Studies in Analytical Geochemistry 9781487583323

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STUDIES IN ANALYTICAL GEOCHEMISTRY

THE ROY AL SOCIETY OF CANADA Special Publications 1. The Grenville Problem. Edited by

JAMES

E.

THOMPSON

2. The Proterozoic in Canada. Edited by

JAMES

3. Soils in Canada. Edited by

LEGGET

ROBERT

F.

E.

GILL

4. The Tectonics of the Canadian Shield. Edited by J. 5. Marine Distributions. Edited by M.

S. STEVENSON

J. D~NBAR

6. Studies in Analytical Geochemistry. Edited by

DENIS

M.

SHAW

STUDIES IN ANALYTICAL GEOCHEMISTRY

THE ROYAL SOCIETY OF CANADA SPECIAL PUBLICATIONS, NO. 6 Edited by Denis M. Shaw

PUBLISHED BY THE UNIVERSITY OF TORONTO PRESS IN CO-OPERATION WITH THE ROYAL SOCIETY OF CANADA 1963

Copyright, Canada, by University of Toronto Press 1963 Printed in Canada

Reprinted in 2018 ISBN 978-1-4875-8203-6 (paper)

PREFACE

IT IS DIFFICULT to define the aims and scope of a scientific discipline except in terms so general as to be of little use. Furthermore, since each science grows, evolves, and gives birth to daughter-disciplines which in time acquire their own creeds and liturgies, no definition has lasting value. It is consequently useful from time to time to gather in one volume a series of original contributions which, in addition to their intrinsic interest, serve to indicate something of the contemporary scope, technique, and philosophy of a field of scientific inquiry. Where such articles combine both original work and a review of relevant background material, they may be expected to appeal both to the specialist and to the interested layman, providing thereby the seeds for future growth. The present volume comprises such a group of papers, presented at a symposium held on Wednesday, June 6th, 1962, as part of the programme of Section III of the annual meetings of the Royal Society of Canada at McMaster University, Hamilton. It will be evident that no attempt was made to cover all fields of geochemistry: rather a series of contributions was solicited which, it was hoped, would illustrate some of the principal fields of interest, some of the methods of inquiry, and both the limitations and the future potential of geochemical research. Perhaps the principal omission is in the area of experimental or deductive geochemistry. The articles here presented are all concerned with inferential, analytical, inductive science and as such are to be considered as classical or Goldschmidtian geochemistry. They interpret, or treat of ways of interpreting, the chemical history of the crust of the earth, and, therefore, all share with geology itself the ineluctable necessity that their conclusions, containing the seeds of decay, will undergo revision in future years. This is, of course, no less true for experimental science, where model replaces model, but experimental geochemistry is so much more familiar to North American earth scientists that no' apology is :necessary for emphasizing here the inductive approach. The first article is by K. K. Turekian · and seeks to explore the contexts in which trace-element distribution studies can or cannot be of value for interpreting past environments or processes. A variety of careful traceelement studies by Professor Turekian and his associates document this interesting and provocative study in geochemical dialectics. A critical appraisal of the value of trace-element studies has long been overdue and this article helps the geologist to adopt the right perspective. The second and third articles are devoted to stable-isotope abundance variations in nature, by H. G. Thode and by R. N. Clayton respectively.

Vl

PREFACE

President Thode is widely-known among geologists and geochemists for his pioneering studies in isotope geology, and particularly for numerous studies of the mechanisms responsible for the fine structure of the natural distribution of sulphur which is provided by variations in the S32/S 34 ratios. His present article shows that the subject is far from being exhausted and provides hints of leading him headlong into the maelstrom of granite petrology. Professor Clayton, discussing oxygen isotope variations, is here concerned with extending the geothermometer conceived by H. C. Urey for measuring past ocean temperatures into the range of igneous and metamorphic conditions. In spite of formidable technical problems of preparation and measurement, isotopic thermometers possess an inherent advantage in being independent of the assumption of ideality of solution which plague element partition thermometers, and therefore offer a persuasive argument for continuing work in this promising field. The fourth paper by M. Fleischer and W. 0 . Robinson affords a synopsis of the geochemical distribution in the United States of America of the common but little-known element, fluorine. Of interest and value both to geochemists and to public health officials, one cannot but deplore the neglect of this kind of evidence in decisions concerning water supply and dental health. Of particular interest is the documentation of the fluorine content of common rocks, soils, and waters, including the possibility of regional variations within narrowly defined rock types. The article also demonstrates the necessity of such comprehensive analytical surveys to delineate the gaps-for example, the significance of bedrock on the fluorine content of water-in our comprehension of earth processes. In the succeeding article by E. H. T . Whitten we find a thorough summary of recent trends (sic) towards the employment of quantitative methods in the interpretation of granite terranes. Professor Whitten has advocated this approach in a number of interesting papers, and although such studies have in the past fallen more in the domain of petrology they hold a great and varied potential for future geochemical investigations, using as they do a powerful statistical approach which is valuable both for academic and for mineral exploration problems. . As all roads are said to lead to Rome, so all attempts to quantify an observational science must lead to probability statements. Following Professor Whitten's demonstration of the value of statistical methods in granite research, it is appropriate to conclude the volume with a more general statement legitimizing the union of statistics and geochemistry. The purpose of this contribution by G. V. Middleton is to indicate some interesting and more or less sophisticated statistical procedures which, although widely used as standard bench equipment in other inductive sciences are only just becoming established in geochemistry. Heedful, perhaps, of the common fallacy that anything can be proved by statistics, Professor Middleton is careful to emphasize that indeed nothing can so be proved, and stresses

PREFACE

vii

that statistics plays a justifiable role only when combined with scientific good sense. It is the lot of the geochemist to encounter from time to time the reproach that the spectrograph, the mass-spectrometer, or the digital computer appear to have superseded the hammer. Perhaps it is therefore worth repeating once again that most, if not all, geochemists are aware that the hammer comes first, and that their labours will be in vain if not preceded by careful field-work. Moreover, it should be remembered that if careful field-work alone cannot reveal all the intricacy of nature, it is not to be expected that our contemporary geochemical techniques will do so either. All we can expect is to see in a glass darkly and in the words of the late President G. P. Gilmour of McMaster University, "we remain confused, but at a higher level." ACKNOWLEDGMENTS THIS SYMPOSIUM could not have been arranged and published without the active encouragement of Dr. H. S. Armstrong, Vice-President, University of Alberta, and formerly Dean of Arts and Science at McMaster University. The assistance of Miss F. G. Halpenny and Mr. R. I. K. Davidson of the Editorial Department of the University of Toronto Press and of Miss J. Barrett, Secretary of the Geology Department, McMaster University, has been invaluable. DENIS M. SHAW

CONTENTS

Preface

v

Contributors

XI

The Use of Trace-Element Geochemistry in Solving Geologic KARL K. TUREKIAN Problems

3

H . G. THODE

25

Oxygen Isotope Geochemistry : Thermometry of Metamorphic ROBERT N . CLAYTON Rocks

42

Some Problems of the Geochemistry of Fluorine MICHAEL FLEISCHER and w. o.

ROBINSON

58

Application of Quantitative Methods in the Geochemical Study of E. H . TIMOTHY WHITTEN Granite Massifs

76

Sulphur Isotope Geochemistry

Statistical Inference in Geochemistry

GERARD V. MIDDLETON

124

CONTRIBUTORS

ROBERT N. CLAYTON,

Ill.

Enrico Fermi Institute, University of Chicago, Chicago,

MICHAEL FLEISCHER,

U .S. Geological Survey, Washington, D.C.

v. MIDDLETON, Department of Geology, McMaster University, Hamilton, Ont.

GERARD

w. o.

ROBINSON,

Falls Church, Va.

Department of Physical Chemistry, McMaster University, Hamilton, Ont.

H. G. THODE,

KARL K. TUREKIAN,

Conn.

Department of Geology, Yale University, New Haven,

E . H . TIMOTHY WHITTEN,

Evanston, Ill.

Department of Geology, Northwestern University,

STUDIES IN ANALYTICAL GEOCHEMISTRY

THE USE OF TRACE~ELEMENT GEOCHEMISTRY IN SOLVING GEOLOGIC PROBLEMS Karl K. Turekian

ABSTRACT

With the accumulation of many trace-element determinations of variable quality on a variety of geologically interesting materials, it has become evident that these data do not generally assist in the solution of geologic problems. The use of trace-elements in stratigraphic correlation ; in the delineation of the origin of certain metamorphic and igneous rock types; and in geochemical palaeoecology rarely give unambiguous results. Indeed, because of the role of mobility in disturbing a primary record, trace elements may find their greatest general use in studies of diagenesis, metasomatism, and processes associated with anatexis. The geochemical cycles of the elements remain of interest to the geochemist, but the scope of such studies may be too vast to be of interest to the geologist seeking local solutions. MY AIMS IN THIS PAPER ARE TWOFOLD: ( 1) to present a critique of some attempted uses of trace elements to solve specific geologic problems; and ( 2) to show how study of the geochemistry of trace elements for the purpose of adding this component to our total knowledge of the geologic realm may provide some limiting conditions for models of the history of the Earth's crust. On the basis of thousands of trace-element determinations on geologically interesting materials made by many investigators it appears that the use of trace-element geochemistry in providing solutions to classic and specific geologic problems has been only rarely successful. In many cases, what is reflected in the trace-element distribution may as easily be seen by more direct and immediate field or petrographic observations, making the trace-element contribution neither a unique nor a strongly confirmatory component to the solution of the geologic problem. In those cases where it is assumed that a direct index of the original trace-element composition is preserved in some phase of the rock and that this original composition gives a unique clue to the conditions of the initial formation of the geologic deposit, the indictment is even stronger: the vicissitudes of diagenesis, weathering, and metasomatism may so alter the original record as to show in its final composition a representation of its total complex history. Once this is suspected, the reconstruction of the original system itself becomes the major problem. On the other hand, a knowledge of the total behaviour of a trace element in the geologic realm, combined with other types of data ( e.g., isotopic, petrographic, oceanographic), may often put limiting conditions on the

4

KARL K. TUREKIAN

history of the Earth's crust and upper mantle. That is, models of the development of some feature of the Earth may also have to explain the observed trace-element distribution. The first part of this paper will deal primarily with a critique of some of the attempts at using trace elements for solving specific geologic problems and the second part will discuss the conditions that some geochemical studies of trace-elements put on various Earth models. METAMORPHIC AND GRANITIC ROCKS

It has become increasingly apparent that most metamorphic processes, from the lowest grade to the point at which an anatectic melt may be formed, involve some degree of metasomatism. This fact will complicate any program for determining the nature of pre-metamorphic materials using trace elements.

Amphibolites One such enterprise has been to try to distinguish amphibolites of originally sedimentary origin from those of igneous origin. It is of course obvious that this distinction arises from the fact that the proportions of the major non-volatile elements of some sedimentary assemblages are the same as in basaltic rocks and amphibolites. Because of the different modes of formation of the possible parental materials it is to be expected, however, that the trace-element complexion will be different. If we compare the trace-element composition of shales ( with the assumption that the carbonate fraction accompanying the shale is a neutral component for all trace components except strontium) with basalts, we see that the elements of Table I TABLE COMPARISON

o~-

I

SOME TRACE-ELEMENT CONCENTRATIONS IN BASALTS AND SHALES

(from Turekian and \'Vedepohl, 1961)

Basalt Shale (parts per million) Lithium Beryllium Boron Arsenic Rubidium Tin Antimony Cesium

17 1 5

2

30

l. 5 0.2 1.1

66 3 100 13 140 6 1.5 5

are the most likely candidates as fingerprints of origin. Unfortunately these elements are also likely to be highly mobile in the wet metamorphism presumably involved in the formation of amphibolites. One of the elements, tin, seemed to be a good one to try for verification or rejection of this method of distinguishing ortho- from para-amphibolites.

COBALT IN GRANITIC ROCKS 1.0

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:! V)

. w

zt!)

::;

OJ

•

~

lot Mt• l.20 + 0.99109Co

0.01.__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __

0.1

1.0

10 PPM COBALT

F10URB

1 (a). Scatter diagram for cobalt and magnesium in granitic rocks (Carr and Turekian, 1961 ) • 10 , - - . . . . . - - - - - - - - - - - - - - - - - . . - - - - - .

5

0

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5

10

50

100

200

PPM CHROMIUM F10URE

1 (b). Scatter diagram for chromium and magnesium in granitic rocks (Carr and Turekian, 1962).

6

KARL K. TUREKIAN

T. Offield, working with me, determined tin in sedimentary, igneous, and metamorphic rocks of approximate major-chemical equivalence and found no simple correlation with rock type or inferred origin. The other elements of Table I are likely to be as mobile as tin, if not more so, and the level of concentration in an amphibolite may as easily be related to the trace-element complexion of the total metamorphosed system as to its originalcomposition. It would be difficult to distinguish between these alternatives from traceelement studies alone. An attempt to use strontium to relate an amphibolite terrane to an unmetamorphosed, possibly related dike swarm proved unsuccessful (Turekian and Kulp, 1956; Wilcox and Poldervaart, 1958) although differences were observed amongst the various amphibolitic groups sampled.

Granites In the light of the processes that make the ongm of amphibolites ambiguous, the problem of the origin of granitic rocks is not likely to be aided by trace-element studies. By this I mean that mechanisms for the formation of granitic material, e.g., by anatectic processes or "granitization," cannot be distinguished by the trace-element assemblage of the resulting granitic rock. Several trace elements studied carefully indicate their concentrations are related to the concentrations of various major elements which in turn are controlled in part by the temperature of formation of the granitic sequence and in part by other factors ( Winkler and von Platen, 1960) . Figure 1 shows the relationships observed for cobalt and chromium in relation to magnesium. Also strontium has been shown (Turekian and Kulp, 1956) to be strongly related to calcium, and other elements may show similar relationships. Certain volatile components such as boron and tin may be higher or lower in various granitic sequences, but the emplacement processes are probably as responsible for this as the original sources of the material composing the rock. At any rate, the petrography and field relations are likely to be better clues to these various factors than the trace-element chemistry. Distribution between Coexisting Phases Under equilibrium conditions the distribution of trace elements must obey the thermodynamic rule that the chemical potential of any particular component must be the same in all coexisting phases. As it is commonly assumed that in regional metamorphism the phases present represent equilibrium assemblages, it has been natural to assume further that the trace elements should demonstrate some regular distribution pattern. In the case of the major components, Mueller ( 1961) has shown that this is generally obeyed for coexisting pyroxenes. For a minor though important component, manganese, both Mueller's data and that of Kretz ( 1959) are consistent with an equilibrium distribution. On the other hand, both Kretz ( 1959) and Turekian and Phinney ( 1962) found that some of the common trace

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1 micron fraction is the same as that for the < 1 micron fraction. The fine fraction is richer in montmorillonite and mixed-layer illite-montmorillonite than the coarse and the reverse holds for illite ( kaolinite is a minor component). Such a result confounds the origins of boron in the clay mineral component as it is related to salinity or for that matter any other parameter. The ultimate composition of a newly deposited clay mineral assemblage then must be a function of: ( 1 ) the proportion of different minerals constituting the clay size fraction chosen; ( 2) the proportion of detrital to authigenic minerals in the clay size fraction chosen; ( 3) the original concentration of boron in the detrital fraction; ( 4) the change in concentration due to incorporation of boron from the sea on the detrital fraction; and ( 5) the boron concentration in the authigenic fraction-the factor which is likely to be the best reflection of the boron concentration of the water from which it is formed. To these conditions, for which knowledge is required to use boron as a salinity indicator, later complicating events must be considered. Where the rate of accumulation is slow, as in deep-sea sediments, the authigenic component may be formed at various depths in the sediment column and, as the salinity and composition of the interstitial waters are not necessaril)' the same as the overlying ocean water, any clay formed or altered in such

THE USE OF TRACE-ELEMENT GEOCHEMISTRY

15

locations "authigenically" will have a boron concentration of uncertain significance. In older rocks formed in regions of geosynclinal sedimentation the high temperatures encountered at depth and the presence of connate brines, as in the Gulf Coast geosyncline, provide suitable conditions for adjusting the boron concentration of the clay fraction to the conditions during diagenesis. Hence I believe that boron and other elements, such as gallium, rubidium, and lithium ( Keith and Degens, 1958) subject to the same uncertainties of interpretation, will rarely give information that is not available from paleontologic and stratigraphic methods of investigation. Stratigraphic Correlation The trace-element geochemistry of the Flon~na shale (Permian) has been studied in collaboration with John Imbric of Columbia University. This unit, at most fourteen feet thick but easily identifiable in surface outcrops and from subsurface records, has a varying trace-element composition both vertically and laterally. Both the influence of local sedimentation conditions and subsequent diagenetic history are considered to be contributing factors. Variations of up to ten times the minimum values were observed for strontium, copper, and lead in a north-south traverse from Nebraska to Oklahoma and somewhat smaller differences within a vertical section ( Fig. 5). With such variations it is doubtful whether trace elements can be used for stratigraphic correlation in place of normal geologic criteria. Even in cases where specific strata may have a particularly high abundance of a trace element because of the presence of a distinctive mineral assemblage, a study of the latter would be more fundamental and profitable than of the derivative trace-element complexion. FOSSILS

Fossil marine carbonate shells have been examined chemically or isotopically in recent studies to find out ( 1 ) what can be learned about the composition of ancient seas; ( 2) what record of local environmental conditions, temperature and salinity, are preserved in the shell; and ( 3) to what extent they can be used for radioactive geochronometry. Of course the fundamental step in approaching these questions from a uniformitarian point of view is to study contemporary effects of water composition, salinity and temperature on the chemical and isotopic compositions of calcareous tests. Such studies have been made for a variety of parameters including the strontium-calcium ratio, the magnesium-calcium ratio, and the oxygen isotopic composition. The next step, namely the application of the observed relationships to fossil remains, encounters difficulties because of the possible disturbance of the original record by diagenetic processes.

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FIGURE S(a), (b). Trace-element distribution in the Florena Shale (Permian) mainly in Kansas. The left-hand side represents the northernmost sections starting in Nebraska and the right-hand side represents the southernmost ending in Oklahoma. Sampling along the Nemaha Ridge primarily. Length of bar represents extreme range of values and circle represents mean.

17

THE USE OF TRACE-ELEMENT GEOCHEMISTRY 40

~ 30

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FLORENA SHALE FIGURE 5(c). Trace-element distribution in the Florena Shale (Permian) mainly in Kansas. See previous page.

To be able to evaluate the strontium-calcium ratio of an ancient sea, for example, one may hope to measure it as preserved by some organism whose original composition and subsequent diagenetic history are known. One may make estimates of the composition by means of models of material balance in the oceans. I believe that if it is possible, both approaches should be attempted and checked against each other. Lowenstam ( 1961) has made an attempt to set limits by the first method using modem and fossil brachiopods. He determined the strontium and magnesium concentrations and oxygen isotope ratios and plotted trends for . modem shells from different marine environments: these are shown as bands defined by the solid lines in Figure 6. Apparently well-preserved fossil brachiopods were similarly analysed and the results plotted and

18

KARL K. TUREKIAN

.20 ~ 0 0

E ,..,.15 0

...

0

(/)

.10

.05 2.0

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-3.0

18 O contents)

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-2.0

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. 18 ratios (not corrected for O contents)

PL= Pliocene

C= Cretaceous

P = Permian

M = Mississippian

6. Curves taken from Lowenstam ( 1961). Note that the "envelope" is constructed from the range of values observed in modern brachiopods and corrected for salinity.

FIGURE

19

THE USE OF TRACE-ELEMENT GEOCHEMISTRY

compared to the contemporary trends ( Fig. 6). On this basis he concludes that the strontium concentration in sea water has remained constant at least since the late Paleozoic. The wide scatter of points in the strontium curve ( half fall out of the modern salinity-corrected trend) and the fact that almost all the magnesium points do not follow the contemporary Mg-oxygen isotope salinity-corrected curve indicate that we are dealing with a system which may have been disturbed by diagenesis. If foolproof methods of eliminating those shells with maximum alteration can be devised, then the method may still have validity, but Lowenstam's published results do not provide that certainty. We have recently completed a study of the mineralogy and chemistry of fossil molluscan shells from concretions in the Fox Hills formation (Turekian and Armstrong, 1961 ) . The study was understaken on this material because the formation represents deposition during the last retreat of the Cretaceous epeiric sea and was hence of paleoecologic significance, and the fossils appeared to be excellently preserved.

