.17 104.18

p D2 = D12 - Δ2 47.23 57.13 70.88

Depth = hav + D2 60.14 70.08 86.85

Table 10.4 shows the maximum depth of ellipsoid volume formulation given by Pulli (1984) at Sknd station at different distance ranges coverage area 7708 12,767 23,187

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Fig. 10.3 Map showing the spatial distribution reference to a single station

Fig. 10.4 Plots of quality factors and central frequencies for all distance ranges with linear regression frequency-dependent relationship ( f ), Qc = Q0f n at lapse time 30 s

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Fig. 10.5 Comparison of Qc values for the Bilaspur region of Himachal Lesser Himalaya, India with the existing Q studies in India

exhibited significant heterogeneity and seismic activity compared to other seismically active zones in India. This Qc relationship aligns with observations from other active regions in India. Acknowledgments The authors are thankful to the Department of Earthquake Engineering, the Indian Institute of Technology, Roorkee, for providing the data to carry out this research work.

References Abercrombie, R. E. (1997). Near-surface attenuation and site effects from comparison of surface and deep boreholes recordings. Bulletin of the Seismological Society of America, 87, 731–744. Aki, K. (1969). Analysis of the seismic coda of local earthquakes as scattered waves. Journal of Geophysical Research, 74(2), 615–631. Aki, K. (1980). Attenuation of shear-waves in the lithosphere for frequencies from 0.05 to 25 Hz. Physics of the Earth and Planetary Interiors, 21(1), 50–60. Aki, K., & Chouet, B. (1975). Origin of coda waves: Source, attenuation, and scattering effects. Journal of Geophysical Research, 80(23), 3322–3342. BIS. (2002). IS 1893–2002 (Part 1). Indian standard criteria for earthquake resistant Design of Structures, part 1 – General provisions and buildings, Bureau of Indian Standards, New Delhi. Del Pezzo, E., Ferulano, F., Giarrusso, A., & Martini, M. (1983). Seismic coda Q and scaling law of the source spectra at the Aeolian Islands, southern Italy. Bulletin of the Seismological Society of America, 73(1), 97–108.

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Frankel, A., & Wennerberg, L. (1987). Energy flux model of the seismic coda: Separation of scattering and intrinsic attenuation. Bulletin of the Seismological Society of America, 77, 1223–1251. Gao, L. S., Biswas, N. N., Lee, L. C., & Aki, K. (1983). Effects of multiple scattering on coda waves in three-dimensional medium. Pure and Applied Geophysics, 121, 3–15. Gupta, S. C., & Kumar, A. (2002). Seismic wave attenuation characteristics of three Indian regions: A comparative study. Current Science, 82(4), 407–413. Gupta, S. C., Singh, V. N., & Kumar, A. (1995). Attenuation of coda waves in the Garhwal Himalaya, India. Physics of the Earth and Planetary Interiors, 87(3–4), 247–253. Gupta, S. C., Teotia, S. S., Rai, S. S., & Gautam, N. (1998). Coda Q estimates in the Koyna region, India. Pure and Applied Geophysics, 153, 713–731. Haskov, J., & Ottemoller, L. (2001). Seisan, the earthquake analysis software, University of Bergen, Norway, 25–40. Havskov, J., Malone, S., Mcclurg, D., & Crosson, R. (1989). Coda Q for the state of Washington. Bulletin of the Seismological Society of America, 79, 1024–1038. Havskov, J., & Ottemoller, L. (2003). SEISAN: The earthquake analysis Softwares for windows, Solaris and Linux, Version 8.0, Institute of Solid Earth Physics, University of Bergen, Norway. Khattri, K. N. (1987). Great earthquakes, seismicity gaps and potential for earthquake disaster along the Himalaya plate boundary. Tectonophysics, 138(1), 79–92. Knopoff, L. (1964). Q. Reviews of Geophysics, 2, 625–660. Kopnichev, Y. F. (1977). The role of multiple scattering in the formation of a seismogram’s tail. Izv. Akad. Nauk SSSR, Fiz Zemli., 13, 394–398. Kumar, R., Gupta, S. C., Kumar, A., & Mittal, H. (2015). Source parameters and f max in lower Siang region of Arunachal lesser Himalaya. Arabian Journal of Geosciences, 8(1), 255–265. Kumar, A., Kumar, A., & Mittal, H. (2013). Earthquake source parameters–review Indian context. Research and Development (IJCSEIERD), 3(1), 41–52. Kumar, A., Mittal, H., Kumar, R., & Ghangas, V. (2014). High frequency cut-off of observed earthquake spectrum and source parameters of local earthquakes in Himachal Himalaya. International Journal of Science and Research, 3(7), 1642–1651. Kumar, N., Parvez, I. A., & Virk, H. S. (2005). Estimation of coda wave attenuation for NW Himalayan region using local earthquakes. Physics of the Earth and Planetary Interiors, 151(3–4), 243–258. Kushwaha, P. K., Maurya, S. P., Rai, P., & Singh, N. P. (2021). Estimation of subsurface rock properties from seismic inversion and geo-statistical methods over F3-block, Netherland. Exploration Geophysics, 52(3), 258–272. Le Fort, P. (1975). Himalaya, the collided range: Present knowledge of the continental arc. American Journal of Science, 275a, 1–44. Lienert, B. R., Berg, E., & Frazer, L. N. (1986). HYPOCENTER: An earthquake location method using centered, scaled, and adaptively damped least squares. Bulletin of the Seismological Society of America, 76(3), 771–783. Lienert, B. R., & Havskov, J. (1995). A computer program for locating earthquakes both locally and globally. Seismological Research Letters, 66(5), 26–36. Maurya, S. P., Singh, R., Mahadasu, P., Singh, U. P., Singh, K. H., Singh, R., Kumar, R., & Kushwaha, P. K. (2023). Qualitative and quantitative comparison of the genetic and hybrid genetic algorithm to estimate acoustic impedance from post-stack seismic data of Blackfoot field, Canada. Geophysical Journal International, 233(2), 932–949. Maurya, S. P., Singh, N. P., & Singh, K. H. (2020). Seismic inversion methods: A practical approach (Vol. 1). Springer. Mayeda, K., Hofstetter, A., O’Boyle, J. L., & Walter, W. R. (2003). Stable and transportable regional magnitudes based on coda-derived moment rate spectra. Bulletin of the Seismological Society of America, 93, 224–239. Mishra, O. P., & Vandana. (2019). Source characteristics of the NW Himalaya and its adjoining region: Geodynamical implications. Physics of the Earth and Planetary Interiors, 294, 106277.

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Mittal, H. (2011). Estimation of ground motion in Delhi (Doctoral dissertation, Roorkee, India). Mittal, H., Kumar, A., Wu, Y. M., Kamal, & Kumar, A. (2016). Source study of M w 5.4 April 4, 2011 India–Nepal border earthquake and scenario events in the Kumaon–Garhwal Region. Arabian Journal of Geosciences, 9(5), 1–15. Rautian, T. G., & Khalturin, V. I. (1978). The use of the coda for the determination of the earthquake source spectrum. Bulletin of the Seismological Society of America, 68, 923–948. Richa, M., S. P., Singh, K. H., Singh, R., Kumar, R., & Kushwaha, P. K. (2022). Application of maximum likelihood and model-based seismic inversion techniques: A case study from KG basin, India. Journal of Petroleum Exploration and Production Technology, 12, 1403–1421. https://doi.org/10.1007/s13202-021-01401-0. Rovelli, A. (1984). Seismic Q for the lithosphere of the Montenegro region (Yugoslavia): Frequency, depth and time windowing effects. Physics of the Earth and Planetary Interiors, 34(3), 159–172. Sandhu, M., Sharma, B., Mittal, H., Yadav, R. B. S., Kumar, D., & Teotia, S. S. (2020). Simulation of strong ground motion due to active Sohna fault in Delhi, national capital region (NCR) of India: An implication for imminent plausible seismic hazard. Natural Hazards, 104(3), 2389–2408. Sato, H. (1977). Energy propagation including scattering effects sengle isotropic scattering approximation. Journal of Physics of the Earth, 25(1), 27–41. Seeber, L., Armbruster, J. G., & Quittmeyer, R. C. (1981). Seismicity and continental subduction in the Himalayan arc. Zagros Hindu Kush Himalaya Geodynamic Evolution, 3, 215–242. Sharma, B., Mittal, H., & Kumar, A. (2015). A reappraisal of attenuation of seismic waves and its relevance towards seismic hazard. International Journal, 3(3), 296–305. Srikantia, S. V., & Bhargava, O. N. (1998). Geology of Himachal Pradesh (Vol. 406). Geological Society of India. Vandana, Kumar, A., & Gupta, S. C. (2016). Attenuation characteristics of body waves for the Bilaspur region of Himachal lesser Himalaya. Pure and Applied Geophysics, 173, 447–462. Vandana, Gupta, S. C., & Kumar, A. (2015). Coda wave attenuation characteristics for the Bilaspur region of Himachal Lesser Himalaya. Natural Hazards 78, 1091–1110. Zeng, Y., Su, F., & Aki, K. (1991). Scattering wave energy propagation in a random isotropic scattering medium: 1. Theory. Journal of Geophysical Research: Solid Earth, 96(B1), 607–619.

Chapter 11

Data-Driven Spatiotemporal Assessment of Seismicity in the Philippine Region Amritansh Rai, Rohtash Kumar, Ankit Singh, Pankhudi Thakur, Raghav Singh, S. P. Maurya, and Ranjit Das

11.1

Introduction

The Philippine Islands have a lot of seismic and volcanic activity. Despite the efforts of various researchers to comprehend the plate tectonics of this region, it remains one of the least known in the western Pacific. The Philippine trench runs along the Philippine Islands’ eastern boundary and is the consequence of the Philippine Sea plate underthrusting westward. This underthrusting is linked with shallow and intermediate-depth earthquakes, as well as active volcanism (Karig, 1973). The I. lanila trench, with its enormous negative gravity anomalies, the occurrence of intermediate-depth earthquakes under western and southwestern Luzon, and the presence of multiple active and inactive volcanoes east of it, is the site of Eurasian plate eastward underthrusting. The Philippines is surrounded by several peripheral basins that define its borders. These basins include the South China Sea, the Sulu Sea, and the Celebes Sea along its western edge, from northern to southern regions. On its eastern side, the West Philippine Sea basin serves as a boundary, while the southeastern border is marked by the Molucca Sea basin (refer to Fig. 11.1 for visual representation). The Philippines’ western and eastern boundaries are marked by subduction zones, and a notable strike-slip fault zone known as the Philippine Fault Zone runs across the entire length of the island. Subduction occurs along different trenches at various geological periods: the Manila Trench during the Early Miocene, the Negros Trench during the Middle Miocene, and the Sulu and Cotabato Trenches from the Late A. Rai · R. Kumar · A. Singh · P. Thakur · R. Singh · S. P. Maurya (✉) Department of Geophysics, Banaras Hindu University, Varanasi, India e-mail: [email protected] R. Das Department of Computer Science and System Engineering, Universidad Católica del Norte, Antofagasta, Chile © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 R. Kumar et al. (eds.), Recent Developments in Earthquake Seismology, https://doi.org/10.1007/978-3-031-47538-2_11

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Fig. 11.1 The topographic map of Philippines Island showing the distribution of earthquake events of magnitude M > 7.8 (Yellow stars) along with plate boundaries

Miocene to the Pliocene. The trenches mentioned generally have an eastward dipping direction. The western boundary signifies the subduction of several geological features: the South China Sea through the Manila Trench, the Sulu Sea basin from the Early to Middle Miocene era via the Negros and Sulu Trenches, and the Celebes basin from the Eocene period through the Cotabato Trench. On the other hand, the Eocene West Philippine Sea basin is undergoing a process of subduction along the archipelago’s eastern edge, facilitated by westward sinking through the East Luzon Trough-Philippine Trench. The Molucca Sea basin is currently undergoing subduction beneath Halmahera and Sangihe islands, ultimately resulting in its eventual closure. To accommodate the strain that the adjacent subduction zones cannot handle, the Philippine Fault Zone, which is characterized by left-lateral strike-slip movement, acts as a stress-relieving mechanism (refer to Fig. 11.1 for visual reference).