Q: . 0

6,MINIMUM VALUES ONLY

500 0.1

10

100

% CALCITE F10URE

7. Curve from Turekian and Armstrong ( 1961) for shell data on Sphenodiscus from concretions in the Fox Hills formation (Cretaceous), South Dakota.

The results of a systematic study of the mineralogy and stronium concentration of a wide variety of shell material from specimens of an ammonite, Sphenodiscus, are seen in Figure 7. Thin sections of some modern and Fox Hill cephalopod tests indicate that shell structure and mineral orientation were retained for the aragonite-rich material during diagenesis. The strontium content of pure aragonite chips of Sphenodiscus shell, however, is twice as high as modern Nautilus and increases in the range 2 to 10 per cent calcite ( due to partial recrystallization) to four times as high. The "normal" decrease in strontium concentration with increase in calcite occurs thereafter. Other trace elements (Mg, Mn, Fe, and Ba) also do not compare with contemporary shell composition.

20

KARL K. TUREKIAN

The common criteria for preservation, either unaltered mineralogy or crystal orientation in this case, do not guarantee a sure knowledge of the trace-element composition of the original shell. The problem of original crystal orientation preservation during diagenesis has received light from the recent work of Raup ( 1959) on echinoids. Although echinoids have highly porous tests when calcite is added to the test during diagenesis, the original crystal orientation is commonly preserved. A mosaic calcite assemblage need not result. It may then be inferred that in the addition or replacement of calcium carbonate in spaces left in the framework of more compact tests ( such as molluscan tests) by the removal of organic material for instance, the process may proceed while crystal orientation is maintained. In such a case crystal orientation cannot be used as a criterion for per£ect chemical preservation.

GEOCHEMICAL CYCLES OF TRACE ELEMENTS WITH RELATION TO GEOLOGIC MODELS

Although the previous discussion was essentially a critique of some attempts to use trace elements in solving geologic problems, there was at least one situation in which a knowledge ( empirical rather than theoretical) of the distribution of some elements in a system provided a limiting condition for the construction of a geologic model. I believe this is the most important role of trace-element geochemistry at the present time and I hope the following examples will show the utility of trace-element geochemistry as a discipline in itself to provide conditions for geologic models.

The Geochemistry of Strontium The possibility of dating limestones by measuring the presumably steadily increasing Sr87 /Sr 86 with time ( due to the perennial addition of Sr87 from the decay of Rb 87 in a closed system) was suggested by Wickman ( 1948). Subsequent revisions in "crustal abundance" estimates for strontium ( Turekian and Kulp, 1956) and rubidium ( Horstmann, 195 7) diminished the Sr87 /Sr86 growth with time in the oceans to be expected from simple crustal models. Cast's ( 1955) data on limestones of various ages indicated only a small variation over the last 2.5 billion years. Hence even the best ratio of "crustal abundances" of Sr to Rb are not adequate to explain this constancy for most models of crustal composition. The conditions set by these data are that ( 1 ) the crust cannot be treated as a closed system-that is, it receives material from the mantle-and (2) neither rocks of all ages nor all rock types are equal contributors of strontium in solutiof! to the oceans. This itself implies that one should be able to find variations in the Sr87 /Sr 86 ratio in limestones which are not simply time-dependent.

THE USE OF TRACE-ELEMENT GEOCHEMISTRY

21

Geochemical Balance If one attempts to construct ever more complicated geochemical balance equations of the type used by Goldschmidt ( 1954) , Wickman ( 1954) , and Goldberg and Arrhenius ( 1958), one must ultimately use the trace elements. For any chemical element i, the material balance equation is: n

L ak txk = m1,

(1)

k=l

where

m,

the total mass of the element in the sea, concentration of element i in rock or sediment type k, and Xk total mass of the rock or sediment type k involved in the trans£er of material during weathering and sedimentation. If there were no errors in sampling or analysis and if the various m, were known, then the simultaneous solution of ten such equations for ten different elements would give a unique value of the amount of each of the ten principal rock types involved in the trans£er of material, provided that the closed system assumption were valid. The sign associated with each rock type would also determine whether that particular rock were a "source" or a "sink"-positive for the former and negative for the latter ( determined by the positive value for m,) . It is actually necessary to consider more than the minimal number of such equations to arrive at a best solution because of unavoidable errors in judgment, sampling, or analysis inherent in the estimations of the elemental concentrations. James C. G. Walker (formerly of Yale University and now at the Lamont Geological Observatory) working with me, programmed such calculations for a high-speed computer. The data, ak, and m,, were derived from the compilations of Turekian and W edepohl ( 1961 ) , Sillen ( 1961), and Goldberg ( 1960). The rock types used were as follows: UM Ultramafic SH Shale SS Sandstone B Basalt GD Granodiorite LS Limestone G Granite C Carbonate deep-sea sediments SY Syenite P Pelagic clay sediments Table V gives the results obtained for four selections of data based on completeness of data and geochemical properties. Selection A includes all non-volatile elements whose abundances have been estimated numerically in at least nine out of the ten rock types, and using an order of magnitude estimate ( e.g. 10 per cent for the order 10-100 per cent) in the remaining rock types. Selection B comprises only those elements of selection A for which the numerical data are complete. Selection C is the same as selection A, except that elements in greatly different concentration in the Atlantic and Pacific pelagic clay deposits have been omitted. Selection D is the same as C but includes only those elements for which the data are complete. aki

TABLE V SOLUTIONS OF GEOCHEMICAL BALANCE EQUATIONS USING VAKIOUS COMBINATIONS OF ROCK DATA AND OCEANIC ABUNDANCE ESTIMATES (units in 1021 grams) Sink

Source

Solution (A, 1) UM 36

S.D. = 34300 G 370 SH 600 LS 80

Solution (B, 1) UM 36 B 17 GD 360 SY 460 ss 100 C 52 P 8.2

S.D.

Solution (B, 2) UM 35 B 16 GD 340 SY 450

S. D.

B

17

GD 360 SY 450 ss 100 C 53 8 .3 P Solution (A, 2) UM 36 B 17 GD 340 SY 450

ss

C

P

A B C

I)

S.D.

= 33900

G 360

SH 590 LS 77

ss

98

P

7.9

Li

Na Mg Al

99

C 49

50

Si

K

Ca

Sc

Source

Sink

Source

= 38400 G 370 SH 600 LS 80

Solution (C, 1) UM 16 B 93 GD 180 G 170 SY 22

V

Solution UM B GD G SY

P 2:30

P 230

= :38000 G 370 SH .'>90 LS 7ti

Solution (C, 2) UM 1/i B 92 GD 170 G 170 SY 21 C

S. D. = 8590 SH 680 ss 44 LS 38

30

P 220

Rock Data (Turekian and Wedepohl) Cr Mn Fe Co Ni Cu Zn Ga Ge As Rb Sr All used

0 + + + + + + + + + + + + + + + + + + + + + + + + 0 + 0 0 + 0 + + + + + + + + + + 0 + 0 0

0 0 0

S.D. = 6670 SH 690 ss 44 LS 42

(D, 1) 16 93 180 170 21

c aa

C 3:3

7.8

Ti

S.D. = 8820 SH 690 ss 43 LS 42

Sink

Source

Sink

s. =D. 6530

Solution (D, 2) UM 15 B 92 GD 170 G 180 SY 20 C 30 P 230

y

SH 680 ss 44

LS

38

Zr Nb Mo Tl Pb Th

+ + + + + 0 + 0 + + 0 + 0 0 + + + + + 0 0 + 0 0 + + 0 + 0 0

0 0 0

+ 0 0

0 0 0

u 0 0 0

Sea-Water Data 1. Sillen 2. Goldberg C

UM = Ultramafic, B = Basalt, GD = Granodiorite, G = Granite, SY = Syenite, SH Carbonate Deep-sea Sediments, P = Pelagic Clay sediments S.D. = Standard deviation of fit, taken as the R.M.S. of the residuals from each element + : Data used; O: data not used

=

=

Shale,

SS

=

Sandstone,

LS

=

Limestone,

THE USE OF TRACE-ELEMENT GEOCHEMISTRY

23

It is evident when comparing A with B and C with D that no great changes in the results arise from the elimination of the slightly less reliable data. On the other hand, there is a significant difference between the pair A, B, and the pair C, D. In both cases, however, the results lack any correlation with known geologic occurrences of these rock and sediment types. This implies that the equations are not complete, reflecting the fact that we really have not represented the composition of the crust accurately, and we are again deflected from an acceptance of a closed system model for the crust and a certainty of the composition of the deep crust. CONCLUSION

Trace-element geochemistry can rarely offer unique or strongly confirmatory solutions to classic specific geologic problems such as the origin of amphibolites or granites and the nature of ancient sedimentary environments. The study of the distribution of trace elements can be useful in setting conditions on models of crustal development and in this role it is a significant contribution to our knowledge of the history of the Earth. REFERENCES AHRENS, L. H ., PINSON, W. H ., and KEARNS, M. M. (1952). Association of rubidium and potassium in common igneous rocks and meteorites. Geochim. et Cosmochim. Acta 2: 229-42 . BARAGAR, W. R . ( 1960) . Petrology of basaltic rocks in part of the Labrador Trough . Bull. Geo!. Soc. Am. 71: 1589-644. CARR, M . H ., and TuREKIAN, K. K. ( 1961) . The geochemistry of cobalt. Geochim. et Cosmochim. Acta 23: 9-60. - - - ( 1962). Chromium in granitic rocks. Geochim ct Cosmochim. Acta 26: 411-15. CHAO, E. C . T., and FLEISCHER, M . ( 1960). Abundance of zirconium in igneous rocks. lnternat. Geo!. Cong., 21st, Copenhagen 1960, Proc. Sec. 1, pt. 1, 106-31. DAWSON, J.B. (1962). Basutoland kimberlites. Bull. Geo!. Soc. Am. 73: 545-70. DEGENS, E. T., WILLIAMS, E. G., and KEITH, M . L . ( 1957) . Environmental studies of Carboniferous sediments, part I: geochemical criteria for differentiating marine and fresh water shales : Bull. Am. Assoc. Petrol. Geologists 41: 2427-55. EvERNDEN, J. F ., CURTIS , G . H ., OBRADOVICH, J., and KISTLER, R. (1961) . On the evaluation of glauconite and illite for dating sedimentary rocks by the potassiumargon method. Geochim. et Cosmochim. Acta 23: 78-99. FAURE, G ., HURLEY, P. M., FAIRBAIRN, H. W., and PINSON, W. H. ( 1962). Isotopic compositions of strontium in continental basic intrusives. J. Geophys. Research 67 : 3556-7. FREDERICKSON, A. F., and REYNOLDS, R. C., JR. (1960). Geochemical method for determining paleosalinity in clays and clay minerals. In 8th Natl. Conf. Clays and Clay Minerals Proc. 203-13. New York: Pergamon Press. GAST, P. W . ( 1955). Abundance of Sr87 during geologic time. Bull. Geo!. Soc. Am. 66: 1449-54. - - - ( 1960). Limitations on the composition of the upper mantle. J. Geophys. Research 65: 1287-97. GOLDBERG, E. D. ( 1960). Composition of sea water. In Encyclopedia of Science and Technology 12 : 549-52. New York : McGraw-Hill.

24

KARL K. TUREKIAN

and ARRHENIUS, G. 0. S. (1958). Chemistry of Pacific pelagic sediments. Geochim. et Cosmochim. Acta 13: 153-212. GOLDSCHMIDT, V. M. ( 1954). Geochemistry. Oxford: Oxford University Press. HARDER, H . ( 1961). Einbau von Bor in detritische Tonminerale. Geochim. et Cosmochim. Acta 21: 284-94. HowER, J., HURLEY, P. M., PINSON, W. H., and FAIRBAIRN, H. W. (1961). Effect of mineralogy on Kl Ar age as a function of particle size in shale. Geo!. Soc. Am. Spec. Paper 68: 201-2. HORSTMAN, E. L. ( 1957). The distribution of lithium, rubidium and caesium in igneous and sedimentary rocks. Geochim. et Cosmochim. Acta 12: 1-28. KEITH, M. L. and DEGENs, E. T. ( 1958). Geochemical indicators of marine and freshwater sediments. In Abelson, ed., Researches in Geochemistry, 38-61. New York: Wiley. KRETZ, R. ( 1959). Chemical study of garnet, biotite, and hornblende from gneisses of Southwestern Quebec with emphasis on distribution of elements in coexisting minerals. J. Geo!. 67: 371-402. LANDERGREN, S. ( 1945) . Contribution to the geochemistry of boron II: The distribution of boron in some Swedish sediments, rocks and iron ores. Arkiv Kemi Mineral. Geol. 19A: no. 26. LOWEN STAM, H. A. ( 1961). Mineralogy, Q18/Q16 ratios, and strontium and magnesium contents of recent and fossil brachiopods and their bearing on the history of the oceans. J. Geo!. 69: 241-60. MUELLER, R. F. ( 1961). Analysis of relations among Mg, Fe and Mn in certain metamorphic minerals. Geochim. et Cosmochim. Acta 25: 267-96. NocKOLDs, S. R., and ALLEN, R. (1956). The geochemistry of some igneous rock series111. Geochim. et Cosmochim. Acta 9: 34-77. RAUP, D. M. (1959). Crystallography of echinoid calcite. J. Geo!. 67: 661-74. RUCKER, J. B., and VALENTINE, J. W. (1961). Paleosalinity prediction using traceelement concentrations on oyster shells. Geo!. Soc. Am. Spec. Paper 68: 257-8. S1LLEN, L. G. ( 1961). The physical chemistry of sea water. In M. SEARS, ed., Oceanography, 549-81. American Association for the Advancement of Science. ToURTELOT, H. A., SCHULTZ, L. G., and HUFFMAN, C. ( 1961). Boron in bentonite and shale from the Pierre shale, South Dakota, Wyoming, and Montana. U.S. Geo!. Survey Prof. Paper 424 C: 282-92. TUREKIAN, K. K. ( 1956). The abundance of Cu, Ni, and Cr, in basaltic rocks. Trans. Am. Geophys. Un. 3 7: 361 (abstract) . - - - and ARMSTRONG, R. L. ( 1961). The composition of fossil shells from the Fox Hills formation, South Dakota. Bull. Geo!. Soc. Am. 72: 1817-28. - - - and CARR, M. H. ( 1960). The geochemistries of chromium, cobalt, and nickel. Report XXI Session, Intern. Geo!. Cong., Pt I, 14-26. - - - and KULP, J. L. ( 1956). The geochemistry of strontium. Geochim. et Cosmochim. Acta 10: 245-96. - - - and PHINNEY, W. C. (1962). The distribution of Ni, Co, Cr, Cu, Ba and Sr between biotite-garnet pairs in a metamorphic sequence. Am. Mineralogist 47: 1434--41 . - - - and WEDEPOHL, K. H. ( 1961). Distribution of the elements in some major units of the Earth's crust. Bull. Geo!. Soc. Am. 72: 175-192. WICKMAN, F. E. (1948). Isotope ratios: a clue to the age of certain marine sediments. J. Geo!. 56: 61-6. - - - ( 1954). The "total" amount of sediments and the composition of the "average igneous rock." Geochim. et Cosmochim. Acta 5: 97-110. W1Lcox, R. E., and PoLDERVAART, A. ( 1958). Metadolerite dike swarm in BakersvilleRoan Mountain area, North Carolina. Bull. Geo!. Soc. Am. 69: 1323-68. WINKLER, H. G. F., and VON PLATEN, H. ( 1960). Experimentelle Gesteinsmetamorphose. III. Anatektische Ultrametamorphose kalkhaltizer Tone. Geochim. et Cosmochim. Acta 18: 294-316. YODER, H. S., and TILLEY, C. E. (1962). Origin of basalt magmas. J. Petrology, 3: 342-532.

SULPHUR ISOTOPE GEOCHEMISTRY H. G. Thode

ABSTRACT

Further studies have been made of the S32/34 ratios in meteorites, basic sills, and other igneous intrusives. The average S32/S34 ratio obtained for meteorites is compared to average values found for terrestrial samples including some basic igneous intrusives. Further, the meteoritic ratio is discussed as a standard for sulphur isotope measurements and as a possible base level from which fractionation of the sulphur isotopes in the earth's crust began. Finally, the sulphur isotope distribution in the Precambrian rocks of the Sudbury and Algoma district will be discussed in the light of our knowledge of sulphur isotope geochemistry.

that many processes in nature are accompanied by isotope fractionation. For example, carbonate precipitated in oceans will become enriched in the heavy isotope of oxygen, 0 18 , relative to the ocean water. Plants are enriched in the light isotope of carbon, C12, relative to carbon dioxide in the air and, finally, sulphate in the sea is enriched in the heavy isotope of sulphur, S3 4, relative to sulphur in meteorites and in basic igneous rock. Studies of variations in the abundance of stable isotopes have already contributed to our understanding of various natural processes and should do so to an even greater extent in the future. Studies of the distribution of the sulphur isotopes in nature have been of particular interest because of the wide distribution of sulphur in the earth and because of the variety of forms of sulphur which exist. The four stable isotopes of sulphur with their approximate relative abundances are: S32 ( 95 per cent) ; S33 ( 0. 7 per cent) ; S34 ( 4 .2 per cent) ; and S36 ( 0.017 per cent). For the most part, we have been concerned with the variations in the S32 /S 34 ratios since these are the two most abundant isotopes. Where both S32 / S34 and S32 /S 33 ratios have been investigated, the variations in the S32/S 34 ratios are always double those found for S32/S 33 in accordance with theoretical predictions. Figure 1 shows, in a general way, the variations that occur in the S32 /S 34 ratio of sulphur from different natural sources. In the measurement of ,·ariations in the S32 / S34 ratios which occur, each sample is compared to a standard and the results are expressed in terms of 8S 34 %0 defined as follows: IT 1s Now KNOWN

26

H . G. THODE

Since the S32 /S 34 ratio for sulphur in meteorites is remarkably constant, this ratio has been taken as the standard and the 8-value for meteorites becomes SS 34 %o meteorites

= 0.

Meteoritic Sulphur Standard It is seen from Figure 1 that the S34 content of sulphur in the earth's crust and mantle varies by ~ 100%0. This is in striking contrast to the sulphur in meteorites ( Macnamara and Thode, 1950; Vinogradov, 1958). Seven+50

+40

+30

+20

+10

----•

Ss34 -,.. -10

••

-20

BAS IC

--- - -

SILLS

----

• ••

IGNEOUS ROCKS

SEA

- - --..

-50

METEORITES

s0

-

-40

-30

of

')

--

VOLCAN I C ORIGIN

WATER

EVAPORITES

RAIN

and

SNOW

SEDIMENTARY

z)

SULPHIDES

PETROLEUM

COAL

FIGURE

1)

INCLUDING

Z)

EXCLUDING

GIUNITIZEO RAIN

ANO

OR

RE ·WORKED

SNOW

fROII

S[Olll[NTS INDUSTRIAL

1. Sulphur Isotope Distribution in Nature ( 3

AREAS

=S84).

teen meteorites of various kinds were found to have S32 /S 84 ratios within 0.2%0 or ( 8S34 0 ± 0.2%0) (Thode, Monster, and Dunford, 1961). Recent studies of the Orgueil meteorite, a carbonaceous chondrite, which contained elemental sulphur, sulphate, and sulphide (FeS) showed some sulphur isotopic difference between the elemental sulphur and the sulphate. However, the isotope fractionation was relatively small, + 2%o, and the

=

27

SULPHUR ISOTOPE GEOCHEMISTRY

=

weighted average for the two forms of sulphur was close to S 0 (Monster, Anders, and Thode, unpublished work) . In the interpretation of the isotope distribution data in terms of natural processes and earth history, it is essential that we know the base levels of isotope ratio from which isotope fractionation occurred. In the case of the sulphur isotopes, meteoritic sulphur provides perhaps the most important base level from which isotopic fractionation may be reckoned. The fact that the sulphur isotope ratio for meteorites is remarkably constant and that its value coincides approximately with the median ratio found for terrestrial samples led Macnamara and Thode ( 1950) to suggest that it was indeed the primordial value. Early results of Macnamara et al. ( 1952) showed that there was considerable spread in the S32 /S 34 ratio for sulphides from igneous rock occurrences and that although the values obtained overlapped the value given for meteorites, there was a preponderance of samples with a slight enrichment of S34 ( 8 3%o). They suggested the possibility of some isotope fractionation during the differentiation and crystallization of magmas. Also, Vinogradov et al. ( 195 7) and Vinogradov ( 1958) reported similar fluctuation in the isotopic content of sulphides in acid and basic rocks, although for ultra-basic rocks, such as pyroxenite and dunite, he obtained a fairly constant sulphur isotope ratio corresponding to the ratio of cosmic sulphur (meteorites). Ault and Kulp ( 1959), on the basis of the average S32 /S 34 ratio for sulphide from a limited number of mafic rocks ( 8 2.3%0), granitic plutonic rocks including pegmatites ( 8 + 3.6%0), and hydrothermal deposits ( 8 4 .1 %0) reported in the literature, concluded that the average isotope ratio for the earth's crust and mantle is 8 3.6%0 rather than 8 0%o. Thode et al. ( 1961) pointed out that this conclusion was based on very limited data. They suggested a detailed study of a number of basic intrusives in order to establish an average S32 /S 34 ratio for the earth's crust and mantle.

=+

=

=+

=+

=+

=

Basic Sills On the assumption that the sulphur occurring in ultra-basic or basic flat-lying intrusive sheets might give an approximation of the primordial 8S34 value of sub-crustal or mantle material, Shima, Gross, and Thode ( 1963) investigated four such large sills in some considerable detail. The following sills were investigated: Palisades Sill, New Jersey, U.S.A.; Cobalt Sill, Ontario, Canada; Leitch Sill, Ontario, Canada; Insizwa Sill, East Griqualand, South Africa. Samples were available for chemical and isotopic analyses from the lower to the upper contact of the Leitch, Cobalt, and Palisades sills, and from 3000 feet of the lnsizwa sheet measured from the lower contact. The four sills range from about 1000 to 4000 feet in thickness and show various degrees of differentiation. Weighted mean values of 8S34 %o were 0.95%0, 1.0%0, 0.70%c, and 0.1%0 for the Palisades, lnsizwa, Cobalt, and Leitch sills respectively. Tables I and II give the

+

+

+

28

H. G. THODE

TABLE I* SULl'Ht:R ISOTOPE DISTRIBUTION: INSIZWA SILL

Location (feet) (Distance above bottom contact)

2200 2100 1900 1800 1700 1600 1500 1400 1300 1200 1100 1000 900 800 700 10 10 10

s

Description Gabbro

(%)

SiO2 (%)

0.10 0 . 13 0 . 12 0 . 18 0.09 0 .02 0 .08 0 .09 0 . 10 0 .07 0 . 12 0 . 12 0 . 15 0.18 0 .20 30 30 30

"

48 .87 47 .31 50.16 51.20 46 .34 52.00

-1.35 -0.40 +3 .25 +3 .05 +0 .85 -0 .70 -0.60 +0.30 -0 .01 +2 . 10 +2 .45 +2 .25 +2 .30 +0.90 -1.95 -2.60 -2.90 -2 .50 -3.05

Massive Pentlandite Massive Pyrrhotite Massive Chalcopyrite 2 Bottom Contact Weighted mean value of oS34 9'00 (excluding massive sulphides and contact samples) = +1.0 *After Shima, Gross, and Thode (1963) TABLE II* SULPHUR ISOTOPE DISTRIBUTION : LEITCH SILL

Location

+2. 50 Upper contact Composite of 10 specimens collected across the upper half of the sill +o. 7t:1 Composite of 11 specimens collected across the lower half of the sill -0 . 60 Weighted mean value of 0S 34 %o (not including Upper Contact) = +o . 10 *After Shima, Gross, a nd Thode (1963)

detailed results for the Insizwa and Leitch sills respectively, the Insizwa sheet being an example of an intrusive showing marked gravity differentiation, and the Leitch sheet showing little or no gravity differentiation. From these results it would appear that the average sulphur isotope ratio for basic magmas is very close to that for meteorites. This suggests that SS34 for the earth's sub-crust or mantle is ~O and that the earth's mantle and meteorites are genetically related. The average value of SS34 for the earth's crust is, of course, a different matter. Wide variations occur and it would be most difficult to determine an average or mean value. Also, even if we assume that there is an enrichment in S34 in the present earth's crust as suggested by the limited

29

SULPHUR ISOTOPE GEOCHEMISTRY

analyses made to date, we still have little information about the S34 content of the primordial crust. Granitic Intrusives As pointed out earlier, the 8S 34 values for sulphur in igneous rocks found in the earth's crust vary above and below the meteoritic value (8 0) with a preponderance of samples showing an S34 enrichment or positive values of 8S34 ( see Figure 1). A survey of results by Ault and Kulp ( 1959) gave an average value for igneous rocks of +3.6%o with spreads from -1.4 to 12%0. All igneous rocks of the Sudbury District of Ontario, including intrusives and extrusives, have 8S34 values in the range of -2 to 10 (Thode et al., 1961) (see Figure 2). Also, igneous rocks in the Yellowknife and Algoma areas of Canada have S34 8-values within the range -8 to +10 (Wanless, Boyle, and Lowdon, 1960; Monster, Shima and Thode 1962). Two large granitic intrusive masses, the Dome stock of Red Lake, Ontario, and the Rice Lake Batholith of Manitoba investigated by Shima, Gross, and Thode ( 1963), are of great interest in view of the fact that their S34

=

+

+

6 534 ¾o +50

+40

+20

+30

I SEO.

+10

I

-10

•

-20

-30

YELLOWKNIFE

IGN.

-40

SULPHIDES

SUDBURY SULPHIDES

• •• • •

PALISADES

SILL

INSIZWA SILL

z )

3 )

3)

3)

SILL

GRANITIC

l)

3)

COBALT SILL

LE ITCH

-50

INTRUSIVES

RED LAKE ,ONT./RICE LAKE, MAN.

FIGURE

2.

a

1)

WANLESS, BOYLE

LOWOON

l 1960)

Z)

THOOE,OUNFORO 8 SHIMA (1962)

3)

SHIMA,GROSS 8THOOE

(1963)

Sulphur Isotope Distribution in Basic Sills (a= S34).

3)

30

H. G. THODE

TABLE Ill* SULPHUR ISOTOPE DISTRIBUTION: GRANITIC INTRUSIVES

Area Dome Stock Red Lake, Ontario Rice Lake Batholith, Manitoba

Pearl Lake Stock, Porcupine, N. Ontario

Location (see Fig. 5) Dome "East" Dome "Middle East" Dome "Middle West" Dome "West" Rice Lake "East Central" Rice Lake "\Vest Central" Rice Lake "\\'est" 1815 Level McIntyre Mine

No. of samples in composite SiO2 (%)

oS3'

%o

24 15 6 9

10

67 .5 66.7 64 .5 59.9 70 . 32

+13.30 + 6 .90 +17.20 +17.20 +30.20

9

67.4

+27.20

88 63

64.9

+19. 70 1. 70

-

*After Shima, Gross, and Thode (1963)

values do not fall within the range of those found to date for igneous rocks (see Table III). The S34o-values obtained ranging from + 7 to +30 are seen to be well above the ranges for primary igneous rocks and fall in the range of values found for sulphate evaporites in sedimentary rocks ( see Figure 2). Whatever the cause of the sulphur isotope fractionation, it seems clear that the sulphides of the granites have passed through sedimentary cycles and that the granites are not primary intrusives. It would, therefore, appear that under certain conditions, sulphur isotopes may be useful in distinguishing between granites formed by melting or reworking of crustal material including sediments and those formed by the intrusion of granitic magmas from depth. Igneous Rocks of Primary and Secondary Origin The idea of using sulphur isotope studies to distinguish between primary intrusives and granitic intrusives of sedimentary origin is, of course, not new. The very first sulphur isotope studies (Thode, Macnamara, and Collins, 1949) , showed that the sulphur isotope ratios of igneous rock sulphides ( e.g., Sudbury intrusive) of primary igneous origin fell in a very narrow range in the region of the meteoritic value, whereas the sulphur isotope ratios for the sulphides and sulphates of sedimentary origin varied over a wide range ( ~ 120%0) . Since then, many sulphides of sedimentary and igneous origin have been studied and range of oS 34 values for primary basic intrusives is being narrowed down. The results of this paper would suggest that in the case of basic sills, the range is very narrow indeed and within 1%o of the meteoritic sulphur value. This means that granitic intrusives whose sulphur isotope ratios have either high negative values or high positive values are probably granitized or reworked sediments. For example, Kulp, Ault, and Feely ( 1956) reported sulphide minerals from pegmatites to be depleted in S34 by 10 to 22%0

SULPHUR ISOTOPE GEOCHEMISTRY

31

( oS 34 = -10 to -22) . These, they suggest, are related to sedimentary sulphides. Also, Dechow ( 1960) suggests that the gneissic granites associated with the Heath Steele ore deposits of Newcastle, New Brunswick, Canada, are of granitized Ordovician sediments. The sulphides of these pegmatites were found to be enriched in S34 by +9 to +17%o. Finally, Jensen ( 1957), ( 1959), in the study of different types of mineral deposits ( pegmatitic, magmatic, hydrothermal, and so forth), has pointed out that sulphur isotope ratios do aid in providing some evidence for subdividing many hydrothermal deposits into magmatic hydrothermal deposits, metamorphic hydrothermal deposits, and ground-water hydrothermal deposits. It is clear that ore solutions derived from magmas of deep-seated origin will give sulphur isotope ratios within a very narrow range close to the meteoritic value. Stanton ( 1960) also discusses the application of sulphur isotope studies in ore genesis. SEDIMENTARY CYCLE

Early investigations of sulphides and sulphates in sedimentary rocks showed wide variations in the abundances of the sulphur isotopes ( ~ 120%0) (Thode et al., 1949). In general, the sulphides and sulphates were found to be depleted and enriched in the heavy sulphur isotope S34 respectively as compared to the sulphur in meteorites. Since then, many samples of sedimentary sulphides and sulphates have been investigated including petroleum and related materials ( see Figure 1 ) . Equilibrium Isotope Effects It is clear from these results that the sulphur isotopes are fractionated in the geochemical and biological processes involved in the sedimentary cycle, with the heavy isotope S34 being favoured in the more highly oxidized state ( e.g., SQ4=). Actually, there is a theoretical basis for these fractionation effects. In the isotope exchange reaction

H2S34

+ S 3204=PH2S 32 + S 3404=,

the equilibrium constant K has been calculated to be 1.071 using the wellknown methods of statistical mechanics (Tudge and Thode, 1950). This means that under conditions of isotopic equilibrium, S34 will be favoured in the SQ4= by 71%0 over that of the associated H2S. Although no direct mechanism is known whereby isotopic equilibrium between SQ4= and H2S may be established, a trend towards this most favoured distribution of the sulphur isotopes might be expected in complex natural processes. Kinetic Isotope Effects It is now well established, however, that large isotope effects are involved in the biological sulphur cycle although these isotope effects are for the most part non-equilibrium or kinetic effects. Kinetic isotope effects have been known since the discovery of the heavy hydrogen isotope deuterium

32

H, G. THODE

in 1932. During the past decade, kinetic isotope effects have been the subject of considerable study, both from the point of view of theory and experiment. The fact is that isotopic mass has a bearing on chemical rates and one isotopic species will react more rapidly than another. For example, laboratory experiments have shown that in the chemical reduction of SQ4= to H2S, the S32Q4= species reacts faster than the S34 O4= species, the ratio of rate constants k1/k2 for the two reactions S 3204= _.!!~ H2S 32 S 3404 = _!!~ H2S 34 being 1.025. This means that the first H2S produced in the chemical reduction of SQ4= will be depleted by 25%0 in S34 as compared to the initial SO4 = ( Harrison and Thode, 195 7) . In nature, the reduction of SQ4= to H2S takes place extensively in the shallow muds at the bottom of lakes and seas in the presence of anaerobic bacteria ( Vibrio desulphuricans). Under these conditions, the reduction processes will be enzyme-catalysed. Extensive investigations have been made of sulphur isotope fractionation that occurs in the bacterial reduction of sulphate under various conditions (Thode, Kleerekoper, and McElchern, 1951; Jones and Starkey, 1957; Harrison and Thode, 1958a). These results indicate that the situation is more complicated in the bacterial reduction than in the straight chemical reduction. In the former case, the kinetic isotope effect varies from 0 to 25%0 depending on the metabolic rate, whereas in the latter case the kinetic isotope effect remains at 25%0 over a wide range of temperatures and concentrations. The kinetic isotope effect in the bacterial reduction of SQ4= approaches that obtained in the chemical reduction ( 25%0) at moderate to slow metabolic rates and approaches Oat very rapid metabolic rates. However, under the normal conditions prevailing in nature and in the laboratories, intermediate values are obtained of the order of 15%0. To explain the range of values found for the kinetic isotope effect in the bacterial reduction of sulphate, Harrison and Thode ( 1958a) proposed a sequence of two reactions ( see Figure 3) . According to their proposal, either Step I or Step II may be rate-controlling. If the former is ratecontrolling, then a small sulphur isotope effect will result, with the S34 O4= I

kt

so,-.oln + enzyme .=:±so.-. k2

II

I enzyme complex I l

ka S-0 bond-breaking step

SOa-

1

rapid reduction relative to I and II

l

H2S. FIGURE

3. Bacterial Sulphate Reduction Mechanism.

33

SULPHUR ISOTOPE GEOCHEMISTRY

species reacting faster. If, however, the latter step is rate-controlling, there will be a large isotope effect ( ~25%o) with the lighter species reacting faster. Most results obtained give intermediate values indicating that both reactions are to some extent rate-controlling. However, extreme conditions can be produced in the laboratory. At very low concentrations of SQ4= or at very rapid metabolic rates ( reaction I), the diffusion of sulphate becomes rate-controlling and the isotope effect drops to zero. However, under conditions where the metabolic rates are low, reaction II becomes rate-controlling and the kinetic isotope effect approaches 25%0. Recently, Ian Kaplan ( 1962), using different H2 donors in the bacterial reduction of sulphate, reported isotope effects much higher than 25%0 at extremely low metabolic rates. So far these high isotope effects have not been confirmed or explained, but it may be that at very low metabolic rates and in the presence of different H2 donors different stages of reduction of SQ4= to H2S come into play in reckoning the over-all isotope effect found. The main point to make here is that in the extensive reduction of sulphate that occurs in the biological sulphur cycle under anaerobic conditions in the shallow muds in association with oceans and lakes, considerable sulphur isotope fractionation can occur, usually of the order of 15%0. In nature, the simple isotope fractionation factor (0-25%0) involved in the bacterial reduction of SQ4= may be multiplied many times by a batch type of process. Just as in the case of a batch distillation process, the residual liquid becomes richer and richer in the heavy component as the distillation proceeds, so in the bacterial reduction of a limited reservoir of SQ4=, the S04 = will get richer and richer in S34 as a larger and larger fraction of the SQ4= is reduced to H2S. The sediments in the Uinta Basin of Utah would seem to have settled out of such a limited basin in which large-scale sulphate reduction took place. Table IV ( Harrison and Thode, 1958b), shows the results of sulphur TABLE IV* SULPHUR ISOTOPE ABUNDANCES IN HYDROCARBON SOURCE ROCKS: UINTA BASIN, UTAH

Formation

Source rock (in order of decreasing age)

:'\on-Marine, upper Wasatch

No. 1245 Ozocerite

Lower Green River l' pper Green River

:No. 2335 Albertite No. 1301 Gilsonite

Cinta

No. 1517 Wurtzilite

*After Harrison and Thode (1958b)

S3•/S32 (o %o) Extracted asphalt

so,-

Pyrite

+ 5.7 + 6 .8 + 4 .6 +12 . 6 +27 .9

-10.7

+3.0

-10.0 +14.8 +29 .0

+28.4 +26 . 4

+26.1 +27.2

+14.1 +30.8 +29 .0 +23.7 +22.8

Total S -

7 .5

- 7.2 +15.0 +29.0 +26.8 +27.2 +268

34

H. G. THODE

isotope analysis of asphalts and inorganic sulphur compounds in the sediments at different depths. It is clear that there is a one-to-one correspondence between the sulphur isotope ratio and depth of sediment. The sulphur in the deep sediments laid down in the early history of the basin shows little isotope fractionation, whereas the sulphur in the shallower sediments shows 30) . considerable enrichment in S34 ( 8S34

=+

Ocean Sulphate In the case of sulphate reduction from a very large reservoir such as the ocean, the isotope ratio of the ocean sulphate will not change perceptibly as reduction takes place and the s= produced will be depleted in S34 , with respect to ocean sulphate, by one simple process factor ( ~ 12 - 15 %0) under normal conditions. The ocean, therefore, provides a base level from which isotope fractionation may be measured. TABLE V* SULPHUR ISOTOPE ABUNDANCES IN SEA-\\ ATER SULPHATE 0

Position and date collected Atlantic Ocean 22°00'N 30°00'W Feb. 14, 1952 0. 9°25'N 20°15'W Feb. 28, 1952 13°00'N 38°58'W March 4, 1952 16°24'N 38°58'W March 31, 1952 16°00'N 46°08'W April 2, 1952 11 °59'N 56°03'W April 9, 1952 19°30'N 64°W 1954 Pacific Ocean 39°23'N 129°55'W 1950 25°3l'N 119°46'W 1950 Pacific Naval Lab. No. 29 Off Mexico 1954 New Zealand, Wellington area 1956 Arctic Ocean Resolute Bay 1950-51 Alexandria Fjord 1954 Beaufort Sea 1954 Wellington Channel

oS34 %ot

Depth (m) 3 samples 10,683, 1213 3 samples 1, 700,1553 3 samples 23,651, 1600 3 samples 21,636, 1432 3 samples 24,975, 1838 3 samples 43,670, 1615 surface Average 2 samples 1 and 2500 2 samples 1 and 2500 180 surface

+19 .9 +20 .2 +20.6 +20.1 +20 .5 +20.0 +20.3 20 . 23

+20.8 +19.3 +19.8 +20 .3

surface

+ 19. 6 Average 19. 9

surface

+ 19 . 8

surface

+ 20 . 2

+20 . 1 surface +20.4 surface Average 20 . 1 Average +20.1±0 .3

*After Thode, Monster, and Dunford (1961) flnstrument precision ±0.01 per cent

35

SULPHUR ISOTOPE GEOCHEMISTRY TABLE VI SULPHUR ISOTOPE ABUNDANCES IN FRESH-WATER LAKES AND OCEAN INLETS

Source sulphate Fresh Water Lake Erie, Ontario* Lindsley Pond, Connecticutt Lindsley Pond, Connecticutt Tokyo Bayt Saanich Inlet, British Columbia, Canada§ Ocean§

osa• %o

Depth Surface Surface 13.2 m 100 m

+ 6 + 7.7 + 7.3 +14 0 +19 +20.1

Average

*Ishii (1953) tJensen and Nakai (1961) tSakai (1957) §Thode, Monster, and Dunford (1961)

In this regard, ocean-water sulphate has been found to be remarkably uniform in sulphur isotope ratio. Samples of water from the Atlantic, Pacific, and Arctic oceans from various locations and from various depths have been investigated (Trofimov, 1949; Szabo et al., 1950; Vinogradov et al., 1956; Sakai, 1957; Feely and Kulp, 1957; Ault and Kulp, 1959; Thode, Monster, and Dunford, 1961). The average SS34 value for presentday ocean sulphate reported by the latter two groups is +20.7%0 + 0.5 and +20.1%0 ± 0.3 respectively. Table V shows some of the data obtained. TABLE VII SULPHUR ISOTOPE ABUNDANCES OF SULPHATES AND SULPHIDES DERIVED FROM SEA WATER

oS 34 %o re meteorites

oS34 %o re sea water

1.*

CaSO,

Present-day sea shell

+20.4

+

0 .3

2.*

CaSO, Gypsum

Evaporite on bottom of Boca de Virrila, Peru; Pacific Inlet into Peru desert (water depth 2 ft.)