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The modern East Luzon Trough, located to the northeast of Luzon, is a renewed version of the original proto-East Luzon Trough. This ancient trough played a crucial role in shaping the Cretaceous to Oligocene Northern Sierra Madre magmatic rocks. The entirety of the Philippine island-arc system displays a combined landmass comprising an aseismic Precollisional Basement (PCB) and a seismically active Postcollisional Magmatic Belt (PMB). Notable references supporting this observation include Gervasio (1971), Tamayo et al. (2001), and Ramos et al. (2005), as illustrated in Fig. 11.1. While the South China Sea was forming, the Precollisional Basement (PCB) originated from the southern part of Mainland China through a rifting process. In contrast, the Postcollisional Magmatic Belt (PMB) is characterized by the assembly and amalgamation of multiple terranes. These terranes likely have their roots in the former Philippine Sea Plate and the border of the Indo-Australian Plate, contributing to the distinctiveness of the PMB. The present research examines contemporary viewpoints regarding seismic activity and the seismotectonic environment of the area under investigation. To create a uniform dataset for this region, specific relationships between earthquake magnitudes are established, connecting various magnitude scales. The spatial distribution of seismic activity attributes, such as the magnitude of completeness (mc) or threshold magnitude, as well as the a and b values, provides a quantitative assessment of different aspects of seismic activity across the geographical area. Subsequently, the variations in seismotectonic features within the region are correlated with the spatial changes observed in these seismic activity attributes. The findings from the spatial analysis of seismic activity, when combined with the arrangement of active fault networks, are employed to categorize overarching seismic source regions.

11.2

Methodology

The frequency–magnitude relationship, originally formulated by Gutenberg and Richter in 1944, is a widely recognized empirical correlation within the field of earthquake seismology. This relationship depicts the occurrence frequency of earthquakes concerning their magnitudes: log 10 N ðM c Þ = a - bM

ð11:1Þ

In this equation, N represents the total count of earthquakes having magnitudes surpassing the magnitude of completion (Mc). The variables “a” and “b” are coefficients that need to be determined, reflecting the characteristics of seismic activity and the distribution of earthquake sizes. It’s worth noting that the magnitude scale employed in this study is the Nuttli magnitude (Mn), as defined by Nuttli in 1973. The a-value serves as an indicator of seismic activity, calculated based on factors such as the highest recorded earthquake magnitude, the duration of the observation period, as well as the dimensions of the area and its stress conditions. On the other hand, the b-value represents the consistent incline of the regression line that outlines the rate at which the earthquake frequency alters as magnitudes progressively rise.

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Two prominent methods are available for estimating the b-value. The first method is the least squares technique, which has been discussed by researchers such as Pacheco and Sykes (1992), Okal and Kirby (1995), Scholz (1997), Main (2000), and López Pineda and Rebollar (2005). However, this method lacks a statistical foundation for its application, as pointed out by Page (1968) and Bender (1983). The second method, investigated by Sandri and Marzocchi in 2007, delves into the biases introduced by the accumulation, logarithmic transformation, and measurement errors inherent in the least squares technique, both numerically and analytically. They demonstrated that, for both the binned and cumulative forms of Eq, the technique yields a considerable underestimating of the uncertainty and a large bias in the estimation of the b-value (both of which are heavily dependent on the data size. Furthermore, the impact of measurement mistakes appears to be less than that of the logarithmic transformation’s bias. However, for the estimate of the b-value (Eq. 4.2), the maximum likelihood technique (Aki, 1965) has been widely utilized (Maurya et al., 2020, 2023; Richa et al., 2022; Kushwaha et al., 2020, 2021). As outlined by Marzocchi and Sandri in 2003, the application of Aki’s formula, which assumes that magnitude is a continuous random variable, introduces a notable bias when estimating the b-value. Additionally, this approach leads to a significant underestimation of the associated uncertainty linked to the b-value estimation. They show, however, that using the corrected formula (binned magnitudes; as used in this study by Zmap) would significantly reduce the b-biases values and uncertainty; yet, the impact of measurement errors appears to be insignificant when compared to the impacts of the binned magnitudes. b=

1 log e M Avg - M min

ð11:2Þ

The employed catalog’s average magnitude is MAvg, and its minimum magnitude is Mmin. Equation (11.3), developed by Shi and Bolt (1982), gives the uncertainty limit of this estimation: The size of the research zone, the length of the catalog, and the number of earthquakes all affect changes in a-value. As a result, the a-value shows notable variations depending on the intensity of seismic activity for various places. The slope of the magnitude-frequency curve may be used to get the b-value. It is one of the most important applications in earthquake physics and has a big impact on how realistic design earthquakes are described for a certain location. According to some estimates, differences in b-value for various seismic zones throughout the world typically range from 0.3 to 2.0 (Utsu, 1971; Maurya & Singh, 2020). Furthermore, Frohlich and Davis (1993) characterized the average b-value to be approximately 1.0. While the b-value portrays the proportional occurrence of minor and major earthquakes, it holds substantial significance from both rheological and geotechnical perspectives. Variations in the b-value are strongly impacted by numerous factors. Studies conducted in laboratory settings regarding rock fractures have revealed that a tendency for reduction is linked to decreases in confining pressure and simultaneous increases in applied shear stress (Scholz, 1997). Conversely,

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higher b-values are correlated with factors such as elevated temperature gradients, augmented fracture density, or increased material heterogeneity, particularly within geologically intricate contexts (Mogi, 1962). The subsequent mathematical approach can be employed to calculate the yearly likelihood of earthquakes of varying magnitudes occurring within any specified time frame (Ali, 2016): PðM Þ = 1 - eN ðM ÞT

ð11:3Þ

where P(M ) is the likelihood that at least one event will take place in a given T year. M originates in Eq. (11.1). Additionally, the following equation (Ali, 2016) may be used to determine the return periods of any earthquakes with varying magnitude values: Q=

1 N ðM Þ

ð11:4Þ

The concept of precursory seismic quiescence was initially proposed by Wyss and Habermann (1988), and later on, Wiemer and Wyss (1994) introduced a technique that can be applied using the ZMAP software. A significant portion of researchers utilize regional and temporal modeling of precursory seismic quiescence before main earthquakes. This approach is employed to characterize and measure fluctuations in seismicity rates across different global regions. One of the widely recognized methods in this regard is the application of the standard normal deviation Z-test, which is extensively utilized for various purposes related to the Z-value in the existing literature. So, from the detailed explanation of Wiemer and Wyss (1994), a concise summary of this approach will be given in this part. The ZMAP program offers a continuous image of seismicity rate variations, and the geographic coordinates of the areas displaying seismic quiescence throughout time and space may be shown. The Long-Term Average (LTA) function is formulated to statistically evaluate confidence levels in terms of standard deviation units. The Z-test is then utilized to identify regions exhibiting precursory seismic quiescence. Z ðt Þ =

Rmean - Rw σ mean 2 nmeen 2

þ σnww 2

2

ð11:5Þ

where n is the number of samples within and outside the window, s is the standard deviation, and Rmean and Rw are the average number of earthquakes in the background window and overall foreground period, respectively. The foreground window can move through the catalog’s period thanks to a Z-value computed as a function of time, also known as LTA. The choice of the time window affects the LTA function’s form (Tw). When Tw is larger than the length of the anomaly, the LTA function’s statistical robustness grows, and its form becomes increasingly smooth. The quiescence period is another important parameter that needs to be evaluated, and its significance increases when Tw reaches that level. The choice of

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Tw has no bearing on the outcomes, though. Because these lengths are in the range of documented seismic quiescence before the crustal major shocks, the time frame fluctuates between 1.5 and 5.5 years because the quiescence duration is unknown (Wyss, 1997).

11.3

Preparation of Catalog for Statistical Analysis

In this study, a data catalog is compiled from USGS for the period 1800 to 2022. However, due to the less availability of data set for the period 1800 to 1940, a total of 33,826 events were used for the analysis for the period of 1940 to 2022. The event’s magnitude range is 0.0 to 8.0 with the depth range of the event up to 678 km. Separating dependent earthquakes from catalogs is an important step in ensuring that seismic hazard analyses are accurate and trustworthy. As a result, earthquake databases must be decluttered, and earthquakes must be classified as primary or secondary occurrences. In order to separate dependent earthquakes from independent ones, each cluster is removed, isolating the associated dependent events. Subsequently, all dependent events are replaced with a singular event. To decluster the earthquake catalog using the ZMAP software, the declustering method implemented in this study is derived from the approach pioneered by Uhrhammer (1986), as adapted by Wiemer (2001). The process of declustering involves certain artificial adjustments. This procedure encompasses various input parameters that are to some extent arbitrary, such as the lookahead time for unclustered events, the maximum lookahead time for clustered events, the effective lower magnitude limit of the catalog, the interaction radius factor for dependent events, and other related factors. These criteria enable researchers to eliminate all related events within a smaller or larger time or spatial range based on the primary shock epicenter. Detailed information regarding these parameters can be found in Uhrhammer (1986). For the current study, all input parameters for earthquake declustering were kept consistent with those outlined in Uhrhammer (1986), as this approach has been extensively adopted for a variety of earthquake catalogs. Mcomp (magnitude completeness) is also an important measure in statistical seismicity investigations. The magnitude threshold for complete recording, denoted as Mcomp, is determined through the analysis of the earthquake magnitude-frequency distribution (Wiemer & Wyss, 2000). This magnitude value encompasses 90% of the earthquakes present in the database, and any alterations in Mcomp, particularly involving b and Z-values, could influence the results of seismicity parameters. To ensure robust and accurate statistical parameter analysis, the earthquake catalog’s largest number of events was selected. For the statistical analyses of regional and temporal aspects, Wiemer’s ZMAP7 software (2001) was utilized in this study. Temporal Mcomp was carefully examined and estimated since magnitude completeness analysis is highly useful for determining the accurate estimation of b-value, Z-value, yearly probability, return period, and the GENAS modeling. The number of

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Fig. 11.2 Histogram of temporal distribution of the earthquake events from 1940 to 2022 in the Philippines island

reported events before 1973 is very less (Fig. 11.2), which might be due to less dense instrumentation. Therefore, earthquakes after 1973 are used for further analysis. To maintain the quality of the solution, the lower magnitude events can be removed as they can not alter the b-value or Mcomp. Therefore, the events magnitude less than the median 3.6 are removed and we are left with 31,548 events. Then we decluttered the events using Uhrhammer’s (1986) approach, which removes some clustered events and now we have a final data set of 26,896 events. As a result, the final data catalog was based on this healthy, homogenous, and consistent earthquake collection. The depth distribution of events is shown in Fig. 11.3.

11.4

Results and Discussion

The primary aim of this study is to conduct a region-time analysis of seismotectonic parameters within the Philippines region. The goal is to gather initial insights that can contribute to assessing seismic risk and hazards in the area. To perform a comprehensive statistical examination, this study focused on various aspects. These included investigating the time-magnitude distribution of earthquake occurrences, assessing the evolution of magnitude completeness over time, analyzing variations in b-value and Z-value across both regional and temporal scales, determining return periods and annual probabilities for earthquakes, and establishing the interconnections between these parameters. The intention was to present an overview of both recent and potential seismic activity, aiming to provide valuable insights into the occurrence of earthquakes in real time within the study region.

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Fig. 11.3 Distribution of event’s depth throughout the period of 1940 to 2022 in Philippines Island

The global seismological network deployed in the region provides extensive coverage of the events. The network is highly sensitive so low-magnitude events are also included in the original catalog. Several researchers, such as Katsumata and Kasahara (1999) and Joseph et al. (2011), have conducted comprehensive evaluations of the spatial and temporal aspects of statistical seismicity features. According to their findings, two critical stages in the statistical assessment of earthquake occurrences are the declustering of the earthquake catalog and the determination of magnitude completeness. These studies emphasize that before any calculations, a thorough declustering analysis is essential, involving the removal of dependent events like foreshocks, aftershocks, and swarms from the catalog. This process leads to a more reliable, consistent, and robust dataset that is better suited for conducting statistical region-time analyses. Hence, the decluttered dataset was utilized for the analysis. First, a decluttered catalog of events for the whole period 1973–2022 has been analyzed. For many investigations relating to seismicity, the minimum magnitude of full recording, Mc, is a crucial metric (e.g., Taylor et al., 1991). Because there are more seismographs and better analytical techniques, it is generally known that it fluctuates with time in most catalogs, often declining. For the best results in seismicity research, it is usually required to employ the greatest number of events possible in the study by Woessner and Wiemer (2005), changes in magnitude completeness (Mc) over time were assessed using a moving window technique called the maximum curvature method (MAXC). This approach was employed to investigate seismic quiescence and the frequency-magnitude relationship. Additionally, as outlined in the same study, Mc was also determined using the entiremagnitude-range approach (EMR). In this particular work, the MAXC method was selected, yielding consistent results with previous findings. For detailed information

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Fig. 11.4 Zmap generated map showing the distribution of magnitude of completion (Mc) for the study region. Mc can be seen to be varied from 4.0 to 5.1 with majority of the study region having the Mc = 4.8

about the methods used to estimate an earthquake catalog’s magnitude completeness, readers can refer to Schorlemmer and Woessner (2008). At each node of the 0.05° grid, the spatial distribution of Mc is likewise displayed (Fig. 11.4). It fluctuates spatially between 4.0 and 5.1 in most of the region. The seismicity resolved to Mc = 4.8 in the majority of the study region, as is seen from the Mc map. The maximum curvature method is employed to calculate the b-value within the context of the Gutenberg and Richter (1944) relationship, as explained by Aki (1965). The power-law representation of earthquake size distribution is commonly referred to as the Gutenberg-Richter (G-R) law. The cumulative number of earthquakes for the study region is plotted against magnitude, depicted in Fig. 11.5. The calculated b-value is 0.97 ± 0.01. The magnitude-frequency distribution of the earthquakes aligns well with the Gutenberg-Richter law, characterized by a b-value typically close to 1. This indicates that the earthquake catalog reflects the inherent occurrence pattern (Reasenberg & Jones, 1989). We took into consideration a spatial grid of points with a grid of 0.05°, the same as in the magnitude completeness map. The b-spatial value’s variations range from 0.8 to 1.8 (Fig. 11.6). The highest b-value around 1.8–1.9 can be observed at the

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Fig. 11.5 Plot of the cumulative number of earthquakes for the study region against magnitude

Philippines Trench, Cotabato Trench, and Sulu Trench. The Manila trench shows a b-value between 1 and 1.2. At the junction of the Philippines Trench and East Luzon Trench b-value is relatively low which may indicate the accumulation of energy. Also, the Negros Trench region between Cotabato Trench and Sulu Trench shows lower seismicity. Therefore, it may be the area of energy accumulation. In regions where higher b-values are determined, this observation can be interpreted as an indication of gradual stress release through numerous small earthquakes, suggesting a significant level of geological intricacy (Casado et al., 1995). In a broader context, the projected b-values acquired through the Gutenberg-Richter technique exhibit a meaningful correlation with tectonic conditions and seismic behavior. Therefore, areas exhibiting lower b-values should be subject to heightened scrutiny and consideration. Based on the work of (Wyss and Habermann and Wiemer and Wyss, 2002), the approach of the z-test of seismic catalogs is used to identify the spatial and temporal regions of seismic quiescence before major earthquakes. With a considerable variation in seismic activity intensity (rate) in the chosen energy range, this technique focuses on identifying spatial-temporal blocks in the seismically active zone. To analyze the distribution of Z-values, the research area is initially divided into rectangular cells using a spacing of 0.05 degrees in both latitude and longitude. Within each cell, the N nearest earthquakes to each node are tallied, with a total count of 50 events. Following the approach of Wiemer and Wyss (1994), a moving time window (TW), also referred to as the Inter-event Window Length (IWL), progresses through the time sequence in increments of a sampling interval. This moving window scans for fluctuations in the seismic activity rate within a specified maximum radius change. To achieve a continuous and densely covered temporal representation, the event data is organized into several time bins spanning 28 days

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Fig. 11.6 Spatial distribution of b-values in the study region during the period of 1973–2022

each. A window length of TW = 4.5 years is selected based on the insight from Wiemer and Wyss (1994), as a window of this duration, such as 5.5 years, enhances the visibility of quiescence zones. Strong seismic quiescence can be observed in almost all study regions. Most of the low b-value regions show a high Z-value (Fig. 11.7), most strongly correlated in the south of North Sulawesi Trench, Sulu Trench Region, and east of Palawan Microcontinental Block near the Philippine fault. However, two region shows the anomalous behavior of b-value with seismic quiescence namely, the Northern and southern part of the Philippine fault. These anomalies can be linked to volcanic activity. Before interpreting the seismic quiescence maps, it is important to characterize the null hypothesis, according to Joswig (2001). This indicates that the success rate for earthquake predictions is essentially random. While these maps of quiescence do not send out any alerts, they should be useful in connecting quiescence sites to impending earthquakes. Therefore, even if the earthquake distribution is fully random, the null hypothesis predicts how many quiescence anomalies would

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Fig. 11.7 Spatial distribution of Z-values in the study region during the period of 1973–2022

precede an actual occurrence. It is possible to view the small-scale quiescence anomalies in certain locations as false alarms that were more significant than the predecessors. By randomly changing the event timings while maintaining their positions for the spatial grouping, this unpredictability might be obtained from the supplied catalog (Joswig, 2001). Therefore, such heterogeneous reporting as a function of time has the potential to cause false alarms and obstruct accurate measurements of changes in natural seismicity rate. Figure 11.8 illustrates the annual probabilities and return intervals associated with different magnitudes. As emphasized by Joseph et al. (2011), it is crucial to perform declustering and determine magnitude completeness when conducting statistical evaluations of seismicity characteristics, especially when estimating return periods for earthquakes. In these applications, a decluttered dataset with Mc was selected from 1973 to 2022. Annual probability of seismic activity at various magnitude levels shows substantially greater values of 0.5–1.0 for earthquakes ranging from 6.8

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Fig. 11.8 Plot showing the (a) annual probability of occurrence of earthquake of certain magnitude, (b) the period after which the earthquake of certain magnitude will occur again (recurrence period)

to 7.0 and comparatively smaller values below 0.3 for events of magnitude greater than 7.5 (Fig. 11.8a). Figure 11.8b also shows return times for earthquake activity at various magnitude levels. For earthquake magnitude less than 7.2, return times less than 2.0 years were computed. For earthquakes of magnitudes 7.3–8.0, intermediate return durations of 2–12 years were predicted, while return periods of 13–40 years can be anticipated for earthquakes of magnitudes 8.0–8.5. Additionally, for earthquakes magnitude greater than 8.0, return times greater than 40 years were

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Fig. 11.9 Plots showing the variation of b-values in 5 different time windows of 10 Years for the time periods (a) 1973–1982, (b) 1983–1992, (c) 1993–2002, (d) 2003–2012 and (e) 2013–2022, respectively, starting from the top left and moving clockwise

computed. These findings indicate that earthquakes of magnitude less than 6.7 are more likely to occur than other earthquakes. To know the temporal variation in b-value and other parameters, the data set is now divided into different periods i.e., 1973–1982, 1983–1992, 1993–2002, 2003–2012, and 2013–2022. The obtained b-value for these periods is shown in Fig. 11.9.It can be noted that the seismicity decreases from 1973 to 1993 and then increases. The high seismicity value in 1973–1982 can be attributed to the December 1972 Pondaguitan earthquake (M 8.0), followed by aftershocks. After the next two decades, there may be an accumulation of strain. However, the high b-value in the last decade may also be due to high sensitivity dense instrumentation.

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Conclusion

In the present study, a retrospective analysis is used for the interpretation of geographical and chronological fluctuations of three basic statistical characteristics of seismicity as an earthquake precursor using a big dataset of events that occurred between 1940 and 2022 in the Philippine region. Due to the lack of availability of events before 1973, we used the event catalog that occurred after 1973. Across the entire Philippines archipelago, an average b-value of 0.97 ± 0.01, along with a magnitude of completeness (Mc) of 4.5, characterizes the seismicity. Furthermore, the derived a-value is 8.581. These findings align with the results presented by Somasundaran et al. in 2020. The relatively low average b-values, which are below 1, suggest zones characterized by relatively lower seismic activity. The study region indicates a notably high probability of experiencing significant earthquakes. For instance, the annual probability of a 7-magnitude earthquake occurrence is 0.8, with a recurrence period of approximately 1.5 years. Additionally, there is a likelihood of a major earthquake taking place approximately every 10 years. The combined spatial analysis of the b-value and z-values reveals that the south of North Sulawesi Trench, Sulu Trench Region, and east of Palawan Microcontinental Block near the Philippine fault are the regions of stress accumulation and need more attention. From the analysis of temporal variation of b-values, it is evident that the seismicity decreased from 1973 to 1992 and then increased. The high seismicity value in 1973–1982 can be attributed to the December 1972 Pondaguitan earthquake (M 8.0), followed by aftershocks. In the next two decades, there may be an accumulation of stress and strain. However, the high b-value in the last decade may also be due to high sensitivity dense instrumentation. Data and Resources The catalog of earthquake events from 1940 to 2022 used in this study is obtained from USGS using the Zmap 7.0 tool in MATLAB version R2019a. All the maps and graphs are plotted using Zmap.