22.5

+

2 .4

3.t

CaSO, .2H2O Gypsum

Currently forming in sea water at Laguna Madre, Texas

20 . 7

+

0.6

4.t

Sulphate

In rain water average of 14 rain and snow samples from Sweden +3 . 2 to 8.2

5.t

Sulphate

In rain water average of 7 samples from Japan nonindustrial areas

+

5.7

-14.4

6.* Sulphate

In rain water

+ 6.0 + 3.8

7. * Sulphides

In recent sediments formed by bacterial reduction of sea water sulphides in shallow muds

+

5 .0

-15.0

Present-day sea water

+20.1

0 .0

8. * Sulphate

*Thode, Monster, and Dunford (1961) tAult and Kulp (1959) Hensen and Nakai .(1961)

-14.1 -16 .2

36

H. G. THODE

Finally, Table VI shows the S34 content of a large fresh-water lake system, several small lakes, and of two ocean inlets fed by rivers in comparison to that of the ocean. It is not surprising to find intermediate S34 8-values in regions where fresh water and sea water mix. Finally, Table VII gives the sulphur isotope abundances of some samples of sulphate and sulphide derived from the sea. It would seem that in all processes where ocean-water sulphate is reduced, isotope fractionation may occur and the extent of this fractionation may be determined by comparing the S32/S34 ratio of the reduced sulphide with that of ocean-water sulphate. Since the ocean provides, in effect, an infinite reservoir of sulphate, its sulphur isotope ratio will not change perceptibly as reduction takes place and the s= produced will, in general, be depleted in S34 by one simple process factor or~ 15%0. Table VII gives the sulphur isotope ratios for some sulphates and sulphides probably derived from ocean water. It is interesting to note that the sulphides in the recent sediments laid down off the coast of Venezuela in association with ocean water are indeed depleted in S34 by about 15%0 with respect to present-day ocean sulphate. Also sulphate in rain water collected from non-industrial areas has sulphur isotope ratios displaced from that of sea water by ~ 15%0. This result suggests that rain-water sulphate is derived from the oceans. Certainly, ocean sulphate is one possible source of this sulphur in rain water. The H2S formed by the bacterial reduction of ocean sulphate from the shallow muds and ocean-mud flats would escape into the atmosphere where it would become oxidized and later fall as sulphate in the rain (Thode et al., 1961; Jensen and Nakai, 1961 ) . The question, of course, arises as to whether bacterially reduced ocean sulphate is the major source of sulphate in rain water. More quantitative data are needed to answer this question. However, the sulphur isotope ratios found for rain-water sulphate are consistent with this view.

Ancient Oceans It is reasonable to assume that the sulphur-containing materials now found in the ancient sediments were also related to the ancient seas from which they were deposited in the same way that present-day deposits are related to the present ocean. Although we can measure the sulphur isotope ratios in the sulphur compounds of the ancient sediments, we cannot measure directly the sulphur isotope abundances of ancient sea water, since we do not have a reliable source of age-labelled ocean water. In the study of sulphur isotope geochemistry, it is, therefore, important to find some method whereby the 8S34 level for the oceans for the various periods of geological time can be established. In this regard, it seems likely that in any short period of geological time the oceans were as uniform in sulphur isotope content as they are today. The question is: what was the isotope content of the sea at a particular point in geological time, and how has this isotope ratio changed with time? A thorough study of the sulphur isotope ratios in

37

SULPHUR ISOTOPE GEOCHEMISTRY

evaporites, anhydrite, and gypsum would seem to provide the best approach to a solution of this problem. It is seen from Table VII that there are gypsum evaporites currently forming from sea water which have sulphur isotope ratios almost identical with that of present-day sea-water sulphate. However, it is well established that anhydrite and gypsum evaporites, in general, have a wide range of sulphur isotope ratios (Thode, Macnamara, and Collins, 1949; Ault and Kulp, 1959). Since this spread in values occurs for evaporites from the same geological period, the question arises as to how, from evaporite studies, the isotopic content of the contemporary oceans can be established. The interpretation of sulphur isotope distribution data in evaporites will, of course, be complicated by the fact that we have gypsum and anhydrite deposits which have been formed under marine, non-marine, and mixed conditions. Monster and Thode ( 1962) have made an extensive study of evaporites in various sedimentary basins and it is their contention that a good approximation of the sulphur isotope ratio of the ancient oceans can be determined from a study of the contemporary evaporites. According to them, the_ lowest S34 enrichment fo'i,J.nd in the evaporites of a given geological period from various sedimentary beds will give the cfosest ap'p roach to the value of the ocean sulphates of that period. In the case where the fresh-water sulphate flowing into a large enclosed shallow sea is negligible and the main source of sulphate is from continuous or intermittent contact with the sea, then all evaporites formed would either have the same S32 /S34 ratio as the sea at the time of deposition or they would show S34 enrichment due to bacterial action. For example, studies of Permian evaporites (Ault and Kulp, 1959) show SS34 values ranging from 12 to 17%c. From these results, one would select 12 as the value nearest to the true S34 level of Permian seas. Recent 10 studies of Permian evaporites suggest that this value is closer to ( Monster and Thode, 1962). Great thicknesses of Permian gypsum and anhydrite deposits from various parts of the world (Texas and Netherlands) give S34 8-values in the 10 to 11 range. In this way, the S34 content of the ancient seas for various geological periods is being determined. Results to date indicate wide variations in the sulphur isotope ratio of ocean sulphate with time.

+

+

+

+

+

+

Petroleum Petroleum and hydrocarbon materials in both marine and non-marine sediments have been the subject of considerable interest from the point of view of their origin and mode of formation. In this regard, sulphur isotope studies of petroleum and related sulphates and sulphides have given information concerning the possible origin of petroleum sulphur and concerning the environment in which the petroleum was formed. For example, petroleum and associated materials in a non-marine environment ( Uinta Basin, Utah) show a very different pattern of sulphur isotope distribution

38

H. G. THODE

from those formed in marine sediments (Harrison and Thode, 1958b; Thode, Harrison, and Monster, 1960). The sulphur isotope distribution in a large number of samples of petroleum and related materials from the United States and Canada has been studied (Thode, Monster, and Dunford, 1958) . Their studies revealed the following: 1. A wide variation in the sulphur isotope ratios of petroleum samples, the total spread being more than 40%0. 2. Petroleum samples from a single oil pool (Leduc, Alberta) are remarkably constant in their sulphur isotope content. 3. Petroleum samples from the same reservoir rocks which are widely distributed over the western plains of Canada and the United States have very nearly the same isotope ratio, but this ratio may vary from one horizon to another. For example, Upper Devonian, Lower Cretaceous (heavy oils) and Upper Cretaceous oils have S34 8-values of +12, +sand +2.5 respectively. 4. H 2 S is very similar in isotopic content to the organically bound sulphur in the associated oils, suggesting that the two are related and that there is little fractionation in the splitting off of H 2S in the oil maturation process. 5. Petroleum from widely different pools in the same reservoir rocks (Devonian, Western Canada) have very nearly the same S34 content even though they differ markedly in sulphur content. From these studies, it may be concluded that the sulphur isotope ratios for petroleum do not change materially with time and that they are indicative of the environment in which petroleum is formed. The sulphur isotope studies to date indicate that the source sulphur and the fractionation of the sulphur isotopes in the reduction of this source sulphur, which occurs before or during petroleum formation, are the two main factors which determine the sulphur isotope content of present-day crude oils. Most oils are formed in a marine environment and it seems reasonable to assume that sea-water sulphate is the main source of sulphur in petroleum. Also since sea-water sulphate is rapidly reduced by bacteria in the shallow muds in contact with the sea, we can expect the reduced sulphur in the sediments to be depleted in S34 by ~ 15%0 with respect to the sulphate in the sea at the time the sediments were laid down. Studies by Thode, Harrison, and Monster ( 1960) of recent sediments showed this to be the case. It is very likely that it would be this reduced sulphur, present in the sediments in various forms, that would be finally incorporated in the petroleum. A comparison of the sulphur isotope ratios in petroleum with those for contemporaneous evaporites, gypsum and anhydrite, indicates that a definite relationship does exist. In general, the S34 8-value for petroleum is displaced ~ 15%0 from that of the associated evaporites. There is some indication from evaporite studies that the sulphur isotope ratios of the sea have changed with time in a complex, but cyclic, fashion and that the sulphur in petroleum has changed in a similar manner but displaced ~ 15%0 from the contemporaneous sea level (Monster and Thode, 1962, unpublished).

SULPHUR ISOTOPE GEOCHEMISTRY

39

FUTURE WORK

Sulphur Isotope Chemistry If we are to explain fully the sulphur isotope patterns found in nature in terms of processes which have taken place and are taking place, we must have a thorough knowledge of sulphur isotope chemistry and know what isotope fractionation can be expected for various natural processes. Although kinetic and equilibrium isotope effects have been studied for a number of reactions involving sulphur, there are still many reactions of sulphur-containing compounds in nature for which the isotope effects are unknown. There are certain samples of pyrite, perhaps with a particular history or mode of formation, which decompose to pyrrhotite and sulphur with a large intramolecular sulphur isotope effect. These isotope effects are being studied further. Also preliminary results have shown that there is a large kinetic isotope effect in the decomposition of thiosulphate and polythionates. Many sulphur reactions are possible in volcanic gases and in hot springs where sulphur in its various oxidation states is present and it is known that sulphur isotope fractionation does take place. Sulphur isotope effects for possible reactions must be investigated if we are to interpret the patterns of isotope distribution found in sulphur compounds of volcanic origin. Meteorites For the most part, sulphur in meteorites is in the form of troilite ( FeS) together with smaller amounts of other sulphides, and the sulphur isotope ratios for the meteorites containing these minerals are remarkably constant. However, the Orgueil meteorite, a carbonaceous chondrite containing sulphur in various forms, showed measurable differences in isotope ratio between the S0 and S04 = fractions. Further work needs to be done to determine whether the average S32 /S 34 ratio for this meteorite is indeed the same as that found for other meteorites. In this regard, other carbonaceous meteorites should be studied. It would, of course, be of great interest to establish a mechanism for the sulphur isotope fractionation which seems to have taken place some time in the history of the Orgueil meteorite. Since S36 is probably formed in interstellar nebulae by a different nuclear process from that of S34 , it would be of interest to measure S32 /S 36 ratios for various meteorite types to see whether these ratios are as uniform as the S3 2 / S34 ratios. Earth's Crust and Mantle The average S32 /S 34 ratio for the sub-crust or mantle as determined from the study of a number of basic sills would seem to be established near the meteoritic value (8S 34 0 ± 1%o). However, it would be well to study other basic sills and rock masses presumably of deep-seated origin to

=

40

H. G. THODE

further substantiate this result. The use of the sulphur isotope method to differentiate between rocks of magmatic origin and granitic intrusives which are granitized or reworked sediments should be investigated further. In this connection, the strontium isotope method of Hurley and his coworkers should be used for comparison. The determination of the average S32 /S 34 ratio for the earth's crust is a most difficult task indeed because of the difficulty in getting quantitative data. However, it is a problem we must continue to study. If we assume that the average 8S34 for the primordial crust was close to the meteoritic value ( 8S 34 0), then a material balance would require this average to remain constant at 8 0 up to the present time. Any isotope fractionation would only result in the change in distribution of S34 between sulphates and sulphides and so on, and any mantle material added would be at the 8S 34 = 0 level. However, there is the possibility that the average S34 content of the primordial crust or skin of the earth was not the same as that for the mantle and meteorite, but was enriched in S34 due to a differentiation process in the original cooling of the earth. In this case, the average 8S34 value would decrease with time due to the dilution of the crust with mantle material ( 8S 34 = 0). A thorough study of crustal rocks of two widely different ages might give some clue to the solution of this problem. Perhaps the most exciting aspect of sulphur isotope geochemistry has to do with the sediments and the large fractionation of the sulphur isotopes that occur in biological and geological processes in the sedimentary cycle. Further work needs to be done to establish the pattern of isotope changes in the sea taken over the whole of geological time. There are obviously some marked changes that have occurred in relatively short periods of time and it may be possible to correlate these with periods of major biological or geological activity. Also further studies of the sulphur isotope distribution in petroleum and related materials can help us answer questions concerning the origin of sulphur in petroleum, the environment in which the petroleum was formed, the relationship between petroleum deposits, and relationships between those deposits and sediments in which the deposits were formed .

=

=

REFERENCES AuLT, W. U ., and KuLP, J. L. ( 1959) . Isotopic geochemistry of sulphur. Geochim. et Cosmochim. Acta 16: 201-35 . DEcHow, E. (1960). Geology, sulphur isotopes and the origin of the Heath Steele ore deposits, Newcastle, New Brunswick, Canada. Econ. Geo!. 55: 539-56. FEELY, H. W., and KULP, J. L. (1957). The origin of the Gulf Coast salt dome sulphur deposits. Bull. Am. Assoc. Petrol. Geologists 41: 1802-53. HARRISON, A.G. , and THODE, H. G. (1957) . The kinetic isotope effect in the chemical reduction of sulphate. Trans. Faraday Soc. 53: 1-4. - - - ( 1958a) . Mechanism of the bacterial reduction of sulphate from isotope fractionation studies. Trans. Faraday Soc. 54: 84-92 . - - - ( 1958b) . Sulphur isotope abundances in hydrocarbons and source rocks of the Uinta Basin, Utah. Bull. Am. Assoc. Petrol. Geologists 42: 2642-9 . HURLEY, P. M ., and .MooRBATH , S. ( 1961). Variations in isotopic abundances of strontium, calcium and argon and related topics. Department of Geology and Geophysics, Massachusetts Institute of Technology, Cambridge 39, Mass. NYO-3942 . Ninth

SULPHUR ISOTOPE GEOCHEMISTRY

41

Annual Progress Report for 1961, U . S. Atomic Energy Commission Contract AT(30-l )-1381. ISHII, M . ( 1953) . Fractionation of sulphur isotopes in plant metabolism of sulphur. Master's thesis, McMaster University, Hamilton, Canada. JENSEN, M . L. (1957). Sulphur isotopes and mineral paragenesis. Econ. Geo!. 52: 269-81. - - - ( 1959). Sulphur isotopes and hydrothermal mineral deposits. Econ . Geo!. 54 : 374-93. - - - and NAKAI, N . ( 1961). Sources and isotopic composition of atmospheric sulphur. Science 134: 2102-4. JONES, G. E., and STARKEY, R . L. ( 1957) . Fractionation of stable isotopes of sulphur by micro-organisms and their role in native deposition of sulphur. Appl. Microbiol. 5: 111- 15. KAPLAN, I. R. ( 1962) . Sulphur isotope fractionations during micro-biological transformations in the laboratory and in marine sediments. Ph.D . thesis, University of Southern California. KULP, J. L ., AuLT, W. U., and FEELY, H. W. ( 1956) . Sulphur isotope abundances in sulphide minerals. Econ. Geo!. 51 : 139- 4 7. MACNAMARA, J. and THODE, H. G. ( 1950). Comparison of isotopic constitution of terrestrial and meteoritic sulphur. Phys. Rev. 78 : 307-8. - - - , FLEMING, W. H., and SZABO, A. (1952). The isotopic constitution of igneous sulphur and the primordial abundances of the terrestrial sulphur isotope. Can. J. Chem. 30 : 73-6. MONSTER, J., ANDERS, E ., and THODE, H . G . (1961) . Unpublished work. University of Chicago and McMaster University. - - - , SHIMA, M ., and THODE, H . G. Sulphur isotope studies of igneous rocks of Algoma Region of Canada. Unpublished work. McMaster University. - - - and THODE, H . G. (1962) . Unpublished work. McMaster University. SAKAI, H . ( 1957). Fractionation of sulphur isotopes in nature. Geochim. et Cosmochim. Acta 12: 150-69. SHIMA, M ., GRoss, W. H ., and THODE, H . G . ( 1963) . Sulphur isotope abundances in basic sills differentiated granites and meteorites. J . Geophys. Research. 68, 2835-48. STANTON, R. L. ( 1960). The application of sulphur isotope studies in ore genesis theory, a suggested model. New Zealand J . Geo!. Geophys. 3 : 375-89. THODE, H . G., MACNAMARA, J ., and COLLINS, C . B. ( 1949) . Natural variations in the isotopic content of sulphur and their significance. Can. J. Research, B-27: 361-73. - - - , KLEEREKOPER, H., and McELCHERN, D . ( 1951). Isotopic fractionation in the bacterial reduction of sulphate. Research (London) 4, 581-2 . - - - , MONSTER, J ., and DUNFORD, H . B. (1958) . Sulphur isotope abundances in petroleum and associated materials. Bull. Am. Assoc. Petrol. Geologists 42: 2619-41. - - -, HARRISON, A. G ., and MoNSTER, J. (1960). Sulphur isotope fractionation in early diagenesis of recent sediments of north-east Venezuela. Bull. Am. Assoc. Petrol. Geologists 44: 1809-1 7. - - - , MONSTER, J., and DUNFORD, H . B. ( 1961) . Sulphur isotope geochemistry. Geochim. et Cosmochim. Acta 25: 150-74. - - - , DUNFORD, H. B., and SHIMA, M. ( 1962) . Sulphur isotope abundances in rocks of the Sudbury District and their geological significance. Econ. Geo!. 57: 565-78. TROFIMOV, A . Isotopic Composition of sulphur in meteorites and in terrestrial objects. Dok!. Akad. Nauk SSSR 66: 181-4. TuooE, A. P., and THODE, H. G. ( 1950) . Thermodynamic properties of isotopic compound of sulphur. Can. J . Research B-28 : 567-78. VINOGRADOV, A. P. ( 1958). Isotopic composition of sulphur in meteorites and in the earth. In: R . C . ExTERMANN, ed., Radioisotopes in Scientific Research, II, 581-91. New York: Pergamon Press. - - -, CHUPAKHIN, M . S., and GRIN EN KO, V. A. ( 1956). Isotopic composition of sulphur in relation to the problem of the age of pyrites of sedimentary genesis. Gcokhimiya 1 : 96-105. - - - ( 1957). Some data on the isotopic composition of the sulphur of sulphides. Geokhimiya 3: 183-6. WANLESS, R . K., BOYLE, R . W., and LowDoN, J. A. (1960) . Sulphur isotope investigation of the gold-quartz deposits of Yellowknife district. Econ . Geol. 55: 1591-621 ,

OXYGEN ISOTOPE GEOCHEMISTRY: THERMOMETRY OF MET AMORPHIC ROCKS Robert N. Clayton

ABSTRACT

The distribution of oxygen-18 between two mineral phases of a rock can be used to determine the temperature at which these phases were last in equilibrium with one another. The original applications of this principle by Urey and co-workers to sedimentary rocks provided important information on the temperature variations in the oceans in the past. Current research is directed towards extension of the method to higher temperature rocks. Studies in areas of regional metamorphism have shown that isotopic equilibrium is probably preserved in low-rank rocks, but that the isotopic distributions in ·some of the highest-temperature equilibria are probably lost by retrograde effects. MUCH ATTENTION HAS BEEN GIVEN in recent years to the quantitative determination of the physical and chemical conditions associated with the formation of rocks. Laboratory studies of phase relationships in silicate systems have placed bounds on ranges of pressure, temperature, and chemical composition for many observed phase assemblages. It is still important to find properties of rocks and minerals which depend on only one of these variables and are virtually independent of others. Hence there is a continuing search for geological thermometers, piezometers, clocks, pH meters, and the like. This paper deals with the question of geological thermometry, and in particular with the development of procedures based on the distribution of stable oxygen isotopes between co-crystallized mineral phases. The emphasis has been placed on metamorphic rocks for a number of reasons. Since isotopic thermometry is based on a distribution of atoms between minerals, it is necessary for successful application that the mineral phases be crystallized at equilibrium with one another. There is considerable evidence, based on the frequent recurrence of phase assemblages known to have fields of stability and on the usual absence of compositional zoning in crystals, that many regionally metamorphosed rocks have been thoroughly recrystallized and have come to equilibrium in their new environments. Metamorphic rocks vary in their temperatures of last crystallization from near room temperature up to almost the freezing range of dry silicate systems. Because of the nature of isotopic fractionation, isotope "thermometers" are inherently more sensitive at lower temperatures than at higher temperatures: analytical errors at 800° C may be on the order of ±50°, whereas at 200°C they are on the order of ±5 °. Hence the most fruitful fields of study will involve lower-rank metamorphic rocks, diagenesis of sediments, and hydrothermal deposits. The temperature effect is in the opposite direction from

OXYGEN ISOTOPE GEOCHEMISTRY

43

geologic thermometers based on solvus relationships, such as the FeS-ZnS system, in which the inherent sensitivity increases with increasing temperature of crystallization. Oxygen isotope thermometers can be established, in principle, for any pair of oxygen-containing phases, so that one can usually work with the major minerals of the rock rather than minor or accessory phases. Thus the FeS-ZnS thermometer has been applied mostly to hydrothermal sulphide systems, whereas oxygen isotope studies have dealt with igneous and metamorphic silicate minerals, and with the gangue minerals of hydrothermal deposits. THE ISOTOPES OF OXYGEN

The heavy isotope of oxygen of mass 18 was discovered by Giauque and Johnston ( 1929) through investigation of the absorption spectrum of oxygen. It occurs in natural oxygen to the extent of about one part in five hundred, with a total range of the 0 18 / 0 16 ratio of about 10 per cent in natural terrestrial materials. During the 1930's and '40's several measurements were made of oxygen isotope ratios in water, atmospheric oxygen, and in rocks. The analytical techniques usually involved measurement of the variations in density of water prepared from the oxygen of the sample. A change in 0 18 /0 16 ratio by 1 per cent produces a change in density of two parts per million in water ( of standardized deuterium content). This technique is sufficiently accurate to demonstrate variability in the abundance of the heavier isotope in natural oxygen. All the modern analyses of oxygen isotopes (since about 1950) are performed by mass spectrometer. Sensitive mass spectrometers of the type designed by Nier ( 194 7) and McKinney et al. ( 1950) can measure differences in 0 18 /0 16 ratio of samples as small as one part in ten thousand ( one tenth permil). One may regard the isotope 0 18 to be a minor element in rocks, with concentration of about 0.1 per cent, or 1000 ppm ( 1 / 500 of total oxygen, which constitutes about 50 per cent by weight of rocks). Then the analytical techniques in use today would permit discrimination between a rock containing 1000.0 ppm 0 18 and one containing 1000.1 ppm 0 18 • This is possible only because measurements are made relative to standard materials. The absolute concentration of 0 18 can be determined with an accuracy of about one part per thousand, but by making comparative measurements, the variations in 0 18/0 16 in natural samples can be measured much more accurately than the absolute abundances. As a result of the measurement technique described above, the analytical results are usually expressed in terms of differences of 0 18/0 16 ratios between samples and an arbitrary standard, rather than as 0 18 /0 16 ratios themselves. These differences are given as a 3-value for each sample, defined as: O- ( -

Reample Retandard

1)1000

44

ROBERT N. CLAYTON

where R = 0 18/0 16 • The standards used by various laboratories are often different, so that it is necessary that published results contain data which permit comparison from one laboratory to another. Some oxygen standards in common use are: mean ocean water, PDB-1 ( a fossil carbonate), NBS-20 ( Solenhofen limestone distributed by the U.S. National Bureau of Standards). In this paper, the standard is chosen to be standard mean ocean water (SMOW) (Craig, 1961 ). There are difficult chemical problems to be solved in the decomposition of minerals and rocks and the extraction of oxygen for isotopic analysis. The precise mass spectrometry described above requires that the sample introduced into the spectrometer be a gas, such as CO2, 02, or CO. It is important to carry out the chemical reactions which convert minerals to gas samples without changing the isotopic composition by contamination, by exchange with extraneous matter, or by chemical isotope fractionation. Usually this requires a series of reactions which are quantitative, and are carried out in an oxygen-free environment. A procedure applicable to most silicates and oxides has been described by Clayton and Mayeda ( 1963). A very powerful oxidizing agent, bromine pentafluoride ( BrF 5), is used to liberate oxygen at temperatures of 400 to 600°C in nickel reaction tubes. The oxygen is purified and then made to react with carbon to produce carbon dioxide which is used in the mass spectrometer. Both the reactions can be carried out with greater then 99 per cent yields, minimizing the chances for spurious fractionations. An example of these reactions for analysis of a quartz sample is: SiO2 + 2 Brf5 ➔ SiF4 + 2 Brf3 + 02 c+o2 ➔ CO2 Special techniques may be used for some minerals, such as the reaction of carbonates with 100 per cent phosphoric acid ( McCrea, 1950). Separated mineral samples of about 50 milligrams provide enough material for analysis in duplicate. Reproducibilities are usually +0.1 to 0.2%0 depending on the difficulty of the chemical treatment with each mineral. An analyst may average one or two duplicate analyses per day. ISOTOPE PALEOTEMPERATURES

In 1946, Urey presented a paper before the Royal Society of London concerning the thermodynamics of isotopic systems (Urey, 1947) and suggested that variations in temperature of precipitation of calcium carbonate from water should lead to measurable variations in the 0 18/0 16 ratio of the calcium carbonate. Therefore it should be possible, in principle, to determine the temperatures of oceans in the past by measurement of oxygen isotope abundances in fossil calcite shells. Isotope fractionations are most simply described in terms of "isotope exchange reactions" such as:

45

OXYGEN ISOTOPE GEOCHEMISTRY

1/ 3 CaC0/ 6 + H20 18 ~ 1/ 3 CaC0/ 8 + H 20 16 For this reaction, the equilibrium constant is _ (CaCOa 18)½/H20 1~ K - CaC0/ 6 H20 16

If the isotopic species of oxygen are distributed randomly among the three positions in the carbonate ion, the expression reduces to: K - (018 / 0!6)ca.coa - (018/ 016)H20

If there were no difference in chemical properties of the oxygen isotopes, the value of K would be exactly 1, that is, the oxygen isotope ratio would be the same in both phases. In fact, the isotopes do not behave identically and exchange equilibrium constants typically differ from 1.0000 by a few percentage points. The value of K for calcite-water exchange is 1.0286 at 25°C (Clayton, 1961) . Thus the 0 18/0 16 ratio is 2.86 per cent greater in calcite than in the water with which it is in equilibrium at 25°C. Like any chemical equilibrium constant, isotope exchange equilibrium constants are functions of temperature. For calcite-water exchange, the temperature coefficient of K was found to be 0.00023 deg-1 at 16°C (Epstein et al., 1953) . With an analytical accuracy of +0.0001 , this permits determination of "paleotemperatures" of carbonate shells to 0.5°C. The remarkable sensitivity of the carbonate paleotemperature scale can be seen in the example in Figure 1, taken from Epstein and Lowenstam ( 1953). SHELL GROWTH TEMPERATURES STROMBUS GIGAS NORTH REEF, BERMUDA RECENT

2& -

,,.,.~\

,u 0

.,.: 23 --

---

, -", I

,'

,,,.,._ I

,,

18

i:£.

,

-

,

..t.'-

.

-,

I

'

\

I

I

,,

I

,

''

'

-·

, '-

\

'

,

''

I

I

''

\

' ' ,_ ''

I

''

''

'

-~~

~

I

I

I

I

I

I

I

I

I

I

I

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

I.I

SUM OF WEIGHTS OF SAMPLES (gs) FIGURE

1. Seasonal temperature variations in a shell, as shown by QlS/ QlG measurements (from Epstein and Lowenstam, 1953) .

46

ROBERT N. CLAYTON

The calcite shell of a gastropod, Strombus gigas, was sampled along a line cutting the growth layers, so that the abscissa represents time during the growth of the animal. The ordinate gives temperature as derived from the measurements of 0 18/0 16 ratios in the carbonate shell. The isotopic composition yields detailed information on the temperature of the water in which the shell grew, including the seasonal variations. Records of the same sort are found also in fossil shells ( Lowenstam and Epstein, 1954). Carbonate paleotemperatures have been used in a number of important studies on the past climates of the earth. Lowenstam and Epstein ( 1954) made a detailed study of ocean temperatures through Upper Cretaceous time based on measurement of 0 18/0 16 in fossil belemnites, brachiopods, and oysters from both sides of the North Atlantic ocean. They conclude that ocean temperatures were warmer and more uniform geographically in the Upper Cretaceous than at the present time. ( Presumably the Cretaceous is more typical of the earth's history, the present situation still being much influenced by glaciation.) A warming trend followed by a cooling trend in late Cretaceous time is also indicated in the data of Lowenstam and Epstein. Emiliani ( 1955a, b; 195 7) has determined ocean temperatures during Pleistocene time by measurements on pelagic foraminifera from deep-sea cores. Large temperature fluctuations are evident which can be correlated by absolute age measurements with the glacial maxima and minima recorded on the continents. The temperature profile in deep-sea cores provides an important tool in stratigraphic correlation from core to core. For example, Rosholt et al. ( 1961) have established a chronology for the last 175,000 years of geologic time, covering the last three major glacial maxima. Similar measurements have been made on foraminifera of Tertiary age from Atlantic deep-sea cores ( Emiliani, 1956). These do not show the wide temperature fluctuations observed in Pleistocene cores. The isotopic composition of oxygen in a calcite shell will remain unchanged after deposition until the shell material recrystallizes or undergoes isotopic exchange in some later geological event. The evidence for later isotopic exchange is usually pretty clear: the record of seasonal variations is erased, leaving a uniform isotopic composition corresponding to an unreasonable ocean "temperature," usually around 70°C. This is presumably the result of exchange and recrystallization in the presence of connate or ground waters. Unexchanged fossil carbonates are common through Mesozoic and Cenozoic times, but are rarely preserved from earlier times. APPLICATION TO HIGH-TEMPERATURE

RocKs

The carbonate paleotemperature scale for sedimentary materials was based on the fractionation of oxygen isotopes between ocean water and the calcite shell material. In principle any pair of oxygen-containing phases could be used, providing that the phases are formed in isotopic equilibrium.

OXYGEN ISOTOPE GEOCHEMISTRY

47

For example, considerable effort has gone towards the establishment of a paleotemperature scale based on oxygen isotope fractionation between calcite and phosphate minerals, to make possible the determination of ocean temperatures without the necessity of assuming a value for the 0 18/0 16 ratio of the oceans in the past (Tudge, 1960). If a carbonatephosphate isotopic thermometer can be developed, it will be possible to determine temperature of shell deposition from analysis of these two phases, then to calculate from that temperature the isotopic composition of water from which the phases were precipitated. One can then determine the variation of 0 18 /0 16 in the oceans with time, information which is most important in the study of history and evolution of the oceans. It was shown by Clayton and Epstein ( 1958) that there are large isotopic fractionations between some pairs of minerals in igneous, metamorphic, and hydrothermal rocks which vary systematically with the geologically estimated temperature of crystallization. Since that time, investigation has continued in order to discover whether the isotopic fractionation between minerals is sufficiently well-behaved to provide a method for quantitative thermometry of these higher temperature rocks. CALIBRATION OF ISOTOPIC THERMOMETERS

The first requirement for any quantitative thermometer is that the scale be calibrated. For each isotope exchange reaction, the equilibrium constant must be known as a function of temperature over the range of geological interest. For the carbonate-ocean-water paleotemperature scale, this was accomplished by growing shells in water of known isotopic composition at known temperature (Epstein et al., 1953). The results obtained were in substantial agreement with those based on inorganically precipitated calcite ( McCrea, 1950) . Analogous calibrations must be made for high-temperature equilibria. The theory of isotopic fractionation in equilibrium reactions as given by Urey (1947) and by Bigeleisen and Mayer (1947) permits accurate calculation of exchange equilibrium constants at any temperature based on knowledge of molecular vibration frequencies alone, but this theory is strictly applicable only to perfect gases. No satisfactory theoretical treatment has yet been made for reactions involving liquids or solids, although some attempts have been made (McCrea, 1950; Grant, 1954; Feder, 1954). Even though we cannot yet make accurate theoretical calculations of exchange equilibrium constants for condensed phases, we may still expect to find generally similar variation of K as a function of T. For perfect gas reactions, there are two temperature regions where behaviour of K is simple: at low temperatures (generally much below room temperature) the equilibrium constant follows a law: ln K

a:

1/T,

48

ROBERT N. CLAYTON

where T is the absolute temperature. At high temperatures the equilibrium constant follows the equation ln K

a:

1/1'2 •

The definition of "high temperature" and "low temperature" depends on the vibration frequencies of the molecules involved in the reaction. Examples

500 30

200

t°C 100

25

0

I. CO 2 -S0 2 2.

co - 02

3 . 02 - H 20

4. COrCO

20

C

0 0 0

10

0

-4 ~--__..___.....______.._____.____,____.....______. 4 14 0 2 10 12 FIGURE

2. Variation of isotopic fractionation with temperature for some simple gas reactions.

49

OXYGEN ISOTOPE GEOCHEMISTRY

of temperatures dependence of exchange equilibrium constant for some simple molecules are shown in Figure 2 (based on calculations of Urey, 1947). As can be seen from the graphs, some systems show "cross-overs," that is, temperatures at which the direction of isotopic fractionation changes. At the present time, only a few experimental measurements have been made of oxygen exchange equilibrium constants in mineral systems. The most thoroughly studied reaction is that between calcite and water. The results are shown in Figure 3. The low temperature points are the data of Epstein et al. ( 1953), based on biologically precipitated calcite covering the temperature range 0-30°C. The high temperature measurements (Clayton, 1959, 1961) cover the range 190-750°C; in these experiments calcite was recrystallized in water in high pressure hydrothermal apparatus. All the Temperature- °C 1000

400

200

100

30

6 FIGURE

IOo/T 2

8

10

12

3. Isotopic fractionation between calcite and wate~.

measurements can be fitted by a straight line on the ln K vs. 1/T 2 plot and can be represented by an empirical linear equation:

ln K

= 2730T-

2

~

.00256.

The "cross-over" at high temperature is to be expected for reactions involving water or other species with OH bonds, since the fractionation contributed by these high-frequency vibrations does - not approach the 1/T2 dependence until ~2000° K. No other isotopic systems have yet been studied over a wide temperature

50

ROBERT N. CLAYTON

range in the laboratory. Pending the results of such studies, an attempt has been made to use the calcite-water fractionation to calibrate other isotopic fractionations by using natural assemblages ( Clayton and Epstein, 1961). Several assumptions were made in order to derive these calibration estimates: ( 1 ) that a number of hydrothermal quartz-calcite assemblages analysed by Clayton and Epstein ( 1958) had crystallized at equilibrium from waters which did not deviate greatly in 0 18/0 16 from some average value; ( 2) that all the fractionations could be represented by an equation of the form: ln K AT-2 - B over the temperature range O - 750° C; ( 3) that the constant B in such equations is zero for systems not involving water. By this means estimates were derived of the temperature variations of fractionations involving quartz, calcite, iron oxides, and water. The empirical equations for these systems relating isotopic fractionation ( expressed as natural logarithm of the equilibrium constant) to absolute temperature, T, are as follows: ln K QW 3629 2 - 0.00256 ln KQc = 899 T -2 ln KQH = 3216 2 ln K cw = 2730 2 - 0.00256 ln KcH = 2317 2 ln KHw = 413 T- 2 - 0.00256 Recently laboratory measurements have been made on the quartz-water and magnetite-water systems (O'Neil and Clayton, 1961; O'Neil, 1962). For the quartz-water system, experimental data from 385 ° C to 800° C are in good agreement with the equation given above. This geologically-derived equation appears to be valid within ~0.5%o over the temperature range of the experiments. Laboratory measurements on the magnetite-water system, however, are considerably different from the predicted values, with magnetite concentrating the light isotope relative to water by as much as 8%0 in the temperature range 600-800 ° C. Lower temperature experimental data are not yet available, but the measurements on natural materials make it very unlikely that the magnetite-water fractionation is more than a few permit at temperatures below ~200 °C. This implies that the behaviour of the magnetite-water system is highly non-linear on the ln K vs. 1/T 2 plot. As a result, "temperatures" calculated from the equation above will be considerably too low in the middle to high temperature region.

=

=

rrrr-

TESTS OF VALIDITY

If a measured isotopic fractionation is to yield the temperature of some past geological event, it is necessary (a) that an equilibrium isotopic distribution between two phases be established in some recognizable geological process and ( b) that the isotopic compositions of the minerals were then frozen in and not subsequently altered.

OXYGEN ISOTOPE GEOCHEMISTRY

51

In ocean-water paleotemperature studies, examples have been found of failure to meet each of these requirements. Some organisms precipitate calcite out of equilibrium with the water in which they grow ( Lowenstam and Epstein, 195 7). Examples are common of shells which have undergone isotopic exchange after their initial precipitation in some postdiagenetic process not sufficiently extreme to be recognized as a metamorphism. For ocean-water phenomena it is usually not too difficult to tell when a sample has failed to meet the above requirements, since a small departure leads to unreasonable temperatures. But for most higher-temperature geological processes, we have little information as to what temperatures are reasonable or unreasonable, so that other criteria must be found. It is possible to test the validity of the results of isotopic temperature measurement by a method rarely possible with mineralogical or elementdistribution geothermometers: several independent isotopic temperatures may be determined for a single rock. A rock containing N oxygen-bearing minerals will give N-1 independent isotopic fractionations, and hence N -1 measures of temperature. If these temperatures are not concordant, then one or other of the requirements has not been satisfied. There is an obvious analogy with the practice of determining absolute ages of rocks and minerals by measurement of decay products of several different radioactive parent nuclides from the same sample. Such tests of isotopic thermometry can only be made after the calibration function is known for several mineral systems, that is, after exchange equilibrium constants have been determined in the laboratory over a wide temperature range for many mineral pairs. The field has not reached this stage of development and other simpler tests must be used at the present time. One line of attack which is now under way (Schwarcz et al., 1961) is to compare the results of istopic measurements with the results of measurements of other properties of the system which may be governed by the temperature of crystallization of the rock. The distribution of elements between phases is such a property, and use of this distribution has been suggested for geological thermometry in several cases: magnesium in the system calcite-dolomite ( Graf and Goldsmith, 1955) ; sodium and potassium in the system muscovite-paragonite (Yoder, 1957); iron in the system sphalerite-pyrrhotite ( Kullerud, 1959). None of these systems provides a fool-proof geological thermometer against which others may be calibrated, but comparisons of results of different approaches may help determine the ranges of applicability of the various procedures. CASE HISTORIES

Hydrothermal Alteration A paper by Engel et al. ( 1958) describes the results of an isotopic study of the hydrothermal alteration of a calcite limestone. The Leadville lime-

52

ROBERT N. CLAYTON

stone ( Mississippian age) in central Colorado is for the most part a rather pure, fine-grained calcitic limestone, in most places not appreciably metamorphosed. Some layers of the formation typically contain abundant chert nodules. In an area of a few hundred square miles around the mining towns of Leadville and Gilman, the limestone has been hydrothermally altered to dolomite. First the fine-grained calcite was replaced by a dark fine-grained dolomite; then this dolomite was recrystallized in part to give coarse-grained white dolomite crystals, usually to produce a black and white banded rock, with the banding not necessarily parallel to the bedding. Associated with the recrystallization of dolomite was the emplacement of large amounts of sulphide minerals, producing the important lead-zinc-silver ore deposits. The channels by which the ore~depositing fluids moved can be located in the areas of most intense mineralization. It is reasonable to assume that these were also pathways for introduction of the solutions which caused the first alteration of calcite to dolomite, and then the recrystallization of the dolomite. Measurements of 0 18/ 0 16 and C 13 / C 12 ratios were made on the various

••

24 23 22

EB 0

•

21

•

• 0

~ ·

~"'

C) 20 C) V)

$

0

19

+ Quartz

1817-

0

8

• Fine grained dolomite

0

EB Medium crystalline dolomite

0

16

Coarse white 0 dolomite crystals

+ 0-100

15 FIGURE

--· --·- -

EXPLANATION

1020

.oil

10,0~0

Distance m feet from Gilman ore 4. Variation in

of hydrothermal dolomite and quartz as a function of dis.tance from major ore bodies. ·

Q18/Q16

53

OXYGEN ISOTOPE GEOCHEMISTRY

carbonate rocks: fine-grained unaltered calcite, fine-grained dolomite, and coarsely recrystallized dolomite, and oxygen isotope measurements were made also on chert nodules and quartz formed by recrystallization of chert The unaltered limestone has oxygen and carbon isotopic compositions typical of Paleozoic marine limestones observed in many parts of the world. At the periphery of the dolomitized area, the calcite limestone, although not apparently recrystallized, shows lower 0 18 /0 16 values, indicating exchange with oxygen of hydrothermal fluids. Figure 4 shows the variations in 0 18/0 16 in dolomite and quartz as a function of distance from the known major ore bodies. The dark, dense dolomite has an isotopic composition very similar to that of the unaltered calcitic limestone farther away, and is rather uniform throughout the halo of dolomitization. The 0 18 contents of the quartz and white crystalline dolomite vary over a considerable range, becoming progressively less as the ore body is approached. Far from the source of hydrothermal fluids, the 0 18 / 0 16 ratio in the white recrystallized dolomite is the same as that in the dark, fine-grained dolomite. Isotopic exchange of carbonates with water at elevated temperatures leads to a decrease in 0 18 content of the carbonates, the decrease being greater the higher the temperature. Engel et al. have interpreted their observations as the result of exchange of carbonate rocks with aqueous hydrothermal fluids in a temperature gradient radiating from the conduits observed in the large ore bodies. It is possible in a few cases to find quartz-calcite mineral pairs from which one can estimate a temperature of crystallization using the isotopic thermometer calibrations discussed above. The results are shown in Table I. TABLE I QUARTZ-CALCITE TEMPERATURES FROM RECRYSTALLIZED LEADVILLE LIMESTONE

Sample no.