References Ali, O. S. (2016). Automatic faults tracking from seismic data using the wavelet transform modulus Maxima lines (WTMM) method. In International Conference and Exhibition, Barcelona, Spain, 3–6 April 2016 (pp. 162–162). Aki, K. (1965). Maximum likelihood estimate of b in the formula logN= a-bM and its confidence limits. Bulletin of the Earthquake Research Institute Tokyo, 43, 237–239. Bender, B. (1983). Maximum likelihood estimation of b values for magnitude grouped data. Bulletin of the Seismological Society of America, 73(3), 831–851. Casado, C. L., de Galdeano, C. S., Delgado, J., & Peinado, M. A. (1995). The b parameter in the Betic Cordillera, Rif and nearby sectors. Relations with the tectonics of the region. Tectonophysics, 248(3–4), 277–292. Gervasio, F. C. (1971). Geotectonic developments of The Philippines. Journal of the Geological Society of the Philippines, 25, 18–38.

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Gutenberg, B., & Richter, C. F. (1944). Frequency of earthquakes in California. Bulletin of the Seismological Society of America, 34(4), 185–188. Joseph, J. D. R., Rao, K. B., & Anoop, M. B. (2011). A study on clustered and de-clustered worldwide earthquake data using GR recurrence law. International Journal of Earth Sciences and Engineering, 4, 178–182. Joswig, M. (2001). Mapping seismic quiescence in California. Bulletin of the Seismological Society of America, 91(1), 64–81. Karig, D. E. (1973). Plate convergence between The Philippines and the Ryukyu Islands. Marine Geology, 14(3), 153–168. Katsumata, K., & Kasahara, M. (1999). Precursory seismic quiescence before the 1994 Kurile earthquake (M = 8.3) revealed by three independent seismic catalogs. Seismicity Patterns, their Statistical Significance and Physical Meaning, 443–470. Kushwaha, P. K., Maurya, S. P., Rai, P., & Singh, N. P. (2021). Estimation of subsurface rock properties from seismic inversion and geo-statistical methods over F3-block, Netherland. Exploration Geophysics, 52(3), 258–272. Kushwaha, P. K., Maurya, S. P., Singh, N. P., & Rai, P. (2020). Use of maximum likelihood sparse spike inversion and probabilistic neural network for reservoir characterization: A study from F-3 block, The Netherlands. Journal of Petroleum Exploration and Production Technology, 10, 829–845. López-Pineda, L., & Rebollar, C. J. (2005). Source characteristics of the Mw 6.2 Loreto earthquake of 12 March 2003 that occurred in a transform fault in the middle of the Gulf of California, Mexico. Bulletin of the Seismological Society of America, 95(2), 419–430. Main, I. (2000). Apparent breaks in scaling in the earthquake cumulative frequency-magnitude distribution: Fact or artifact? Bulletin of the Seismological Society of America, 90(1), 86–97. Maurya, S. P., & Singh, N. P. (2020). Effect of Gaussian noise on seismic inversion methods. The Journal of Indian Geophysical Union, 24(1), 7–26. Maurya, S. P., Singh, R., Mahadasu, P., Singh, U. P., Singh, K. H., Singh, R., Kumar, R., & Kushwaha, P. K. (2023). Qualitative and quantitative comparison of the genetic and hybrid genetic algorithm to estimate acoustic impedance from post-stack seismic data of Blackfoot field, Canada. Geophysical Journal International, 233(2), 932–949. Maurya, S. P., Singh, N. P., & Singh, K. H. (2020). Seismic inversion methods: A practical approach (Vol. 1). Springer. Mogi, K. (1962). Magnitude-frequency relation for elastic shocks accompanying fractures of various materials and some related problems in earthquakes. Bulletin of the Earthquake Research Institute, University of Tokyo, 40, 831–853. Okal, E. A., & Kirby, S. H. (1995). Frequency-moment distribution of deep earthquakes; implications for the seismogenic zone at the bottom of slabs. Physics of the Earth and Planetary Interiors, 92(3–4), 169–187. Pacheco, J. F., & Sykes, L. R. (1992). Seismic moment catalog of large shallow earthquakes, 1900 to 1989. Bulletin of the Seismological Society of America, 82(3), 1306–1349. Ramos, N. T., Dimalanta, C. B., Besana, G. M., Tamayo, R. A., Yumul, G. P., & Maglambayan, V. B. (2005). Seismotectonic reactions to the arc-continent convergence in the Central Philippines. Resource Geology, 55(3), 199–206. Reasenberg, P. A., & Jones, L. M. (1989). Earthquake hazard after a mainshock in California. Science, 243(4895), 1173–1176. Richa, Maurya S. P., Singh, K. H., Singh, R., Kumar, R., & Kushwaha, P. K. (2022). Application of maximum likelihood and model-based seismic inversion techniques: A case study from KG basin, India. Journal of Petroleum Exploration and Production Technology, 12, 1–19. Scholz, C. H. (1997). Size distributions for large and small earthquakes. Bulletin of the Seismological Society of America, 87(4), 1074–1077. Schorlemmer, D., & Woessner, J. (2008). Probability of detecting an earthquake. Bulletin of the Seismological Society of America, 98(5), 2103–2117.

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Shi, Y., & Bolt, B. A. (1982). The standard error of the magnitude-frequency b value. Bulletin of the Seismological Society of America, 72(5), 1677–1687. Tamayo, R. A., Jr., Yumul, G. P., Jr., Maury, R. C., Polvé, M., Cotten, J., & Bohn, M. (2001). Petrochemical investigation of the antique ophiolite (Philippines): Implications on volcanogenic massive sulfide and podiform chromitite deposits. Resource Geology, 51(2), 145–164. Taylor, S. R., Rambo, J. T., & Swift, R. P. (1991). Near-source effects on regional seismograms: An analysis of the NTS explosions PERA and QUESO. Bulletin of the Seismological Society of America, 81(6), 2371–2394. Utsu, T. (1971). Seismological evidence for anomalous structure of island arcs with special reference to the Japanese region. Reviews of Geophysics, 9(4), 839–890. Wiemer, S., & Wyss, M. (1994). Seismic quiescence before the Landers (M = 7.5) and Big Bear (M = 6.5) 1992 earthquakes. Bulletin of the Seismological Society of America, 84(3), 900–916. Wiemer, S., & Wyss, M. (2000). Minimum magnitude of completeness in earthquake catalogs: Examples from Alaska, the western United States, and Japan. Bulletin of the Seismological Society of America, 90(4), 859–869. Woessner, J., & Wiemer, S. (2005). Assessing the quality of earthquake catalogues: Estimating the magnitude of completeness and its uncertainty. Bulletin of the Seismological Society of America, 95(2), 684–698. Wyss, M. (1997). Second round of evaluations of proposed earthquake precursors. Pure and Applied Geophysics, 149, 3–16. Wyss, M., & Habermann, R. E. (1988). Precursory seismic quiescence. Pure and Applied Geophysics, 126, 319–332.

Chapter 12

Determination and Identification of Focal Mechanism Solutions for the 2016 Kumamoto Earthquake from Waveform Inversion Using ISOLA Software Ankit Singh, Rohtash Kumar, Amritansh Rai, Shatrughan Singh, Raghav Singh, Satya Prakash, and Pnkhudi Thakur

12.1

Introduction

Various methodologies have been developed to comprehend the origins of earthquakes. Among these, determining the focal mechanism stands as a prominent technique employed by numerous researchers to gain insights into the earthquake’s source. In regions prone to seismic activity, investigating the manner of faulting responsible for earthquakes is achieved through the analysis of focal mechanism solutions. These solutions unveil details about the characteristics of the fault plane, including its strike, dip, and rake angles. The method involves polarity inversion of initial motion in seismogram data. This technique gives a good focal mechanism solution. It is quite helpful in case of good azimuthal coverage of data. It fails to give the solution where poor azimuthal data is available. As we know japan is an island and it rests upon active tectonic plates (Fig. 12.1). The data for the earthquakes that occurred in Japan are limited in azimuthal coverage as seismograms are installed only on land and some earthquakes occurred at sea. The estimation of focal mechanisms using these poor azimuthal data using polarity inversion is not possible. Alternate techniques have been developed to find the focal mechanism using these poor azimuthal waveform data. Finding the moment tensor solution is one of the alternatives. Numerous investigations have demonstrated the feasibility of determining moment tensor solutions using limited azimuthal data or even waveform data from a single station (Dreger & Helmberger, 1991). To use a few station waveform data to find the moment tensor solution accurate knowledge of the crustal velocity model

A. Singh · R. Kumar · A. Rai (✉) · S. Singh · R. Singh · S. Prakash · P. Thakur Banaras Hindu University, Varanasi, Uttar Pradesh, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 R. Kumar et al. (eds.), Recent Developments in Earthquake Seismology, https://doi.org/10.1007/978-3-031-47538-2_12

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Fig. 12.1 Topographic map of Japan showing the major fault lines, plate boundaries, and coastlines generated by Zmap

and quality factor of the layers is needed as the waveform is very sensitive to these parameters (Kim & Kraeva, 1999). As instrumentation progressed, seismograms were equipped with three components to capture data in three orientations: NorthSouth, East-West, and vertical directions. Studies showed that three-component seismogram data of a single station is enough for waveform inversion to find moment tensor solutions (Dreger & Helmberger, 1993; Kim & Kraeva, 1999).

12.2

Methodology

The green function is calculated at every depth by the vertical grid searching method. The grid search helps to optimize the correlation between the synthetic waveform formed using Green’s function (s) and the observed waveform recorded at the seismograms (u):

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us Corr =

ð12:1Þ u2 s2

where

us =

ui ðt Þsi ðt Þdt is the summation over all components and all of the i

stations. The L2 norm is used to find the misfit of the two waveforms: ðu - sÞ 2

misfit =

ð12:2Þ

And/or using the global variance reduction: VR = 1 -

misfit

:

ð12:3Þ

u2 Synthetic signals are determined through the process of minimizing the least-squares misfit. The correlation is linked to the reduction in variance using a straightforward formula. Corr 2 = VR

ð12:4Þ

The forward and inverse problems are addressed as follows: We examine a seismic wave’s point source with a specified position and origin time. Displacement u is represented using a moment tensor M and the spatial derivative of Green’s tensor G (Aki and Richard, 2002). 3

3

ui ð t Þ =

M pq  Gip,q

ð12:5Þ

p=1 q=1

Here, * signifies temporal convolution, while p and q represent three Cartesian coordinates. The moment tensor can be formulated as a linear combination of six fundamental (dimensionless) tensors, denoted as Mi: 6

M pq = i=1

ai M ipq

ð12:6Þ

This serves as a convenient parameterization since it allows the source to be described using six scalar coefficients ai.

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The fundamental tensors employed are those incorporated in the AXITRA discrete-wavenumber code (Bouchon, 1981): 0 M = 1

M = 4

1

0

1

0

0

0

0

0

-1 0 0 0

0 0

0

0

0 M = 2

M = 5

1

0

1

0 M = 3

0

0

0

1

0

0

0 0

0 0 -1 0

0

0

0

0

0

0

-1

0

-1

0

M = 6

1

1 0

0 0 1 0

0

0 1

ð12:7Þ

The tensors M1 to M5 correspond to five instances of double-couple (DC) focal mechanisms, whereas M6 signifies a purely isotropic source. It’s important to note that the six elementary tensors utilized in this context to facilitate MT inversion should not be mistaken for the diverse tensors employed in literature for decomposing MT in order to achieve its physical interpretation:

M=

- a4 þ a6 a1

a1 - a 5 þ a6

a2 - a3

a2

- a3

a4 þ a5 þ a 6

ð12:8Þ

where ai represents the coefficients in the linear combination given in Eq. (12.2). The trace of the moment tensor is represented as tr(M) = 3 a6. The scalar seismic moment is defined as the Euclidean magnitude of the MT (Silver and Jordan, 1982): 3

3

p=1 q=1

M0 =

M pq

2

ð12:9Þ

2

By merging Eqs. (12.1) and (12.2), we obtain: 6

ui ðt Þ = p

j=1

q

aj M jpq

ð12:10Þ

 Gip,q

and then: 6

ui ðt Þ =

6

M jpq  Gip,q =

aj j

p

q

aj E ji ðt Þ j=1

ð12:11Þ

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Here, E j represents the elementary seismogram associated with the jth elementary moment tensor. In this context, it is assumed that the temporal function of the moment is already identified. In a matrix representation: u=E a

ð12:12aÞ

The (mathematically) over-determined linear inverse problem (8a) to determine ‘a’ can be addressed using the least-squares approach: aopt = E T E

-1

ET u

ð12:12bÞ

In this context, T and - 1 denote matrix transposition and inversion, respectively. The least-squares formulation employed is standard (Kikuchi, Inversion of complex body waves—III. 1991), though the elementary moment tensors (3) used in ISOLA differ from those cited in the reference papers. The difference is purely formal and does not impact the outcome. The comprehensive processing of observed seismograms u, the calculation of elementary seismograms E for a specified time function, and the inversion of aopt are all executed using ISOLA software (Sokos and Zahradnik, 2008). No artificial temporal adjustments are introduced to enhance the match between observed and synthetic seismograms (Zahradnik et al., 2008). When assuming that all six a-coefficients are generally nonzero, the term “full-MT inversion” is employed; in the case of a6 = 0 (absence of an isotropic component), it’s referred to as “deviatoric inversion.” In scenarios where the source position and time are unknown and nonlinearly linked to displacement, a grid search is utilized to identify these supplementary parameters (centroid position and time, concealed within E). In essence, the linear problem (8a) for a is continually solved, albeit with varying E on each iteration.

12.3

Data and its Processing

This research employs data from the Kik-net (Kiban Kyoshin Network) strongmotion seismograph network for the 2016 Kumamoto earthquake analysis. The Kik-net network comprises pairs of seismographs situated both in boreholes and on the ground surface, totaling around 700 stations across the nation. These station networks were established by the National Research Institute for Earth Science and Disaster Resilience (NIED) as part of the ‘Fundamental Survey and Observation for Earthquake Research program, guided by the “Headquarters for Earthquake Research Promotion.” The strong-motion seismograph network established by NIED captures velocity data. However, for moment tensor solutions, the ISOLA code requires displacement data. The seismogram data must be first converted into displacement data. A low-pass filter is utilized to eliminate microseismic noise (Tiwari et al., 2018;

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Maurya & Singh, 2018, 2019a, b). Prior to commencing the inversion process, specific files and details are necessary, including latitude, longitude, depth, and origin time of the event. These must be provided as inputs in the event information window. We need the station location files which contain the information of the station code and its latitude and longitude. It will be used to load the data at their respective locations so that synthetic data can be generated at these sites.

12.3.1

Crustal Model

This is a 1D model composed of homogeneous layers with constant velocities. This is not a gradient model. It is used to calculate the green function, check polarity, and generate synthetic seismograms. ISOLA needs both Vp and Vs. We can also use the ratio Vp/Vs if available density plays a crucial role in ensuring accurate values for the seismic moment (Mo) and moment magnitude (Mw).

12.3.2

Source Definition

The prospective source locations are determined for the event using the seismic source definition tool. The moment-tensor inversion is made for each position, [at each position we also grid search the source time], and the best position [and time] is searched. The “best” position is understood in the sense of the match between observed and computed waveforms. The trial sources are situated beneath the earthquake’s epicenter. It will be used in the green function calculation. At each depth position, the green function will be calculated and used in the inversion process.

12.3.3

Green’s Function Calculation

The frequency-wavenumber technique is employed to compute Green’s function (Bouchon, 1981). The software autonomously generates files for Green’s function and the associated elementary seismograms. We refer to the moment-rate function as a “time function.” The delta function and the triangle function of a specific duration are two possibilities in the current GUI version. We work at relatively low frequencies in most single-source applications so that the earthquake corner frequency fc (inversely proportional to the source duration, fc ~1/duration) is more than fmax, i.e., fc > > fmax. The true time function of the source is irrelevant in this scenario, and we can use the delta-function option only in this case. If fc is near to, or even equal to, fmax, the true source duration must be considered.

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12.3.4

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Inversion

Four possible types of inversion are available in the ISOLA tool. The three: Full MT (i.e., the full, unconstrained moment tensor, six independent parameters), Deviatoric MT (i.e., the MT characterized by five nonzero parameters, while the 6th parameter is zero, which guarantees zero volume component), and Fixed mechanism. The fourth (needs also prescription of the strike, dip, and rake) is good in case of multiple-point source solutions where we need to stabilize the problem by decreasing the number of the free parameters; hence, for each sub-event, we calculate its scalar moment and source time, but the three source angles are kept fixed from a previous single-source inversion. The Full MT inversion is good for research purposes (Kushwaha et al., 2019; Maurya, 2019; Maurya et al., 2019a, b). In single-source inversions, practically, the most useful is the Deviatoric MT. It’s still a linear inversion problem; the CLVD component is the sole variation from pure DC. Because the CLVD is frequently an artifact of the inversion (e.g., due to incomplete knowledge of the inversion). Occasionally, it can be advantageous to analyze not just the optimal solution but also a solution with a reduced fit accompanied by a smaller CLVD component.

12.4

Results and Discussion

The ISOLA-GUI software is employed to derive the focal mechanism solution for the 2016 Kumamoto earthquake with a magnitude of Mw 6.5. This estimation is achieved through waveform inversion of a three-component seismogram centered around the earthquake’s vicinity. The best-fit depth position of the focus is estimated by changing the depth of the source keeping its horizontal position fixed. For each depth, the waveform inversion is estimated and the calculated green function for each depth has been correlated with the observed seismogram. The plot shows the correlation of the green function with the observed seismogram. The best model is the one that has a high correlation as well as a high DC% value. The plot is shown in Fig. 12.2. For each depth level, the correlation value is computed by comparing the synthetic and observed waveforms. Additionally, the double-couple portion of the moment tensor is graphed against the depth position based on the moment tensor solution. Figure 12.3 illustrates the graphical representation of correlation versus time shift, including source position and the double-couple percentage. The largest correlation was found for source position 5, which corresponds to a source depth of 11 km and a time shift of 3.5 seconds. Focal mechanism shading changes according to DC%. The obtained solution is shown in a red beach ball with a slightly larger size. From the plot, we can see that the correlation of the obtained solution is close to 0.8, which is a good correlation. The plot of source depth and correlation also gives the same correlation value. This plot suggests a DC% between 60% and 80%.

Fig. 12.2 Correlation between observed and synthetic waveforms and focal mechanism of solutions is plotted against the depth of the source. The DC% value scale has been shown on the right side

Fig. 12.3 Plot of correlation v/s time shift. Source position and DC%

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Fig. 12.4 Plot of an observed and synthetic waveform. Black represents the observed waveform and red represents the synthetic waveforms. The blue color number represents the VR between the waveforms Table 12.1 The obtained focal plane solutions

Strike 1 Dip 1 Rake 1 Strike 2 Dip 2 Rake 2 DC% VR

223 60 78 66 33 110 67.38 0.60

The plot between synthetic and observed seismograms is shown in Fig. 12.4. It demonstrates the adequacy of the seismogram produced through Green’s function in comparison to the observed seismogram from the stations involved in the inversion procedure. The concordance between the observed and synthetic seismograms is indicated by the variance reduction (VR) value, depicted in blue adjacent to each plot. The focal mechanism of the earthquake by waveform inversion using ISOLA software for the 2016 Kumamoto earthquake is shown in Table 12.1. We possess two collections of parameters specifying the strike, dip, and rake of the focal mechanism. This phenomenon arises from the double couple source mechanism, which yields two distinct sets of strike, dip, and rake values. One set corresponds to the fault plane’s geometry, while the other pertains to the auxiliary plane’s geometry,

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which is perpendicular to the former. Without prior knowledge, we cannot tell the exact fault plane geometry that causes the earthquake. In this scenario, we possess a pre-existing understanding of the faulting system and its alignment at the earthquake’s specific location. Table 12.1 displays the focal mechanism solution for the 2016 Kumamoto earthquake. Using the geological information of the area, we find the strike/dip/rake (223/60/ 78) of the earthquake. This is the probable solution between the two solutions regarding the geological information. The same earthquake has been studied using different methods. Hallo et al. (2017) studied it using a modified version of the Bayesian full-waveform CMT inversion in ISOLA-ObsPy. Bayes ISOLA is a Python tool for solving the inverse problem of seismic sources. It characterizes the source through the centroid moment tensor and employs the point source approximation (Vackář et al., 2017). Himematsu, Y. and Furuya, M. utilized the offset tracking technique with ALOS2/PALSAR-2 data to determine the focal mechanism solution for the identical earthquake. Additionally, the Japan Meteorological Agency (JMA) and the National Research Institute for Earth Science and Disaster Resilience (NIED) conducted their independent investigations on the same earthquake. The result that we got is in close range of the results derived by other individuals and agencies. The centroid position is searched in vertical directions only in our NIED techniques to infer CMTs. On the contrary, JMA pursued an exploration in both the vertical and horizontal orientations to deduce the centroid moment tensors (CMTs). The horizontal centroid is fixed at the JMA epicenter, and we simply look for the centroid depth. Using ALOS-2/PALSAR-2 data (Himematsu and Furuya, 2016) the focal mechanism was found to be Strike/Dip/ as 230.77/65.61. The DC% value varies from 64% to 96%. The outcomes of this study broadly align with the solutions provided by other institutions, concerning both the percentage of double couple (DC%) and the orientation of the plane. The DC percentage varies, ranging from 64% (Hallo et al., 2017) to 75% (JMA) to 96% (NIED). The focal mechanism solutions for the Mw 6.2 (Mj 6.5) foreshock predominantly exhibit strike-slip motion on a fault with an NE-SW orientation and a northwestern dip at 60–850 (Lin, 2017). The waveform inversion utilizes the S-wave part of the seismogram. First, the instrument correction is applied using the PZ files of the instrument. The low-frequency segment of the seismogram is isolated and employed through a filtering process. The crustal model for the Kumamoto region (Shito et al., 2017) is utilized to generate the Green’s function. For the inversion process, the frequency range exhibiting a high signal-to-noise ratio (SNR) is selected. The inversion specifically adopts the frequency band of 0.04–0.09 Hz. The plot depicting the signal-to-noise ratio (SNR) against frequency can be observed in Fig. 12.5. We can see that the SNR value is high in the desired frequency, which is suitable for the inversion process. The more the SNR the better the result will be.