Locality

LV86

Barida Cabins

LV274

Taylor Pass

LV2

Fulford

LV4

Gilman mine

LV8

Marble, Colo.

Description unaltered cherty limestone unaltered cherty limestone incipiently recrystallized calcite and chert Crystalline quartz and calcite Contact metamorphic marble

llQ

Ile

t °C.

29 . 4

21.8

50°

28.0

21.0

80°

22 . 2

17.8

175°

16.1

13.4

300°

22 . 7

21.1

570°

The sulphide mineralized areas in the Leadville limestone are small in area compared to the dolomite halo. Presumably there are other mineralized areas within the halo, which are unknown because they are not exposed at the surface. ( Most of the dolomitized area is not exposed.) It seems likely that drill samples taken on a grid with separation of the order of one mile would permit contouring of 0 18 /0 16 levels, leading to the discovery of other conduits for hydrothermal fluids, and possibly other ore bodies.

54

ROBERT N. CLAYTON

Progressive Regional Metamorphism James and Clayton ( 1962) studied vanat10ns in oxygen isotope composition in the metamorphosed Precambrian iron formations of the Lake Superior region. The rocks studied consist of banded quartz-magnetite or quartz-hematite iron formations in which individual silica-rich or iron oxide-rich layers are on the order of one or two millimeters thick. The rocks are of sedimentary origin, and have all been metamorphosed to a greater or less extent. The metamorphism has been discussed by James ( 1955) , and zones of progressive metamorphism have been mapped by observation of the mineralogy of pelitic schists associated with the iron formations. It is possible, therefore, to sample iron formation from known metamorphic rank over a fairly wide range of metamorphic conditions. The iron formations provide a particularly attractive situation for a study of isotopic thermometry. The oxygen isotope fractionation between quartz and magnetite is the largest yet known for any mineral pair; that is, at equilibrium quartz concentrates 0 18 relative to all other mineral phases, magnetite concentrates 0 16 relative to other phases. This means that the quartz-magnetite thermometer is intrinsically more sensitive than thermometers based on other mineral pairs. Also, the quartz-magnetite and quartz-hematite mineral assemblages are stable over a wide range of conditions, so that the iron formations represent a simple two-phase chemical system in all the metamorphic zones studied. TABLE II QUARTZ-IRON OXIDE ISOTOPIC TEMPERATURES FROM METAMORPHOSED IRON FORMATIONS

Sample no.

47-49 14-50 24-59 56-52 66-51 132-51 61-58 54-53 40-58 13-59 10-59 57-58 3-58 59-30 36-58 39-59

Locality

Metamorphic zone

Chlorite Cayia mine, Mich. Iron River, Mich. Chlorite Auburn Pit, West. Chlorite Mesabi, Minn. Chlorite Vicar Mine, Mich. Iron Mt., Mich. Biotite Iron Mt., Mich. Biotite Shouldeis-Doane Expl., Garnet Mich. Greenwood Mine, Mich. Garnet Florence County, Wis. Garnet Staurolite Champion Mine, Mich. Champion Mine, Mich. Staurolite Groveland Mine, Mich . Staurolite Felch Ridge, Mich. Staurolite Republic, Mich. Sillimanite Republic, Mich. Sillimanite Babbitt Mine, Minn. >Sillimanite

llQ

19 . 1 19.0 20 .8

t °C.

llM -llH

1.2

16 .5 15.9 16 .2 13.3

-1.4 3 .9

11. 9 15.2 11.5 11.2 16.1 15.0 10.4 8.7 14 .4

3.5 4 .3 -0.9 -0 . 1 -0 . 1 -0.5 5.3

-0.9 -0 . 2

5.4 3.4

0.6 6.6 7.7

130 135 130 150 245 275 295 345 270 235 320 310 390 280 320 320

Some numerical results of this work are shown in Table II. It should be emphasized that the absolute values of the "temperature" numbers will surely be changed as our knowledge of the quartz-magnetite "calibration function" improves. The changes could easily be more than 100°C. However, the relative values and trends will remain as shown in the table.

55

OXYGEN ISOTOPE GEOCHEMISTRY

Up through the garnet zone, the isotopic fractionations decrease regularly with metamorphic rank as is to be expected with increasing temperature of recrystallization. Above the garnet zone, a large spread is found in isotopic "temperature" and the mean seems to level off at about 350°C. This phenomenon in the higher-rank metamorphic rocks is difficult to understand. James and Clayton ( 1962) have suggested that it is due to retrograde effects: isotope exchange rates between minerals may be too high at higher temperatures to permit the quenching in of the smaller isotopic fractionation expected for the higher temperature rocks. Igneous Rocks

Oxygen isotope measurements have not yet been applied to the question of temperatures of crystallization of igneous rocks, primarily because of lack of knowledge of the relevant isotopic fractionations in laboratory systems. Many measurements have been made on separated minerals from igneous rocks ( Taylor and Epstein, 1926a, b). The distribution of oxygen isotopes among the major mineral phases of an igneous rock is determined primarily by the chemical and crystallographic properties of the phases. In all the rocks examined, the 0 18 / 0 16 ratios of minerals within a rock were always ranked in the order: quartz, feldspars, hornblende, pyroxenes, olivine, biotite, magnetite. Examples for some igneous rocks are shown in Table III ( taken from Taylor and Epstein, 1962a). This ordering is observed TYPICAL 0 18 / 0

16

TABLE III \'ALt:ES FOR MINERALS FRO!\! IGNEOUS ROCKS a-values

Rock Duke Island Gabbro San Marcos Gabbro Bonsall Tonalite San Jose Tona lite Shake Flat Quartz Monzonite Rock Creek Pegmatite

Quartz

Kfeldspar

Plagioclase

Hornblende

7.4

Pyroxene

Biotite

5 .9

2.1

,'> . 9

1 .6

10 . 2

7.5

6 .5

10 .3

8 ..~

6 .9

5.4

9 .7

8 .0

6 .6

;)

6.4

5 . -1

10. :J

9 .0

8 .9

11 . 9

10 .5

10.3

Magnetite

- __ •)

7.1

to hold for a wide variety of rocks ranging from ultrabasic rocks to acidic granites and pegmatites. The simplest explanation for this over-all regularity is that the isotopic fractionations represent something close to equilibrium values at temperatures when the oxygen atoms became immobile in their crystals. This may not be identical with the temperature of solidification of magma as usually thought of, but such distinctions cannot be resolved until actual numerical isotopic temperatures can be determined.

56

ROBERT N. CLAYTON CONCLUSIONS

The current research activity in high-temperature oxygen isotope geothermometry is concentrated along two lines: the determination in the laboratory of exchange equilibrium constants as functions of temperature, and measurements of natural mineral assemblages selected so that the isotopically deduced "temperatures" may be compared with temperatures of formation of the same minerals as estimated from other, non-isotopic, measurements. It will be some years yet before one can hope to apply isotopic thermometry with its full potential accuracy to the solution of petrological problems. We must learn which mineral systems are most likely to produce equilibrium isotopic distributions, and to preserve these distributions through long geologic periods after formation of the minerals. We must learn how to interpret the temperature of last isotopic exchange in relation to the thermal history of the sample, particularly in cases where there is a long, slow cooling following initial crystallization. The results obtained so far have been encouraging, and there is every reason to be confident that oxygen isotope measurements will eventually provide accurate quantitative information on crystallization temperatures of many important rocks and minerals. REFERENCES BIGELEISEN, J., and MAYER, M. G. ( 1947). Isotopic exchange reactions. J. Chem. Phys. 15: 261. CLAYTON, R. N. (1959). Oxygen isotope fractionation in the system calcium carbonatewater. J. Chem. Phys. 30: 1246. - - - ( 1961). Oxygen isotope fractionation between calcium carbonate and water. J. Chem. Phys. 34: 724. - - - and EPSTEIN, S. ( 1958). The relationship between 01s;o1s ratios in coexisting quartz, carbonate and iron oxides from various geological deposits. J. Geo!. 66: 352. - - - and MAYEDA, T . K . ( 1963). The use of bromine pentafluoride in the extraction of oxygen from oxides and silicates for isotopic analysis. Geochim. et Cosmochirn. Acta 27: 43. CRAIG, H . (1961) . Standard for reporting concentrations of deuterium and oxygen-18 in natural waters. Science 133: 1833-4. EMILIANI, C. ( 1955a) . Pleistocene temperatures. J. Geo!. 63: 538. - - - ( 1955b). Pleistocene temperature variations in the Mediterranean. Quaternaria 3: 87. - - - ( 1956). Oligocene and Miocene temperatures of the equatorial and subtropical Atlantic Ocean. J. Geol. 64: 281. - - - (1957). Temperature and age analysis of deep-sea cores. Science 125: 383. ENGEL, A. E. J., CLAYTON, R. N., and EPSTEIN, S. ( 1958). Variations in isotopic composition of oxygen and carbon in Leadville limestone (Mississippian, Colorado) and its hydrothermal and metamorphic phases. J. Geo!. 66: 374. EPSTEIN, S., BucHsBAUM, R., LOWEN STAM, H. A., and UREY, H'. C . ( 1953). Revised ·carbonate-water isotopic temperature scale. Bull. Geo!. Soc. Arn. 64 : 1315. - - - and LowENSTAM, H. A. ( 1953). Temperature-shell-growth relations of Recent and interglacial Pleistocene shoal-water biota from Bermuda. J. Geo!. 61: 424. FEDER, H. M. ( 1954) . Ionic hydration: an isotopic fractionation technique. Ph.D. thesis, University of Chicago.

OXYGEN ISOTOPE GEOCHEMISTRY

57

GIAUQUE, W. F., and JOHNSTON, J. L. (1929). An isotope of oxygen, mass 18: J. Am. Chem. Soc. 51: 1436. GRAF, D. L., and GOLDSMITH, J. R. ( 1955). Dolomite-magnesian calcite relations at elevated temperatures and CO 2 pressures. Geochim. et Cosmochim. Acta 7: 109. GRANT, F. S. (1954) . The geological significance of variations in the abundances of the isotope of silicon in rocks. Geochim. et Cosmochim. Acta 5: 525. JAMES, H . L. (1955) . Zones of regional metamorphism in the Precambrian of northern Michigan. Bull. Geol. Soc. Am. 66: 1455. - - - and CLAYTON, R. N. ( 1962). Oxygen isotope fractionation in metamorphosed iron-formations of the Lake Superior region and in other iron-rich rocks. In Petrologic Studies: A Volume to Honor A. F. Buddington, Geo!. Soc. Am.: 217. KuLLERUD, G. ( 1959). Sulfide systems as geological thermometers. In P. H. Abelson (ed.), Researches in Geochemistry (New York : Wiley), 301-35. LowENSTAM, H . A. and EPSTEIN, S. ( 1954) . Paleotemperatures of the Post-Aptian Cretaceous as determined by the oxygen isotope method. J. Geo!. 62: 207. - - - ( 195 7). On the origin of sedimentary aragonite needles of the Great Bahama Bank. J. Geo!. 65: 364. McCREA, J. M. ( 1950). On the isotopic chemistry of carbonates and a paleotemperature scale. J. Chem. Phys. 18: 849. McKINNEY, C. R., McCREA, J. M., ALLEN, H. A., EPSTEIN, S., and UREY, H. C. ( 1950). Improvements in mass spectrometers for the measurement of small differences in isotope abundance ratios. Rev. Sci. Instr. 21 : 724. NIER, A. 0. C. ( 194 7). A mass spectrometer for isotope and gas analysis. Rev. Sci. Instr. 18: 398. O'NEIL, J. R. (1963). Ph.D. thesis, University of Chicago. - - - and CLAYTON, R . N. ( 1961). Oxygen isotope fractionation in the system quartz-water. Paper at annual meeting of G.S.A. RosHoLT, J. N., EMILIANI, C., GEISS, J., KoczY, F. F., and WANGERSKY, P. J. (1961). Absolute dating of deep-sea cores by the Pa23 1 /Th230 method. J. Geol. 69: 162. SCHWARCZ, H. P., CLAYTON, R. N., and MAYEDA, T . K. ( 1961). Oxygen isotope variations in metamorphosed calcareous rocks of New England. Paper at annual meeting of G.S.A. TAYLOR, H. P., and EPSTEIN, S. ( 1962a). Relationship between Ql8/Ql6 ratios in coexisting minerals of igneous and metamorphic rocks ( Part 1). Bull. Geol. Soc. Am. 73: 461. - - - ( 1962b) . Relationship between 0 18/016 ratios in coexisting minerals of igneous and metamorphic rocks (Part 2). Bull. Geo!. Soc. Am. 73: 675. TuDGE, A. P. ( 1960). A method of analysis of oxygen isotopes in orthophosphateits use in the measurement of paleotemperatures. Geochim. et Cosmochim. Acta 18: 81. UREY, H. C. (1947). The thermodynamic properties of isotopic substances. J. Chem. Soc., 562-81. YoDER, H. S. (1957). Experimental studies on micas: a synthesis. Proc. 6th Nat.'!. Conf. Clays and Clay Minerals, Berkeley, Calif., 42-60.

SOME PROBLEMS OF THE GEOCHEMISTRY OF FLUORINE* Michael Fleischer and W. 0. Robinson

ABSTRACT

The available literature on the abundance of fluorine is reviewed critically. Arithmetic averages obtained are (in ppm. F): basalts 360, andesites 210, rhyolites 480, phonolites 930; gabbros and diabases 420, granites and granodiorites 810, alkalic rocks 1000. Similar averages for sedimentary rocks are limestones 220, dolomites 260, sandstones and graywackes 180, shales 800, oceanic sediments 730, soils 285 ppm. F. Uncertainties in these averages are discussed; the distribution of analyses suggests that the modal value may be more significant than the arithmetic mean. Maps of the United States are presented which show the maximum reported values of F in ground waters for each county, with emphasis on unsolved problems of the relation of fluorine content of ground water to the types of rocks from which the waters come.

THIS PAPER IS ESSENTIALLY AN ABRIDGEMENT of a review of the geochemistry of fluorine, prepared in 1959 for publication as part of a symposium on the Physiological Effects of Fluorine to be published by the U.S. Public Health Service. In the present paper, emphasis has been placed on data of geological interest and only the most important literature is cited. Recent reviews of the geochemistry of fluorine by Barth ( 194 7), Borchert (1952), Correns (1956, 1957), Kokubu (1956), Koritnig (1950, 1951), and Gmelin's H andbuch ( 1959) were invaluable in the preparation of this report. GENERAL GEOCHEMICAL CONSIDERATIONS Fluorine is the lightest element of Group VII of the periodic table of the elements, with atomic number 9 and atomic weight 19.00. It consists of a single isotope. Its valence in all naturally occurring compounds is minus one. Fluoride ion has the ionic radius 1.36 A. It is therefore readily isomorphous with the hydroxyl ion, (OHt1 (radius 1.40 A), a fact of great importance in its geochemical occurrence and behaviour. To a lesser degree, fluoride ion may isomorphously replace chloride ion, c1- 1 ( radius 1.81 A), and oxygen ion, 0-2 (radius 1.40 A). Fluorine is strongly lithophilic in character; that is, it occurs mainly in the silicate minerals of the Earth's crust. During the course of crystallization of magmas, fluorine is concentrated in the last fractions to crystallize and *Publication authorized by the Director, U.S. Geological Survey.

59

THE GEOCHEMISTRY OF FLUORINE

in the residual solutions and vapours. It is consequently enriched in rocks of high silica content and in the alkalic rocks and especially in the pegmatitic fades of such rocks, in hydrothermal solutions, in volcanic gases and the associated fumaroles and hot springs, and in the products of pneumatolytic reactions. This concentration is the main reason for the large number of minerals that contain fluorine in significant amounts. ABUNDANCE OF FLUORINE IN ROCKS

General Considerations Some of the problems involved in estimating abundances of elements, especially the adequacy of sampling and the accuracy of results, have been discussed previously ( Fleischer, 1955; Ahrens, 195 7; Fleischer and Chao, 1960). One would like to use determinations of fluorine made very carefully on well-described rocks, especially on consanguineous series of igneous rocks. Hundreds of determinations of fluorine in rocks have been published; using them involves the compiler in considerable difficulty. It is known that the methods of analysis for fluorine in rocks were inadequate until the 1930's and that even now the methods are of such difficulty that there is considerable uncertainty attached to them. We have therefore chosen to give in Tables I and IV averages based on analyses taken from papers in which attention was focused on fluorine. This should have the effect of ensuring the accuracy of the determinations of fluorine used, at the cost, however, of reducing the sample size and of including analyses made on insufficiently characterized rocks, thereby increasing the danger of inadequate sampling. For comparison with the figures given in Table I, we have summarized TABLE I (see Fig. 1) FLUORINE CONTENT OF IGNEOUS ROCKS (Literature)

Rock name*

:'llo. of samples

F, ppm Range

Average

A. Extrusive rocks 130 20-1060 Basalt 77 0-780 Andesite 79t 0-6850 Rhyolite, obsidian, liparite} 78t 0-1700 Phonolite 14 860-1490

Gabbro, diabase Granite and granodiorite Alkalic rocks

B. Intrusive rocks 26 50-1100 94t 20-6500 } 93§ 20-2700 651/ 200-2250

*Rock names as given by each author tAH data included tExcluding the highest value of 6850 §Excluding the highest value of 6500 lllncluding syenites, nepheline syenites, essexites, shonkinites

360 210

575 480 930 420 870 810

1000

60

MICHAEL FLEISCHER AND W. 0 . ROBINSON

TABLE II FLl,ORI::-:E CONTENT OF IGNEOUS ROCKS

(U. S. Geo!. Survey, 1959-1961)

Rock name*

No. of samples

F, ppm Range

Average

Basalt, Hawaii Basalt, others Andesite Rhyolite, obsidian I Rhyolite, obsidian IIt

A. Extrusive rocks 80 200-1300 58 100-2400 6 200-700 66 100-4600 65 100-1900

340 500 470 850 790

Gabbro, diabase Granite and granodiorite Alkalic rocks!

B. Intrusive rocks 21 100-900 89 100-2600 6 300-900

440 810 570

*Rock names as given by collector tExcluding the highest value of 4600 tSyenites and nepheline syenites

in Table II analyses of igneous rocks made from 1959 to 1961 in the Denver laboratory of the U.S. Geological Survey; these analyses reported to the nearest 0.01 per cent, were made by the same method in a single laboratory. Comparison of the data of Tables I and II shows good agreement for basalts for gabbro and diabase, and for granites and granodiorites, and poor agreement for rhyolites. Inspection of Figure 1, which is a plot of the data used for Table I, shows that there is a wide range of fluorine content for each type. It will be noted that the average content and median content differ considerably for some types of rocks; it may well be that the median values are more meaningful than the averages. Estimates of fluorine contents of igneous rocks are collected in Table III. There are not enough data to state whether or not regional variation is a major cause of the variability noted, nor whether systematic analytical error is a factor. It seems likely, however, that the mineralogical nature of the samples is a major factor; this is especially true of the granitic rocks, because it is well known that granites that have undergone greisenization have very high fluorine contents. It is quite possible that some of the highest values for granitic rocks refer to greisenized rocks; four such samples analysed by the U.S. Geological Survey contained 2300-4900 ppm F. In addition to the data given in Tables I to III, Menyailov, Danilova, and lndichenko ( 194 7) give 30-250 ( average 150) ppm F in four dunites, peridotites, and serpentinites, and Seraphim ( 1951 ) reports 450 and 860 ppm F in two kimberlites. Seraphim (1951) found 330 to 1100 ( average 660) ppm F in four samples of diorite and quartz diorite; recent analyses by the U.S. Geological Survey of nine diorites and quartz diorites gave 300 to 1300 (average 740) ppm F. It is evident that the ranges of fluorine content of the various rock types overlap greatly; nevertheless, there is in both the extrusive and intrusive

THE GEOCHEMISTRY OF FLUORINE

61

M

•

FLUORINE DISTRIBUTION IN IGNEOUS ROCKS

Andesites 77 samples Median 175 Average 210

M

• Cf)

20

Basalts

Lu

92 samples

..J CL ~

~ u. 0

Median 275 Average 380

10

0:

~ :;;

::,

z

0

Obsidians, Rhyoliles, etc.