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Fig. 12.5 Plot of SNR v/s frequency

Fig. 12.6 Plot of power spectrum v/s frequency

The power spectrum shows that the noise level is very low as compared to the data; hence, better results are obtained using this data (Fig. 12.6). The instrument correction is done by using the poles and zeros files (PZ files) of each station. The amplitude response of the PZ files is shown in Fig. 12.7. It has a linear response between 0.03 Hz and 60 Hz frequency. We have used the low-frequency component to calculate the green function.

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Fig. 12.7 Amplitude response of the PZ files of the instrument

12.5 Conclusion This study employs waveform inversion in conjunction with the ISOLA software to determine the focal mechanism of the 2016 Kumamoto earthquake. The focal mechanism solution for the earthquake, achieved through waveform inversion with limited azimuthal coverage data, is presented in the table. The moment tensor solution relies on various factors, including crustal velocity structure, data quality, distance from the hypocenter, and the frequency band employed for inversion. These factors were considered during the inversion process. In the case of the Kumamoto earthquake, the frequency band utilized for inversion is 0.04–0.09 Hz. This strategy is particularly beneficial when there is a lack of azimuthal data coverage for an earthquake. This method gives information about the focal mechanism of the earthquake using very few stations. We can see that the DC% is high which indicates that double Couples sources can be considered as the major source of the earthquake. The variation in the result may possibly be because there is not enough azimuthal coverage (Šílený and vavrycuk, 2000). In addition, a large-magnitude earthquake has high DC% as compared to a low-magnitude earthquake. The SNR and power spectrum are also shown in Figs. 12.5 and 12.6, respectively, which show that the data used are of good quality with less noise level. The synthetic and observed waveform plot is also shown, which suggests that the synthetic waveform fits well with the observed waveform. This well-fitting suggests that the synthetic waveform created by the green function is in good accordance with the real event. Seismic

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inversion investigations (Asano & Iwata, 2016) indicate that the southwestern part of the source fault is primarily characterized by right-lateral strike-slip displacement, whereas the northeastern portion of the seismogenic fault features normal-slip components. These outcomes align with my own findings. Recent analyses conducted through trench investigations have uncovered evidence of two to four morphogenic earthquakes affecting the Futagawa-Hinagu faults during the late Holocene.

References Aki, K., & Richards, P. G. (2002). Quantitative Seismology. University Science Books. Asano, K., & Iwata, T. (2016). Source rupture processes of the foreshock and mainshock in the 2016 Kumamoto earthquake sequence estimated from the kinematic waveform inversion of strong motion data. Earth, Planets and Space, 68(1), 1–11. Bouchon, M. (1981). A simple method to calculate Green's functions for elastic layered media. Bulletin of the Seismological Society of America, 71(4), 959–971. Dreger, D., & Helmberger, D. (1991). Source parameters of the Sierra Madre earthquake from regional and local body waves. Geophysical Research Letters, 18(11), 2015–2018. Dreger, D. S., & Helmberger, D. V. (1993). Determination of source parameters at regional distances with three‐component sparse network data. Journal of Geophysical Research: Solid Earth, 98(B5), 8107–8125. Hallo, M., Asano, K., & Gallovič, F. (2017). Bayesian inference and interpretation of centroid moment tensors of the 2016 Kumamoto earthquake sequence, Kyushu, Japan. Earth, Planets and Space, 69(1), 1–19. Hashimoto, M., & Jackson, D. D. (1993). Plate tectonics and crustal deformation around the Japanese Islands. Journal of Geophysical Research: Solid Earth, 98(B9), 16149–16166. Himematsu, Y., & Furuya, M. (2016). Fault source model for the 2016 Kumamoto earthquake sequence based on ALOS-2/PALSAR-2 pixel-offset data: evidence for dynamic slip partitioning. Earth, Planets and Space, 68(1), 1–10. Kim, S. G., & Kraeva, N. (1999). Source parameter determination of local earthquakes in Korea using moment tensor inversion of single station data. Bulletin of the Seismological Society of America, 89(4), 1077–1082. Kushwaha, P. K., Maurya, S. P., Singh, N. P., & Rai, P. (2019). Estimating subsurface petrophysical properties from raw and conditioned seismic reflection data: A comparative study. The Journal of Indian Geophysical Union, 23, 285–306. Lin, A. (2017). Structural features and seismotectonic implications of coseismic surface ruptures produced by the 2016 M w 7.1 Kumamoto earthquake. Journal of Seismology, 21, 1079–1100. Maurya, S. P. (2019). Estimating elastic impedance from seismic inversion method. Current Science, 116(4), 628–635. Maurya, S. P., & Singh, N. P. (2018). Application of LP and ML sparse spike inversion with probabilistic neural network to classify reservoir facies distribution-a case study from the Blackfoot field, Canada. Journal of Applied Geophysics, 159, 511–521. Maurya, S. P., & Singh, K. H. (2019a). Predicting porosity by multivariate regression and probabilistic neural network using model-based and coloured inversion as external attributes: A quantitative comparison. Journal of the Geological Society of India, 93(2), 207–212. Maurya, S. P., & Singh, N. P. (2019b). Characterising sand channel from seismic data using linear programming (l1-norm) sparse spike inversion technique: A case study from offshore, Canada. Exploration Geophysics, 50(4), 449–460.

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Maurya, S. P., Singh, K. H., & Singh, N. P. (2019a). Qualitative and quantitative comparison of geostatistical techniques of porosity prediction from the seismic and logging data: A case study from the Blackfoot field, Alberta, Canada. Marine Geophysical Research, 40, 51–71. Maurya, S. P., Singh, N. P., & Singh, K. H. (2019b). Use of genetic algorithm in reservoir characterisation from seismic data: A case study. Journal of Earth System Science, 128, 1–15. Shito, A., Matsumoto, S., Shimizu, H., Ohkura, T., Takahashi, H., Sakai, S., Okada, T., Miyamachi, H., Kosuga, M., Maeda, Y., & Yoshimi, M. (2017). Seismic velocity structure in the source region of the 2016 Kumamoto earthquake sequence, Japan. Geophysical Research Letters, 44(15), pp.7766–7772. Sokos, E. N., & Zahradnik, J. (2008). ISOLA a Fortran code and a Matlab GUI to perform multiplepoint source inversion of seismic data. Computers & Geosciences, 34(8), 967–977. Šílený, J., & Vavryčuk, V. (2000). Approximate retrieval of the point source in anisotropic media: numerical modelling by indirect parametrization of the source. Geophysical Journal International, 143(3), 700–708. Silver, P. G., & Jordan, T. H. (1982). Optimal estimation of scalar seismic moment. Geophysical Journal International, 70(3), 755–787. Tiwari, A. K., Maurya, S. P., & Singh, N. P. 2018. TEM response of a large loop source over the multilayer earth models. International Journal of Geophysics, 2018. Vackář, J., Burjánek, J., Gallovič, F., Zahradník, J., & Clinton, J. (2017). Bayesian ISOLA: New tool for automated centroid moment tensor inversion. Geophysical Journal International, 210(2), 693–705. Zahradnik, J., Jansky, J., & Plicka, V. (2008). Detailed waveform inversion for moment tensors of M 4 events: Examples from the Corinth Gulf, Greece. Bulletin of the Seismological Society of America, 98(6), 2756–2771.

Chapter 13

Regression Relations for Magnitude Conversion of Northeast India and Northern Chile and Southern Peru Ranjit Das, Claudio Meneses, Marcelo Saavedra, Genesis Serrano, Franz Machaca, Roberto Miranda-Yáñez, and Bryan A. Urra-Calfuñir

13.1

Introduction

Earthquake databases generally consist of time of origin (occurrence time), geographical coordinates, i.e., latitude and longitude, earthquake size, and other related earthquake information. Earthquake information is mainly derived from heterogeneous seismic networks in the spatiotemporal domain. The earthquake database yields information for understanding seismicity, seismic hazard, and risk, as well as information about seismic tectonics. A unified earthquake database is of critical importance for studies such as seismicity, seismotectonic, and seismic hazard and risk. These studies have various applications, such as land use planning and infrastructure development. All these studies need accurately measured and well-defined earthquake magnitude scales that do not saturate. Existing past earthquake records don’t fulfill these criteria. Therefore, regression analysis plays a vital role in this case for converting different magnitude scales to unified unsaturated magnitude scales, such as Mw or Das magnitude scale Mwg (Das et al., 2019). Because “earthquake magnitude” is the most frequently used descriptor for describing “earthquake size,” a summary is provided below for the reader’s convenience. The first earthquake size determination scale is the local magnitude scale or Richter scale developed by Richter (1935), which relies on earthquakes in Southern

R. Das (✉) · C. Meneses Department of Computer Science and System Engineering, Universidad Católica del Norte, Antofagasta, Chile e-mail: [email protected]; [email protected] M. Saavedra · G. Serrano · F. Machaca Facultad de Ingeniería y Ciencias Geológicas – Universidad Católica del Norte, Antofagasta, Chile R. Miranda-Yáñez · B. A. Urra-Calfuñir School of Engineering, Universidad Católica del Norte, Coquimbo, Chile © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 R. Kumar et al. (eds.), Recent Developments in Earthquake Seismology, https://doi.org/10.1007/978-3-031-47538-2_13

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California and depends on body wave amplitudes from standard Wood-Anderson torsion seismometers. Seismologists later saw the need to expand this scale to include varied seismic wave types and conditions (Maurya et al., 2023). Gutenberg (1945) formulated the scale for body wave magnitudes, which was subsequently refined by Gutenberg and Richter (1956). The initial version of this body wave magnitude scale, referred to as MB, was developed using instruments capable of detecting the most significant ground displacement amplitudes across intermediate to long periods. Utilizing the initial cycles of short-period P waves recorded by short-period instruments, an alternative magnitude scale known as MB is reported in ISC and NEIC bulletins. Employing the Prague formula introduced by Kárník (1962) for shallow focal depths, the calculation of the surface wave magnitude, Ms., is derived by considering the amplitude and equivalent period of Rayleigh waves spanning periods from 10 to 60 seconds. The magnitude scales ML, mb, and Ms scales exhibit nonuniform behavior for various magnitude ranges and experience saturation for bigger earthquakes. To remove these limitations, another magnitude scale was given by Hanks and Kanamori (1979) based on Californian seismicity: M w = ð2=3Þ log M 0 - 10:7

ð13:1Þ

where M0 stands for the seismic moment in dyne-cm. One of the main criteria of Mw scale development was comparison with other scales (i.e., Ms and ML). As estimation of Mw, given by Eq. (13.1), was similar to Californian Earthquakes (see Table 13.1 of Hanks and Kanamori, 1979) and able to estimate bigger earthquakes without saturation, therefore, Hanks and Kanamori (1979) suggested an unsaturated scale. There was no validation of this scale with observed energy radiation. Recently, Das et al. (2019) developed another magnitude scale based on global seismicity. The scale was named Das magnitude scale Mwg. The scale was validated with observed magnitudes and observed radiated energy. The Mwg scale is defined by: M wg = ðlog M 0 Þ=1:36 - 12:68

ð13:2Þ

Due to its direct correlation with the underlying physics of earthquake sources, including factors such as average slip, fault area, and the coefficient of rigidity Table 13.1 Error estimations of different types of magnitudes (Wason et al., 2018) Study Kagan (2003)

Catalog/events data Global catalog (1980–2000)

Scordilis (2006)

Global catalog (1964–2003)

Das et al. (2011)

Global catalog (1964–2007)

Error estimates mb σ = 0.25 (10,496 events) 4.5 ≤ mb ≤ 7.0 σ = 0.2 (215,163 events)

σ = 0.17 (25,960 events)

σ = 0.2

σ = 0.12

Ms σ = 0.2 (1746 events)

Mw σ = 0.12 (992 events) 6 ≤ Mw ≤ 8 σ = 0.11 (3756 events) 5 ≤ Mw ≤ 8 σ = 0.09

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modulus, the Mwg scale demonstrates consistent behavior across all magnitudes. Unlike other scales, it doesn’t reach a saturation point even for extremely large earthquakes. Due to the extremely old scale’s 1979 derivation, the majority of the extant earthquake catalog is expressed in terms of Mw. To establish the necessary magnitude conversion relationships for developing standardized earthquake catalogs, various regression methods are employed. These techniques encompass standard linear regression (SLR), inverted standard regression (ISR), orthogonal regression (OR), and general orthogonal regression (GOR). In the context of SLR and ISR, one of the variables is treated as having no measurement error. In SLR, the independent variables are considered error-free and the regression line is constructed to minimize the vertical deviations (residuals). Conversely, in ISR, the regression line is established by minimizing the horizontal displacements to achieve the optimal fit to the line. General orthogonal regression (GOR) is grounded in the concept of minimizing statistical Euclidean distances, as outlined by Williamson in 1968. This method considers the presence of errors in both variables involved (as indicated by Madansky in 1959, Fuller in 1987, Gusev in 1991, and Ristau in 2009). The formulation of GOR is expressed as follows: n i=1

ð Y i - β 0 - β 1 xi Þ 2 ð X i - xi Þ 2 þ σ 2u σ 2e

ð13:3Þ

In the context of GOR, (Xi, Yi) represent the observed values and (xi, yi) denote the true values for a set of n data pairs of the independent and dependent variables, respectively. The GOR line is characterized by an intercept denoted as β0 and a slope indicated as β1. The terms σ2ɛ and σ2u correspond to the errors associated with Xi and Yi, respectively. Several researches (e.g., Ristau, 2009; Das et al., 2011, 2012, 2013, 2014; Wason et al., 2012) have found GOR connections between various magnitude classes based on various datasets. Das et al. (2018) have noted that this equation is misrepresented in various publications (such as Eq. (13.8) from Castellaro et al., 2006). This chapter describes regression connections for mb and Ms magnitudes to seismic moment magnitude (Mw) conversion utilizing GOR1, GOR2, and SLR techniques for Northeast India, Northern Chile, and Southern Peru regions. Regions such as Northeast India in the Indian subcontinent, Northern Chile and Southern Peru within the South American continent. This comprehensive reference catalog could serve as a valuable resource for precise assessments of seismic hazards and other explorations related to seismic activity in these areas.

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Catalogs for Northeast India, Northern Chile, and Southern Peru

The earthquake database for Northeast India mainly extends to only about 150 years or so. Oldham (1883) prepared an earthquake catalog for near India up to the time 1869. This earthquake catalog was updated by Bapat et al. (1962) from the ancient times to 1979. For Northeast India, an earthquake catalog prepared by Gupta et al. (1986) considered 504 historical earthquakes for the period 1897–1962 with focal depths of about 89 earthquakes. This is one of the very basic catalogs for any seismic study of Northeast India. Das et al. (2013) along with other researchers have made several attempts to prepare a unified earthquake database.

13.3

Regression Procedures

It is crucial to understand the various magnitude determinations and the accompanying flaws to unify earthquake catalogs. Applying the general orthogonal regression (GOR) methodology necessitates the presence of errors in both the dependent and independent variables. It is of paramount importance to comprehend the error variance ratio (denoted as η) that exists between these distinct types of variables. A brief explanation of the GOR process is provided below. The approach is described in the literature (e.g., Madansky, 1959; Fuller, 1987; Kendall & Stuart, 1979; Carroll & Ruppert, 1996; Das et al., 2011). Assume that two variables Ry and Rx are linearly connected and their measurement errors ε and δ are unrelated normal variates with variances σ 2ɛ and, σ 2δ , respectively. We can thus write: ry = Ry þ ε,

ð13:4Þ

rx = Rx þ δ,

ð13:5Þ

Ry = α þ βRx þ ε,

ð13:6Þ

ε = ε þ δ:

ð13:7Þ

and the regression-like model:

where

The error variance ratio η is given by: η=

σ 2ε , σ 2δ

where σ 2ε = σ 2ry and σ 2δ = σ 2rx , provided that σ 2ɛ andσ 2δ are constants.

ð13:8Þ

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The general slope orthogonal estimator, as put forth by Fuller in 1987, is determined based on s2ry , s2rx and srx ry stands for the sample variance of the Ry and Rx and the sample covariance between the two variables:

β=

s2ry - ηs2rx þ

s2ry - ηs2rx

2

þ 4ηs2rx ry

ð13:9Þ

,

2sr x r y

and the estimator of the intercept is: α = r y - βr x ,

ð13:10Þ

where r x and ry stands for the average values. The subsequent equations can be employed for the estimation of errors associated with the regression parameters, as shown by Fuller (1987):

σβ =

σ r x ð n - 1Þ n þ β

2

σ δ þ ðσ δ Þ2 ðn - 1Þ η þ β2

2

- ðn - 2Þ - βσ δ

ðn - 2Þðn - 1Þσ 2 rx

2

, ð13:11Þ

and

σ

2

α

=

ð n - 1Þ η þ β

2

n ð n - 2Þ

σδ

þ r x 2 σ 2β ,

ð13:12Þ

where

σr x =

s2ry - ηs2rx

2

þ 4ηs2rx ry - s2ry - ηs2rx 2η

,

ð13:13Þ

:

ð13:14Þ

and

σδ =

13.4

s2ry - ηs2rx -

s2ry - ηs2rx 2η

2

þ 4ηs2rx ry

Observation Errors in Different Magnitude Types

Earthquake data is collected from diverse sources and institutions, including the National Earthquake Information Center (NEIC) and the US Geological Survey (USGS) in the United States, the International Seismological Center (ISC) in the

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United Kingdom, and the Global Centroid-Moment-Tensor project at LamontDoherty Earth Observatory (LDEO). In the case of India, seismic data is sourced from the India Meteorological Department (IMD) located in New Delhi. Das et al. (2011) estimated errors for different magnitude determinations. To estimate the error of body wave magnitudes 238,525 events from NEIC and 348,423 events from ISC were used. For estimation of error in surface wave magnitude determination 16,019 events from NEIC and 81,974 events from ISC have been considered. For understanding the error of moment magnitude for 7634 events from NEIC and 27,229 events from 1976 to May 2007 have been considered. The errors of different magnitude types have been reported in Table 13.1. In our examination of Chilean seismic data, we incorporated information from multiple sources, specifically the National Earthquake Information Center (NEIC), which was accessed most recently in December 2016, and the National Seismological Service of the University of Chile (CSN). The CSN encompasses various databases, such as SISRA and NOAA. Additionally, we consulted the International Seismological Centre (ISC), with our last access to their data also occurring in December 2016.

13.5

Magnitude Conversion Relations

Magnitude data from multiple reputable sources such as the International Seismological Centre (ISC), National Earthquake Information Center (NEIC), Global Centroid Moment Tensor (GCMT) project, and specialized databases such as the Indian Meteorological Department (IMD) for the Indian region are commonly used to establish the relationships between different magnitude scales and the moment magnitude of seismic events. The following subsections explore magnitude conversion relations for the Indian subcontinent using various regression approaches as reported in various research. The most popular methods for converting magnitudes are the SR and ISR approaches, which presuppose that one of the variables (magnitudes) is constant and error-free. When considering uncertainties in the measurements of both the magnitudes being studied as well as the magnitudes they are being compared to, the general orthogonal regression (GOR) method is recommended for regression analysis. In such cases, using the standard regression (SR) and independent samples regression (ISR) techniques may lead to potentially unreliable estimations of the conversion magnitude.

13.5.1

Surface Wave Magnitude to Moment Magnitude (Ms/Mw)

Numerous research investigations have scrutinized the surface wave magnitudes calculated by both the National Earthquake Information Center (NEIC) and the

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International Seismological Centre (ISC), demonstrating their comparability (Utsu, 2002; Scordilis, 2006; Das & Wason, 2010). This equivalence is attributed to the fact that both sets of magnitude estimates rely on the same methodology. Scordilis (2006) utilized a standard regression (SR) approach to establish a relationship between the Ms., ISC, and Ms., NEIC magnitudes, validating their equivalence. In contrast, Das et al. (2011) established a relationship using the general orthogonal regression (GOR) method for the same purpose. Scordilis (2006) used a global dataset for shallow focus occurrences for the years 1978–2007 to determine the following SR connections between Ms and Mw: M w = 0:67 ð ± 0:005Þ M s þ 2:07 ð ± 0:03Þ, 3:1 ≤ M s ≤ 6:1

ð13:15Þ

M w = 0:99 ð ± 0:02Þ M s þ 0:08 ð ± 0:03Þ, 6:2 ≤ M s ≤ 8:7

ð13:16Þ

Using 24,807 occurrences for the Indian subcontinent, Das et al. (2011) were able to determine the following GOR correlations between Ms and Mw. M w = 0:67 ð ± 0:0005Þ M s þ 2:12 ð ± 0:0001Þ, 3:1 ≤ M s ≤ 6:1

ð13:17Þ

M w = 1:06 ð ± 0:0002Þ M s - 0:38 ð ± 0:006Þ, 6:2 ≤ M s ≤ 8:7

ð13:18Þ

13.5.2

Body Wave Magnitude to Moment Magnitude (mb/Mw)

Research has been conducted to analyze the disparities in body wave magnitude assessments offered by the National Earthquake Information Center (NEIC) and the International Seismological Centre (ISC). Through the utilization of a global dataset and employing a Standard Regression (SR) analysis, Scordilis (2006) identified certain deviations between the two magnitudes within the magnitude interval of 2.5 ≤ mb, NEIC ≤7.3. Das et al. (2011) examined seismic events data, comprising 23,281 events from ISC and 22,960 events from NEIC, spanning the period from January 1, 1976 to May 31, 2007. These events were associated with assigned moment magnitudes (Mw) values from the Global Centroid Moment Tensor (GCMT) project. The analysis revealed that the typical difference between mb, ISC, and mb, NEIC magnitudes is approximately ±0.04 magnitude units. However, the overall average difference is slightly larger, at around ±0.2 magnitude units. Notably, a slight discrepancy between the two mb determinations was also observed by Utsu (2002). Because of this, Das et al. (2011) took into account the two sets of data independently when determining the regression associations between mb and Mw. (a) SLR Relations For the magnitude range of 3.5 ≤ mb, ISC ≤ 6.2, Scordilis (2006) calculated a global SR relationship between mb, ISCand Mwas follows.