99 samples Median 275 Average 480

•

M Granites and Granodiorites

44 samples

10

12 F FIGURE

IN HUNDREDS OF ppm

1. Distribution of fluorine in igneous rocks.

series, excepting the phonolites and the alkalic intrusives, a definite tendency towards higher fluorine contents with increasing content of Si02. The average for andesites in Table I is lower than one might expect; the analyses are mostly of andesites from Japan and the low average may be a regional effect. There is no apparent correlation of fluorine content with that of any major element other than Si02 in the rocks. The alkalic rocks are definitely the richest in fluorine in both series. Except perhaps for the granitic rocks, there is but little difference between the contents of fluorine in the extrusive rocks and their intrusive equivalents, although the latter seem to have slightly higher contents on the average.

62

MICHAEL FLEISCHER AND W. O. ROBINSON

TABLE III FLUORINE CONTENT OF IGNEOUS ROCKS: COMPARISON OF AVERAGES OF VARIOUS INVESTIGATORS Rock name

Reference

Basalt Basalt, Hawaii Basalt Basalt* Basalt* Basalt* Basalt* Basalt, Columbia R.* Andesite Andesite Andesite* Andesite* Rhyolites, etc. Rhyolites Rhyolites* Rhyolites* Rhyolites* Rhyolites* Rhyolites*

A. Extrusive rocks Table I Table II Table II Barth and Bruun (1945) Comucci and Mazzi (1957) Kokubu (1956) Koritnig (1951) Seraphim (1951) Table I Table II Kokubu (1956) Koritnig (1951) Table I Table II Comucci and Mazzi (1957), liparites Kokubu (1956), dacites Kokubu (1956), liparites Shepherd (1940) , obsidians Shepherd (1940), rhyolites

Gabbro & diabase Gabbro & diabase Gabbro* Gabbro* Gabbro* Diabase* Granite and granodiorite Granite and granodiorite Granodiorite* Granodiorite* Granodiorite and tonalite* Tonalite* Granite* Granite* Granite* Granite* Granite* Alkalic Rocks Alkalic Rocks Syenite* Syenite* Syenite* Nepheline Syenite* Nepheline Syenite* Nepheline Syenite* Shonkinite*

B. Intrusive rocks Table I Table II Kokubu (1956) Koritnig (1951) Troeger (1935) Seraphim (1951) Table I Table II Koritnig (1951) Troeger (1935) Kokubu (1956) Seraphim (1951) Jahns (1953) Kokubu (1956) Koritnig (1951) Sahama (1945) Seraphim (1951) Table I Table II Saito (1950) Seraphim (1951) Troeger (1935) Koritnig (1951) Saito (1950) T roeger (1935) Shepherd (1940)

No. of samples 130 80 58 5 18 21 3 16 77 6 52 2 78 65 8 6 16 16

41

26 21 3 11 11 93 89 2 19 5 23 5 13 20 40 6.5 6 7 16 22 17 6

Average F, ppm 360 340 500 180 480 280 730 540 210 470 260 505 480 790 750 260 280 700 1080 420 440 480 310 300 450 810 810 500 200 1050 670 1900 830 1330 2950 800 1000 570 1100 1480 600 1190 500 8000 1380

*These data are included in the averages given in Table I

Shepherd ( 1940) gave a series of analyses of obsidians from Little Glass Mountain, California, that showed a decrease of fluorine content from 640 to 340 ppm F with increasing vesicularity of the samples, which seems to indicate a considerable loss of fluorine as the volatile phase escapes. Fluorine may also be lost by leaching of volcanic rocks and especially of porous varieties; this has been emphasized by Menyailov, Danilova, and

63

THE GEOCHEMISTRY OF FLUORINE

lndichenko ( 194 7 ) and by Danilova ( 1949) , and is corroborated for volcanic ash by the data of Basharina ( 1958) and of Stefannsson and Sigurjonsson ( 195 7) which are discussed further under "Fluoride in Waters." Similar data are not available for intrusive rocks. It is generally agreed that fluorine concentrates in late stages of the sequence of crystallization, but quantitative data are few. Jahns ( 1953), from modal analyses of two lithium-rich pegmatites and chemical analysis of a composite sample of a third, gave 0.4, 0.55, and 0.9 per cent F for the entire pegmatite dikes. It was formerly believed that nearly all the fluorine of crystalline igneous rocks is present as fluor-apatite, and it was suggested that multiplying the P205 content by the appropriate F /P205 ratio would give a fair estimate of the fluorine content; the estimate of abundance ( 300 ppm F) by Clarke and Washington ( 1924) was based chiefly on this calculation. Work in recent years by many investigators, especially Koritnig ( 1951 ) , has shown, however, that in many crystalline rocks, including both igneous and sedimentary, much or even most of the fluorine is present in silicate minerals, especially mica, amphibole, and sphene, so that such calculations can give misleading results. Metamorphic Rocks The available data are too scattered to permit giving averages of specific types of metamorphic rocks. The general range is indicated by a compilation of sixty-nine analyses that show 60 to 1500 (average 380) ppm F. In general, rocks rich in mica and amphibole are highest in fluorine. The TABLE IV FLUORINE CONTENT OF SEDIMENTARY ROCKS (see Fig. 2)

Rock name Limestone* Dolomite Sandstones and graywackest Sandstones and graywackest Shales It Shales II§ Oceanic sediments Volcanic ash and bentonite Gypsum, anhydrite, and polyhalitell Soils,r

F, ppm

;',lo. of samples

Range

Average

98 14 50 49 82 79 79 270

0-1210 110-400 10-1100 10-880 10-7600 10-7600 100-1600 100-2900

220 260 200 180 940 800 730 750

30 327

10-890

> = > "" >

A

~

•5 •5 •7 • 75 •9

B

@)

~

N 14

N 16

D

C

E

I

F

5---1

1·5

MG

K

·4-

3·5 66

64

SI

61

64

70

I

I

• 66

SI I

I

68 I

70

I

I

I

FIGURE 11. Relationships between variables in the Climax Stock granodiorite, Nye County, Nevada, based on analyses by Houser and Poole (1959) and Izett (1960). Figures (A) through (D) indicate strength of correlation coefficients between pairs of variables; all coefficients positive except where minus sign against tie line. Symbols Fe 2 O 3 ; FeO MgO; FE SiO 2 ; MG Na 2 O; SI Al 2 O 3 ; NA are AL quartz; plagioclase; Q specific gravity; P SG K 2 O; SP CaO; K CA chlorite; B = biotite; weight of magnetics; C KF = potash feldspar; WM W, the height above sea level; N indicates the magnetic susceptibility; W MS number of samples included {as shown in Table III). Figures ( E) and ( F) indicate scatter diagrams and regression lines for MgO (MG) and SiO 2 (SI), and K 2 O (K) and SiO 2 (SI), respectively.

= =

=

=

=

=

= = =

=

=

=

=

=

+ =

burg granite were products of metasomatism; they reported that the centre of the mass does not show these effects. In the central area both potash and soda have very small variances, whereas in the megacrystic zone soda has a variance of 0.08 and potash of 0.19 (Table III). It would be interesting to know whether the variance of the alkalis is always greater in metasomatized granites than in other granites; more data are required from other masses before generalizations can be attempted. However, the

THE QUANTITATIVE STUDY OF GRANITE MASSIFS

113

high K2O variance in the Climax Stock is interesting; it may reflect heterogeneity produced by intrusion of the adjacent quartz monzonite ( see Houser and Poole, 1961 ) , some other local variability, or even errors in the analyses. Alternatively, in granodiorites K2O percentage may commonly have a variance as large as 0.2. Many correlation coefficients and regression lines for the Climax Stock data have been computed; some of the correlation coefficients are indicated diagrammatically in Figure 11 with the aid of diagrams similar to those utilized by Chave and Mackenzie ( 1961). Intuitively several strong correlations might be expected between the variables; thus, the actual correlations proved to be rather unexpected. Modal and chemical variates are available for seven samples only ( see Table III) so their interrelationships are not shown in Figure 11. Perhaps the most surprising feature shown by Figure 11 is the lack of correlation between K2O percentage and the other oxides; the scatter of K2O percentage with respect to SiO2 percentage is shown in Figure 11£, and this should be contrasted with that for MgO and SiO2 percentages (Fig. 1 le). The lack of correlation between quartz and potash feldspar percentages, and between both of these variables and biotite percentage and weight of magnetic minerals is also unexpected. It would be instructive to compare these correlation coefficients with those for other granites. Unfortunately, there are virtually no published data for individual granite masses with which these intriguing results can be compared. Probably the correlations and variances would have been markedly different if the whole of this stock had been sampled in such a way that equal weight had been given to each unit volume of the mass. It is hoped that presentation of these limited results will provoke geochemists and petrologists to ascertain the variance of quantitative attributes within other massifs and to determine the correlations between various variables. It is almost shocking that the variance of major oxides within different types of granite masses is not known; in this situation the significance to be associated with the chemical analysis of a "typical" sample is uncertain. Whitten ( 1962b), in relation to the Wollaston pluton, Ontario, provided some evidence of the inadequacy of a single chemical analysis to typify a granite mass. In most geochemical and petrological studies isolated specimens have been analysed, and used as the bases of theory, without any assessment of the three-dimensional variability of the granite mass. In an important study of the granitic rocks of central Tien Shan, Vistelius ( 1962) published data for fifty-two samples. He showed that phosphorus bears a strong negative correlation with modal quartz and positive correlation with plagioclase and colour index. Vistelius claimed that the phosphorus content can be predicted on the basis of the modal composition of these granites, and computed the plane of phosphorus regression in the "space" of modal components by using the equation P2O5

= ao + a1Q + a2K + aaP + a4M

114

E. H. TIMOTHY WHITTEN

where Q, K, P, and M are modal volume percentages of quartz, potash feldspar, plagioclase, and mafic minerals, respectively. This method is likely to have wide use in the study of granites and other types of rocks. FUTURE DEVELOPMENTS IN QUANTITATIVE GEOCHEMISTRY

The flow chart ( Fig. 3) suggests the progress made in quantitative petrology and geochemistry within the past decade. It is useful to have some concept of the future goal of these studies. Hopefully, they should lead to realistic petrogenetic models on all scales, but such models may be markedly dissimilar to the current hypotheses based on essentially qualitative and subjective evaluations. Scientific disciplines generally involve development of hypotheses which allow prediction on the basis of facts already known. Subsequent research may indicate inadequacies and demand development of new hypotheses. When enough is known about the behaviour of the variables involved it is logical to develop differential equations as predicting tools. For sedimentation, stratigraphic models, and some mapped variables, Vistelius ( 1946), Sloss ( 1962), and Krumbein ( 1962b) pointed towards this approach. The aim of quantitative granite studies should also be towards the development of unifying differential equations; this is impracticable at the present time because of the inadequate documentation and understanding of the quantitative composition and variability of individual granite masses. Three dimensional variability of many variables for a wide variety of granite masses must be assayed, and the interlock between the variables evaluated carefully. "Automatic data acquisition" is indicated as a potential aid in the development of differential equations and petrogenetic models for granites ( Fig. 3). Although it is difficult to visualize any development which would limit the necessity for more and more critical field work, quantitative data gathering will undoubtedly be susceptible to automation. In sedimentary petrology and stratigraphic analysis progress has been made in this direction. Machines for making continuous digitized mechanical, textural, and compositional analyses of sediments are in operation. In modern drilling operations numerous bulk physical properties of rocks are measured by remote control on a routine basis. Bunker and Bradley ( 1961 ) described a nuclear irradiation technique ( involving gamma-ray absorption) suitable for field determination of the specific gravity of drill cores; such methods could be adapted for automatically digitizing data. With development of devices such as the electron probe, continuous digitized logs of bulk chemical composition will probably be a possibility within the not too distant future. To acquire sufficient data to evaluate the geochemical nature and genesis of granitic rocks automatic data acquisition is likely to become essential. Throughout this paper non-vectoral variables have been discussed, but vectoral properties must be considered in any complete study of the geo-

THE QUANTITATIVE STUDY OF GRANITE MASSIFS

115

chemical nature and evolution of granites. Such properties are susceptible to quantitative evaluation, although little work along these lines has been published. Space only permits discussion of a few facets of these important topics. Newhouse and Hagner (1947, 1949) and Newhouse, Hagner, and DeVore ( 1949), in studies of noritic and anorthositic rocks in Wyoming, suggested that the mineralogical composition is areally controlled by the regional stress system. In a detailed unpublished study of the Sherman granite, Wyoming-Colorado, Harrison ( 1951) used these concepts and plotted the poles of the planar structures on stereograms; on the stereograms Harrison recorded the modal composition for each sample locality, and then contoured the modal variables on the stereograms. The resulting diagrams suggested a strong correlation between the attitude of the planar structures within the granite and the modal composition. This ingenious technique deserves further attention. As in structural geology, one shortcoming of stereographic analyses is that the plots are divorced from geography, but the method could be adapted readily to show the geographical variation of the structural-modal correlations. Almost all granites have undergone varying degrees of neocrystallization since initial crystallization. As a result accurate quantitative measurements of structural and textural attributes, and study of their areal variability, are likely to yield important light on the geochemical evolution of individual granites. Even the quartz and the feldspar in the apparently simple Beinn an Dubhaich granite, Scotland, manifest neocrystallization effects ( e.g., Tuttle and Bowen, 1958) It is frequently suggested that the "space problem" is fundamental to the understanding of granite genesis. Evaluation of the space problem has been essentially subjective, although scientific evaluation of the problem requires objective reappraisal. Space may be made available by one, or any combination, of these mechanisms: a. mechanical removal of country rocks: ( i) stoping and internal accommodation of the mechanically removed blocks; (ii) ejection of the country rocks and some magmatic materials onto the earth surface; b. mechanical dilation of the envelope rocks; c. replacement, whereby the country rocks became pseudomorphed by granite : (i) one-way migration ("fronts") of material (e.g., ions); (ii) twoway diffusion. Detailed quantitative structural studies of the envelope rocks, the rafts of country rock within the granite, and of the granite itself, cannot fail to yield significant data on the space problem. Such work should involve modern macroscopic, mesoscopic, and microsopic structural analyses. The resulting data, although not directly geochemical, will find a place in syntheses involving assessment of granites in terms of differential equations. Recently great interest has been aroused in ignimbrites, and in the widespread sheets of basic lava and agglomerate such as those of the western

116

E. H . TIMOTHY WHITTEN

U .S.A. These extrusive materials represent immense volumes of rock, and their outpouring may be connected with the granite space problem. The section through the western U .S.A. by van Bemmelen ( 1961 ) is worthy of careful study; if erosion removed all the surfician ignimbrites and sedimentary rocks, etc. shown in his sectio~, the exposed granites would doubtless show few indications that they were penecontemporaneous with ignimbritic eruptions. However, an increasing number of vent-like features is being found associated with granites ( e.g., Reynolds, 1954 ; Whitten, 1959b ; Cater, 1960). These, however, are interesting speculations, and methods must be found to test these and other available hypotheses about the space problem. The study by Moore ( 1962) may mark a beginning in this direction, and it would be useful to extend work on the areal variability of granites to the areal variability of the chemical differences discernible in welded tuffs ( cf. Roberts and Peterson, 1961) . The study of granite and the granite controversy appears to have reached a point at which accumulation of more and more qualitative observations is unlikely to achieve major progress. If advances are to be made new objective quantitative methods of approach are essential. Only these can permit evaluation of current dogmas involving such fundamental concepts as the consanguinity of plutonic and volcanic magmas, or the discreteness of volcanic and plutonic associations. Rather than being settled, the granite controversy appears to be entering a new dimension. ACKNOWLEDGMENTS

This paper was made possible by the financial support of the National Science Foundation and the facilities of the Northwestern University Computing Center. REFERENCES ALLEN, P., and KRUMBEIN , W. C . ( 1962). Secondary trend components in the top Ashdown Pebble Bed : a case history. J. Geol. 70 : 507-38. ANDERSON, R . L., and BANCROFT, T. A. (1952). Statistical theory in research. New York: McGraw-Hill. BAIRD, A. K. , McINTYRE, D . B., and WELDAY, E. E. ( 1963) . Chemical composition of a granite pluton (Abstract) . Geol. Soc. Am. Spec. Paper 73 : 22. BARTH, T. F. W . ( 1961) . Abundance of the elements, areal averages and geochemical cycles. Geochim. et Cosmochim. Acta 23 : 1-8. - - - and DONS, J. A. (1960). Precambrian of southern Norway. Norges Geol. Undersokelse 208: 6-67. BAYLY, M. B., ( 1960) . Modal analysis by point-counter-the choice of sample area. J. Geol. Soc. Australia 6: 119-30. BEARTH, P. ( 1945) . Ueber spatalpine granitische Intrusionen in der Monte RosaBernhard-Decke. Schweiz. Mineral. Petrog. Mitt. 25 , 1-22 . BEMMELEN, R. W. VAN ( 1961) . Volcanology and geology of ignimbrites in Indonesia, north Italy, and the U .S.A. Geol. en Mijnbouw 40 (N.S.23): 399-411. BISHOP, M. S. (1960) . Subsurface mapping. New York: John Wiley. BowEN, N. L. ( 1928) . The evolution of the igneous rocks. Princeton: Princeton University Press.

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BoYER, R. E ., and KING, H. D. ( 1962) . Petrogenetic significance of heavy minerals in the San Isabel batholith, Wet Mountains, Colorado (Abstract). Geol. Soc. Am. Spec. Paper 68: 84-5. BROCK, M . R ., and HEYL, A. V. (1961) . Post-cambrian igneous rocks of the central craton, western Appalachian Mountains and Gulf Coastal Plain of the United States. U .S. Geol. Survey Prof. Paper 424D: 33-5. BROWN, P. E., and RusHTON, B. J. ( 1960). Some chemical data on the Mourne Mountain granite G2 . Geochim. et Cosmochim. Acta 18: 193-9. BUDDINGTON, A. F. (1927). Coast Range intrusives of southeastern Alaska. J. Geol. 35: 224-46. BUNKER, C . M ., and BRADLEY, W. A. (1961) . Measurement of bulk density of drill core by Gamma-ray absorption. U .S. Geol. Survey Prof. Paper 424B: 310-313. BUTLER, J . R ., BowDEN, P., and SMITH, A. Z. (1962). K / Rb ratios in the evolution of the younger granites of Northern Nigeria. Gcochim . et Cosmochim. Acta 26: 89-100. CAIN, J. A. (1962) . Precambrian granitic complex of northeastern Wisconsin. Ph. D. thesis, Northwestern University. CALLEGARI, E., and Monese, A. ( 1959a). La distribuzione del sodio e de! potassio nelle rocce de! massiccio del Gran Paradiso. Nota I: Accad. Nazi. Lincei Rend. Classe Sci. Fis. Mat. e Nat. 27 : 60-70. - - - ( 1959b) . La distribuzione de! sodio e de! potassio nelle rocce de! Massiccio del Gran Paradiso. Accad. Nazi. Lincei Rend. Classe Sci. Fis. Mat. e Nat 27 : 131-5. CARTER, N. L. (1962). Petrology of the Venas granite and the surrounding rocks, East Telemark, Norway. Norsk. Geo!. Tidsskr. 42: 45-75. CATER, F. W. ( 1960) . Chilled contacts and volcanic phenomena associated with the Cloudy Pass batholith, Washington. U . S. Geo!. Survey Prof. Paper 400B : 471-3. CHAVE, K . E., and MACKENZIE, F. T. (1961) . A statistical technique applied to the geochemistry of pelagic muds. J. Geol. 69: 572-82 . CHAYEs, F. (1949). Ratio correlation in petrography. J . Geo!. 57: 239-54. - - - (1951) . Modal composition of granites. Carnegie Inst. Wash. Year Book, 50 : 41-2. - - - (1952) . The finer-grained calcalkaline granites of New England . J. Geo!. 60: 207- 54. - - - ( 1956) . Petrographic modal analysis : An elementary statistical appraisal. New York : John Wiley. - - - (1957) . A provisional reclassification of granite. Geol. Mag. 94: 58-68. - - - ( 1960) . On correlation between variables of constant sum. J. Geophys. R esearch 65 : 4185-93. (1961) . Numerical petrography. Carnegie Inst. Wash. Year Book, 60: 158-65. - - - ( 1962a) . Numerical correlation and petrographic variation. J . Geol. 70: 440-52. - - - ( 1962b) . Variance relations in some published Harker diagrams. Carnegie Inst. Wash. Year Book, 61 : 118-19. - - - and SuzuKI, Y. ( 1963). Geological contours and trend surfaces. J. Petrology 4: 307-12 . CHENG, Y. C. ( 1944). The migmatite area around Bettyhill, Sutherland . Quart. J. Geo!. Soc. London 99 (for 1943): 107-54. Cocco, G., ( 1959). Considerazioni geochimico-petrografiche sulla granodiorite dell' Isola del Giglio (Arcipelago Toscano) . Atti Soc. Toscana Sci. Nat. 64A: 273-332. - - - GoTTARDI, G., and ToNANI, F. (1957). Richerche di metodologia geochimica. III . Confronto fra metodo chimico e metodo fotometrico di fiamma nella determinazione degli alcali. Distribuzione degli alcali nella granodiorite del Monte Capanne (Isola d' Elba) . Periodico di Mineralogia 26, 305-15. COMPTON, R. R. ( 1955). Trondhjemite batholith near Bidwell Bar, California. Bull. Geol. Soc. Am. 66 : 9-14. CONOLLY, H . J. C. (1936) . A contour method of revealing some ore structures. Econ. Geol. 31 : 259-71. CoRADossI, N., and ToNANI, F. ( 1961) . Dosatura spettrografica de! berillio nella granodiorite de! M .te Capanne (Elba) e dell'Isola del Giglio. Atti Soc. Toscana Sci. Nat. 68A .