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M w,GCMT = 0:85 ð ± 0:04Þ mb,ISC þ 1:03 ð ± 0:23Þ

ð13:19Þ

Das et al. (2011) discovered a similar association for the magnitude range 2.9 ≤ mb, ISC ≤ 6.2 in the form: M w,GCMT = 0:65 ð ± 0:003Þ mb,ISC þ 1:65 ð ± 0:02Þ

ð13:20Þ

(b) GOR Relations A GOR link between mb and Mw was recently discovered by Wason et al. (2012), and it has the form: M w,GCMT = 1:13 ð ± 0:04Þ mb,ISC - 0:416 ð ± 0:23Þ,

ð13:21Þ

utilizing a better GOR technique taking η = 0.2.

13.5.3

Regression Relations for Northeast India Region

For the region of Northeast India, several regional regression relations have been constructed for the conversion of body wave magnitudes to moment magnitudes (e.g., Thingbaijam et al., 2008; Das et al., 2012, 2013). Thingbaijam et al. (2008) developed the following GOR relation depending on 30 events data and supposing η = 1, M w = 1:3691 ð ± 0:211Þ mb,ISC - 1:7742 ð ± 1:139Þ, for 4:4 ≤ mb,ISC ≤ 6:7

ð13:22Þ

The following GOR and SR relationships were determined by Das et al. (2012) for the magnitude range 4.7 ≤ mb, ISC ≤ 6.6. M w = 1:060 ð ± 0:05Þ mb,ISC þ 0:151 ð ± 0:263Þ, M w = 1:4 ð ± 0:0043Þ mb,ISC þ 1:98 ð ± 0:122Þ,

η = 0:36

ð13:23Þ ð13:24Þ

Similar to the above relation, Das et al. (2012) used146 events to develop the following SR and GOR relationships for mb, NEIC to Mw, and GCMTin the magnitude range 4.6 ≤ mb, NEIC ≤ 6.8 M w = 0:983 ð ± 0:054Þ mb,NEIC þ 0:216 ð ± 0:286Þ, M w = 1:37 ð ± 0:006Þ mb,NEIC - 1:77 ð ± 0:1567Þ,

η = 0:36:

ð13:25Þ ð13:26Þ

For the conversion of mb to Mw in the lack of region-specific relations, equivalent worldwide relations can be applied, especially for smaller magnitudes.

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13.5.4

187

Regression Relations for Northern Chile and Southern Peru

To convert mb, ISC to Mw, GCMT within the magnitude range of 4.3 ≤ mb, ISC ≤ 6.1, a similar transformation was performed for mb, NEIC to Mw, GCMT, considering magnitudes between 4.6 ≤ mb, NEIC ≤ 6.1, spanning the period from 1976 to 2013. Additionally, the conversion of mb, IDC to Mw, and GCMT were carried out for magnitudes falling within the range of 4.4 ≤ mb, and IDC ≤ 6.0, covering the period from 1989 to 2013. These transformations were established using General Orthogonal Regression 1 (GOR1) relationships, employing a parameter η of 0.2. The relationships were developed based on specific datasets containing 646 events for mb, ISC to Mw, GCMT conversion, 500 events for mb, NEIC to Mw, GCMT conversion, and 36 events for mb, IDC to Mw, GCMT conversion, as documented in the studies by Das et al. in 2011 and 2014. The regression parameters achieved for these conversion relations using GOR1 are given below: M w = 0:945 mb,ISC þ 0:496

ð13:27Þ

M w = 0:996 mb,ISC þ 0:159

ð13:28Þ

M w = 0:945 mb,ISC þ 0:496

ð13:29Þ

Das and Meneses (2021) derived conversion relationships for magnitude range 4.1 ≤ Ms, ISC ≤ 6.1 using 277 events as follows: M w = 0:677 M s,ISC þ 2:12

ð13:30Þ

Similarly, conversion relationships for MsNEIC to Mw have been estimated for magnitude range 4.1 ≤ Ms, NEIC ≤ 6.1 using 93 events as follows: Mw = 0:756 Ms,NEIC þ 1:715

ð13:31Þ

Recently, Das et al. (2023) established regression relationships between various magnitudes and Das Magnitude scale (Mwg) using a global dataset.

13.6

Conclusion

For any seismic study, particularly seismic hazard estimations, land use control, and other seismological applications, a unified earthquake catalog is essential. Various types of earthquake magnitudes needed to be converted into one unsaturated

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magnitude scale. Regression relationships have been utilized for converting one magnitude into a preferred magnitude. As earthquake magnitudes are in error, therefore, it is needed to use general orthogonal regression (GOR). The use of GOR needs η value and appropriate utilization of η values are critically important for slope estimation of regression analysis. In this chapter, the focus is on examining magnitude conversion relationships specific to the Northeast Indian region. These relationships have been documented in various works utilizing different regression techniques, including standard regression (SR), independent samples regression (ISR), and general orthogonal regression (GOR) methods. Notable studies in this context include works by Thingbaijam et al. (2008), Yadav et al. (2009), Das et al. (2011, 2012), and Wason et al. (2012). Additionally, the chapter also presents regression relationships for magnitude conversion relating to both body and surface wave magnitudes, which are relevant to regions such as Northern Chile and Southern Peru. To cover the complete magnitude range, Das et al. (2023) additionally included several GOR regression relations that were based on global data. When creating a unified earthquake catalog, the conversion regression relationship is crucial since any mistake in the magnitude conversion procedure could cause significant bias in the seismicity metrics.

References Bapat, A., Kulkarni, R. C., & Guha.S. K. (1962). Catalogue of earthquakes in India and neighbourhood. Indian Society of Earthquake Technology. Carroll, R. J., & Ruppert, D. (1996). The use and misuse of orthogonal regression in linear errors-invariables models. The American Statistician, 50(1), 1–6. Castellaro, S., Mulargia, F., & Kagan, Y. Y. (2006). Regression problems for magnitudes. Geophysical Journal International, 165(3), 913–930. Das, R., & Menesus, C. (2021). A unified moment magnitude earthquake catalog for Northeast India. Geomatics, Natural Hazards and Risk, 12(1), 167–180. Received 18 Jun 2019, Accepted 08 Dec 2020, Published online: 06 Jan 2021, ISSN 1947–5705 (Print). Das, R., Sharma, M. L., Wason, H. R., Choudhury, D., & Gonzalez, G. (2019). A seismic moment magnitude scale. Bulletin of the Seismological Society of America, 109(4), 1542–1555. Das, R., & Wason, H. R. (2010). A homogeneous and complete earthquake catalog for Northeast India and the adjoining region. Seismological Research Letters, 81, 232–234. Das, R., Wason, H. R., & Sharma, M. L. (2011). Global regression relations for conversion of surface wave and body wave magnitudes to moment magnitude. Natural Hazards, 59, 801–810. Das, R., Wason, H. R., & Sharma, M. L. (2012). Magnitude conversion to unified moment magnitude using orthogonal regression relation. Journal of Asian Earth Sciences, 50, 44–51. Das, R., Wason, H. R., & Sharma, M. L. (2013). General orthogonal regression relations between body-wave and moment magnitudes. Seismological Research Letters, 84(2), 219–224. Das, R., Wason, H. R., & Sharma, M. L. (2014). Unbiased estimation of moment magnitude from body-and surface-wave magnitudes. Bulletin of the Seismological Society of America, 104(4), 1802–1811. Das, R., Wason, H. R., Sharma, M. L., & Gonzalez, G. (2018). Reply to “comments on ‘Unbiased estimation of moment magnitude from body- and surface-wave magnitudes’ by R. Das, H.R. Wason and M. L. Sharma and ‘Comparative analysis of regression methods used for seismic magnitudes conversions’ by P. Gasperini, B. Lolli, and S. Castellaro” by J. Pujol. Bulletin of Seismological Society of America, 108(1), 540–547.

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Index

A Aftershocks, 33, 99–101, 103–106, 154, 160, 161 Arias intensity, 18–20

B Back scattering model, 121, 126 B values, 149–153, 155–157, 160, 161

C Coda Q, 125, 126, 130, 131, 133–143 Coda waves, 121, 122, 124–126, 129, 130, 133–138, 140 Coulomb stress model, 100, 102, 105, 106 Cut-and-paste (CAP) approach, 48, 52, 54, 60

E Earthquake catalogues, 5 Ecuador, 121–131

F fc, 28–31, 34, 40, 170 fmax model, 25–41, 170 Focal mechanism, 4, 39, 48, 165–177

G Garhwal-Kumaon Himalayas, 47–60 General orthogonal regression (GOR), 181, 182, 184–186, 188 Global positioning system (GPS), 65–68, 70–75, 77, 78, 101, 137 Gravity Recovery and Climate Experiment (GRACE), 65–78

H Himachal Lesser Himalaya, 133–143 Himalaya, 4, 5, 8–10, 15, 16, 21, 47–60, 68, 134, 140 Himalayan tectonics, 48 HK stacking, 81–97 Hydrological mass, 65

I Inverted standard regression (ISR), 181, 184, 188 ISOLA, 59, 165–177

J Japanese arc, 112–114

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 R. Kumar et al. (eds.), Recent Developments in Earthquake Seismology, https://doi.org/10.1007/978-3-031-47538-2

191

192 K κ-model, 26, 28–30, 34–38, 40, 41

L Lapse time windows, 125, 126, 130, 131

M Moho, 81–97, 126, 131 Moment constraint, 10–12 Moment tensor inversion, 52, 59, 170

N Northern Chile, 81–97, 179–188

P Philippines region, 153 Probabilistic seismic hazard analysis (PSHA), 1, 10–11

Index S Seismic hazards, 4, 5, 9, 10, 12, 40, 48, 60, 100, 106, 133, 152, 179, 181, 187 Seismicity, 2, 4, 5, 7–12, 16, 40, 48, 49, 60, 69, 82, 83, 97, 114, 124, 151, 152, 154–156, 158, 160, 161, 179, 180 Seismicity constraint, 10–12 Seismicity metrics, 188 Seismology, 1, 40, 47, 60, 149 Self-similarity, 25–41 Single backscattering model, 122, 125, 134, 135, 137 Source characteristics, 30, 112, 115, 118 Standard linear, 181 Statistical approach, 25–41 Strong-motion, 16, 17, 21, 25–41, 112, 169 Subduction zones, 39, 82, 84, 100, 103, 147, 148 Sumatra earthquake, 100, 101, 103 Surface and borehole data, 25–41

V Vertical crustal deformation, 66, 72–75 Q Qc, 122, 124–127, 130, 133, 136, 139, 140, 142, 143

R Receiver function, 81–97 Regression, 25, 33, 35, 40, 41, 115, 136, 138, 140, 142, 149, 179, 181–188

W Waveform inversion, 165–177

Z ZMAP, 151, 152