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DALY, R. A. (1933). Igneous rocks and the depths of the Earth. New York: McGrawHill. DAVIES, R. G. (1959). The Cader Idris granophyre and its associated rocks. Quart. J. Geo!. Soc. London 115: 189-216. DA wsoN, K. R . ( 1958) . An application of multivariate variance analysis to mineralogical variation, Preissac-Lacorne batholith, Abitibi County, Quebec. Can. Mineral. 6: 222-33. - - - and WHITTEN, E . H. T. (1962) . The quantitative mineralogical composition and variation of the Lacorne, La Motte, and Preissac granitic complex, Quebec, Canada. J. Petrology 3: 1-37. DELURY, D . B. ( 1950). Values and integrals of the orthogonal polynomials up to n 26. Toronto : University of Toronto Press. DMITRIYEV, L. V ., KoTINA, R . P., and MoISEYEVA, R. P. ( 1962). Variations in the composition of biotite and the conditions of its stability in granites of different petrochemical types as illustrated by the Kaib massif ( central Kazakhstan). Geochemistry 1962: 248-66. EsKOLA, P. ( 1950). The nature of metasomatism in the processes of granitization. Rept. XVII lnternat. Geo!. Congr. London 1948, Part III: 5-13. EMERSON, D. 0. ( 1959). Granitic rocks of the northern portion of the Inyo batholith. Ph.D. thesis, Pennsylvania State University. EXLEY, C. S. (1959). Magmatic differentiation and alteration in the St. Austell granite. Quart. J. Geo!. Soc. London 114 (for 1958): 197-230. - - - ( 1961). Relationships and origins of the South-western granites (Abstract). Proc. 4th. Confer. Geologists Geomorph. working SW. England. Camborne. FAIRBAIRN, H. W., et al. (1951). A cooperative investigation of precision and accuracy in chemical, spectrochemical and modal analysis of silicate rocks : U .S. Geo!. Survey Bull. 980. FowLER-BILLINGs, K . ( 1949). Geology of the Monadnock region of New Hampshire. Bull. Geo!. Soc. Am. 60: 1249'-80. GERRIE, W. ( 1927) . Molybdenite in Lacorne and Malartic townships, Quebec. Univ. Toronto Stud. Geo!. 24: 37-40. GoTTARDI, G. ( 1954) . Studi sulla distribuzione des sodio e del potassio nella granodiorite elbana. Rend. Soc. Min. Ital. JO: 373-85. GRANT, F. ( 1957). A problem in the analysis of geophysical data. Geophysics 22: 30944. GRIFFITHS, W. R ., and NAKAGAWA, H. M. ( 1960). Variations in base-metal contents of monzonitic intrusives. U.S. Geo!. Survey Prof. Paper 400B: 93-5. GRoss, W. H. ( 1950). A study of the spatial relation of gold ore to intrusive bodies in northwestern Ontario. Proc. Geo!. Assoc. Can. 3: 123-39. - - - ( 1952). Radioactivity as a guide to ore. Econ. Geol. 47 : 722-42 . - - - ( 1956). The direction of flow of mineralizing solutions, Blyklippen Mine, Greenland. Econ. Geo!. SI : 415-26. Gussow, W. C. ( 1937). Petrogeny of the major acid intrusives of the Rouyn-Bell River area of north-western Quebec. Trans. Roy. Soc. Can. 31 , sect. 4, 129-61. HAMILTON, W. B. ( 1956a) . Variations in plutons of granitic rocks of the Huntington Lake area of the Sierra Nevada, California. Bull. Geo!. Soc. Am. 67: 1585-98. - - - ( 1956b). Geology of the Huntington Lake area, Fresno County, California. California Dept. Nat. Resources Div. Mines Spec. Rept. 46. HARKER, A. ( 1909). The natural history of igneous rocks. London : Macmillan. - - - ( 1917) . Some aspects of igneous action in Britain. Proc. Geo!. Soc. London 73 : 67-96. HARME, M. ( 1959). Examples of the granitization of gneisses. Bull. Comm. Geo!. Finlande J84: 41-58. HARRISON, J.E. (1951). Relationship between structure and mineralogy of the Sherman granite, southern part of Laramie Range, Wyoming-Colorado. Ph.D. thesis, University of Illinois. HATCH, F. H., WELLS, A. K ., and WELLS, M. K. ( 1949). The petrology of the igneous rocks (10th ed.). London: Thomas Murby. HIETANEN, A . (1961) . A proposal for clarifying the use of plutonic calc-alkaline rock names. U .S. Geol. Survey Prof. Paper 424D : 340-2.

=

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HousER, F. N. (1961). Lithologic logs of three exploration core holes, U15b area, Climax Stock, Nevada Test Site, Nye County, Nevada. U .S. Geo!. Survey open file report TEI-792. - - - and POOLE, F. G . ( 1959). "Granite" exploration hole, Area 15, Nevada Test Site, Nye County, Nevada-Interim report, Part A, Structural, petrographic, and chemical data. U.S. Geo!. Survey open file report TEM-836A. - - - ( 1961) . Age relations of the Climax composite stock, Nevada Test Site, Nye County, Nevada. U .S. Geo!. Survey Prof. Paper 424B: 176-7. HUANG, W . T. (1962). Petrology. New York : McGraw-Hill. HUNTER, D . R. (1957) . The geology, petrology and classification of the Swaziland granites and gneisses. Trans. Geo!. Soc. South Africa 60: 85-125. IDDINGS, J.P. (1892). The origin of igneous rocks. Bull. Phil. Soc. Wash. 12B: 89-213 . lsHII, K ., SENDO, T., and UEDA, Y. ( 1956). The diversity of the Tanohata granitic mass, northern Kitakarni Mountains, Iwate Prefecture. Sci . Rept. Tohoku Univ. 3rd Ser. 5: 153-67. lzETT, G . A. ( 1960). "Granite" Exploration hole, Area 15, Nevada Test Site, Nye County, Nevada-Interim report, Part C, Physical properties. Trace elements memorandum report 836-C. U .S. Geo!. Survey open file report TEM- 836- C. JOHANNSEN, A. (1937) . A descriptive petrography of the igneous rocks. Chicago : University of Chicago Press. JUDD, J. W. (1886). On the gabbros, dolerites, and basalts, of T ertiary age, in Scotland and Ireland. Quart. J . Geo!. Soc. London 42: 49-97. KING, H . D . ( 1960) . Zircons-a petrogenetic indicator in the San Isabel batholith, Wet Mountains, Colorado. M .S. thesis, University of Texas. KomE, H . ( 1958). Dando granodioritic intrusives and their associated metamorphic complex. Japan Soc. Promotion Sci. KRUMBEIN, W. C . ( 1956) . Regional and local components in fades maps. Bull. Arn. Assoc. Petrol. Geologists 40 : 2163-94. - - - ( 1959). Trend surface analysis of contour-type maps with irregular control-point spacing. J. Geophys. Research 64: 823-34. - - - ( 1960a) . Stratigraphic maps from data observed at outcrop. Yorkshire Geo!. Soc. Proc. 32 : 353- 66. - - - ( 1960b) . The "geological population" as a framework for analysing numerical data in geology. Liverpool Manchester Geo!. J. 2: 341-68. - -- ( 1962a). Open and closed number systems in stratigraphic mapping. Bull. Arn. Assoc. Petrol. Geologists 46: 2229-45 . - - - (1962b) . The computer in geology. Science 136: 1087-92. - - - ( 1963) . Confidence intervals on low-order polynomial trend surfaces. J . Geophys. Research 68: No. 20. - - - and SLACK, H. A. (1956). Statistical analysis of low-level radioactivity of Pennsylvanian black fissile shale in Illinois. Bull. Geo!. Soc. Arn. 67: 739-62. - - - and TuKEY, J. W. ( 1956) . Multivariate analysis of rnineralogic, lithologic, and chemical composition of rock bodies. J . Sediment. Petrol. 26: 322-37. LAPADU-HARGUEs, P. (1946). Sur !'existence et la nature de l'apport chirnique clans certaines series cristallophylliennes. Soc. Geo!. France Bull. ( 5 ser. ) , I SB ( for 1945) : 255- 310. LARI, I., and MmAILOVICI, N . ( 1958). Notes on the use of an algebraic theory for the formation of a general method of prospecting and surveying rare deposits. Proc. Second U .N . Internat. Conf. Peaceful Uses Atomic Energy (Geneva) 3: 95-104. LARSEN, L. H ., and PoLDERVAART, A. ( 1961). Petrologic study of Bald Rock batholith, near Bidwell Bar, California. Bull. Geo!. Soc. Arn. 72 : 69-92. LAWTON, K. D. (1954). The Round Lake batholith and its satellitic intrusions in the Kirkland Lake area. Ph.D. thesis, University of Toronto. LEIBLE, 0 . ( 1959). Verteilung der Radioaktivitat, der Thorium- und Urangehalte irn Malsburggranit (Siidschwarzwald). Erzbergb. u. Metallhiittenw. 12: 1-4. LIPPITT, L. ( 1959). Statistical analysis or regional facies change in Ordovician Coburg limestone in northwestern New York and southern Ontario. Bull. Arn. Assoc. Petrol. Geologists 43: 807-16. LINK, R. F., and KocH, G. S. ( 1962). Quantitative areal modal analysis of granitic complexes: discussion. Bull. Geo!. Soc. Arn. 73: 411-14.

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MACK, J. W ., and HAUBRICH, R. A. (1962). Gravity analysis in gas storage exploration (Abstract) . Soc. Explor. Geophys. Yearbook, p. 267. MANDELBAUM, H. ( 1963) . Statistical and geological implications of trend mapping with nonorthogonal polynomials. J. Geophys. Research 68: 505-19. MARFUNIN, A. S. ( 1962). Some petrological aspects of order-disorder in feldspars. Min. Mag. 33: 298-314. MARINELLI, G. ( 1959 ). Le intrusioni terziarie dell'Isola d'Elba. Atti Soc. Toscana Sci. Nat. 66A: 50-253. - - - ( 1961) . L'intrusioni terziaria di Gavorrano. Atti Soc. Toscana Sci. Nat. 68A: 117-94. MEHNERT, K. R . ( 1960) . Zur Geochemie der Alkalien im tiefen Grundgebirge. Beitr. Miner. u. Petrog. 7 : 318-39. - - - and WILLGALLIS, A. ( 1961). Die Alkaliverteilung im Malsburger Granit (Siidschwarzwald). J. Geol. Landesamt Baden-Wiirttemberg 5: 117-39. MERCY, E. L. P. ( 1960) . The geochemistry of the Older Granodiorite, Co. Donegal, Ireland. Trans. Roy. Soc. Edinburgh 64: 101-27. - - - ( 1960b) . The geochemistry of the Rosses granitic ring complex, Co. Donegal, Ireland. Trans. Roy. Soc. Edinburgh 64 : 128-38. MICHENER, C. D ., and SOKAL, R . R . ( 1957) . A quantitative approach to a problem in classification. Evolution 11: 130-62. MILLER, R . L . ( 1956) . Trend surfaces : their application to analysis and description of environments of sedimentation . J. Geol. 64 : 425-46. MITTEMPERGHER, M . ( 1954). L'Isola di Montecristo ricerche petrologiche e psammagrafiche. Atti Soc. Toscana Sci. Nat. 61 A: 167-218. MooRE, J. G. ( 1959) . The quartz diorite boundary line of the western United States. J. Geol. 67 : I 98-210. - - - ( 1962). K / Na ratio of Cenozoic igneous rocks of the western United States. Geochim. et Cosmochim. Acta 26: 101-30. - - - GRANTZ, A., and BLAKE, M . C . ( 1961) . The quartz diorite line in northwestern North America. U.S. Geol. Survey Prof. Paper 424C: 87-90. - - - (1963) . The quartz diorite line in northwestern North America. U.S. Geol. Survey Prof. Paper 450E : 89-93 . NEWHOUSE, W. H ., and HAGNER, A. F. ( 1947). Zoned metasomatic gneisses related to structure and temperature, Laramie Range, Wyoming (Abstract) . Bull. Geol. Soc. Am. 58 : 1212- 13. - - - (1949) . Cordierite deposits of the Laramie Range, Albany County, Wyoming. Wyoming Geol. Survey Bull. 41. - - - and DE VoRE, G . W. ( 1949). Structural control in the formation of gneisses and metamorphic rocks. Science 109 : 168. OFTEDAL, I. (1959) . D istribution of Ba and Sr in microcline in sections across a granite pegmatite band in gneiss. Norsk. Geol. Tidsskr. 39: 343-9. - - - (1961) . Remarks on the variable contents of Ba and Sr in microline from a single pegmatite body. Norsk. Geol. Tidsskr. 41 : 271-7. OLDHAM, C . H . G ., and SUTHERLAND, D. B. (1955) . Orthogonal polynomials: their use in estimating the regional effect. Geophysics 20: 295-306. OSBORNE, F . F. ( 1956) . Chemical compositions of the Grenville and the southern part of the Timiskaming-Keewatin Subprovince in Quebec. Trans. Roy. Soc. Can. 50 ( Sect. 4) : 53-63 . PARRAS, K . ( 1958). On the charnockites in the light of a highly metamorphic rock complex in southwestern Finland. Bull. Comm. Geol. Finlande 181 . PEIKERT, E. W. ( 1962) . Three-dimensional specific-gravity variation in the Glen Alpine stock, Sierra Nevada, California. Bull. Geol. Soc. Am. 73: 1437-42. - - - ( 1963) . IBM 709 program for least-squares analysis of three-dimensional geological and geophysical observations. Tech. report No. 4, Office Naval Research, Geog. Branch, Task. No. 389-135, Contract Nonr. 1228(26) . PETTIJOHN, F. J. (1957). Sedimentary Rocks (second ed.) . New York : Harper. PITCHER, W. S. ( 1953a) . The migmatic older granodiorite of Thorr district, Co. Donegal. Quart. J. Geol. Soc. London 108 (for 1952) : 413-46 . - - - ( 1953b). The Rosses granitic ring-complex, County Donegal, Eire. Proc. Geol. Assoc. 64: 153-82 .

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- - - and READ, H . H. ( 1959). The Main Donegal granite. Quart. Geol. Soc. London 114 (for 1958): 259-305. PUTNAM, G. W., and BURNHAM, C. W. (1963). Trace elements in igneous rocks, Northwestern and Central Arizona. Geochim. et Cosmochim. Acta 27: 53-106. RAGLAND, P. C., and ADAMS, J. A. S. (1963). Partial trend surfaces within the Enchanted Roalimpsestic ghost-stratigraphy from modal

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analysis of a granitic complex. Rept. XXI Intern. Geol. Congr. Norden, Pt. 14, 182-93. - - - ( 1961a) . Quantitative areal modal analysis of granitic complexes. Bull. Geol. Soc. Am. 72: 1331-60. - - - ( 1961b) . Systematic quantitative areal variation in five granitic massifs from India, Canada, and Great Britain. J. Geol. 69: 619-46. - - - ( 196 lc). Modal variation and the form of the Beinn an Dubhaich granite, Skye. Geol. Mag. 98: 467-72. - - - ( 1961d) . Quantitative distribution of major and trace components in rock masses. Trans. Am. Inst. Min. (Metall.) Engrs. 220: 239-46. - - - ( 1962a). Sampling and trend-surface analyses of granites: a reply. Bull. Geol. Soc. Am. 73 : 415-18. - - - ( 1962b) . A new method for determination of the average composition of a granite massif. Geochim. et Cosmochim. Acta 26: 545-60. - - - ( 1962c) . Areal variability of alkalis in the Malsburg granite, Germany. Neues Jahrb. Miner. Monat. 9 : 193-200. - - - ( 1963a) . Systematic quantitative areal variation in five granitic massifs: a reply. J. Geol. 71: 119-21. - - - ( 1963b). A reply to Chayes and Suzuki. J. Petrology 4: 313-6. - - - ( 1963c). A surface-fitting program suitable for testing geological models which involve areally distributed data. Tech. report No. 2, Office Naval Research, Geog. Branch, Task No. 389-135, Contract No. 1228 (26). WILLIAMS, H ., TURNER, F. J. and GILBERT, C. M. (1958). Petrography. San Francisco: W. H . Freeman. ZHIROV, K . K., and URusovA, M.A. (1962). Geochemistry of the alkalis in granites of the Tarak massif in the Yenisei Range. Geochemistry 1962 : 116-30.

STA TISTICAL INFERENCE IN GEOCHEMISTRY Gerard V. Middleton

ABSTRACT

With the development of rapid analytical methods, geochemists have at their disposal an embarrassing abundance of analytical data on major, minor, and traceelement content of rocks and minerals. Proper interpretation of such data implies the use of more sophisticated techniques than the old graphical aids. Multivariate analysis may assist the geochemist in interpreting his data, by condensing the data to a more manageable form and by revealing relationships between variables or groups of variables which would not be apparent from graphical analysis. In descriptive geochemistry, a more careful attention to the design of experiments and to problems of sampling is necessary, now that the science has grown beyond the initial exploratory stage. At present, however, probably more attention should be given to problems of estimation than to problems of statistical significance and hypothesis testing.

TWO MAIN APPROACHES TO GEOCHEMISTRY are possible, the observational and the experimental. The methods of experimental geochemistry are the traditional, proven methods of the experimental sciences. The methods of analytical and observational geochemistry, though they may borrow certain techniques from the experimental sciences, are more closely allied with traditional modes of thought in geology, and have much in common with the methods of the social sciences, biology, agriculture, and medicine. Information provided by both types of approach to geochemistry can be of great interest to the geologist. In what follows, however, only observational geochemistry will be considered, since it is only for this branch of geochemistry, together with much of geology and observational geophysics, that statistical methods have much application. There are four main types of problems in geochemistry which may be approached by statistical methods: (a) problems of estimation ( of both distributions and parameters) ; ( b) problems of efficient sampling and experimental design; ( c) problems of hypothesis testing and confidence intervals; and ( d) problems of classification. ESTIMATION Perhaps the oldest and most common problem in geochemistry is that of estimating the "average" chemical composition of the crust, or of a certain class of rocks. Even in a problem of such theoretical simplicity as this, statistics can contribute greatly to the clarification of ends and means.

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125

We must be clear what we mean by an average, and what information we expect it to convey. With the realization that many trace and minor elements do not show symmetrical frequency distributions, it has become clear that the arithmetic mean, which is calculated as an estimate of geochemical abundance, may in other respects be a poor average: for example, even if the distribution shows only one mode, the mean of a skewed distribution is a poor estimator of the composition of a "typical" specimen. Figure 1 shows a skewed distribution of a type commonly

(a) Arithmetic base

GM~I

4

2

0

AM

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8

(b) Geometric base GM ➔

AM

2 FIGURE

4

8

1. The distribution of Na 2O (wt. % ) in eugeo-

synclinal sandstones.

exhibited by minor and trace elements. A logarithmic plot shows a nearly symmetrical histogram, and it may also be seen that the geometric or logarithmic mean almost exactly coincides with the median and mode of the distribution. The arithmetic mean, however, is clearly too high to be regarded as a good "typical" value. Estimation of a parameter, such as a mean or standard deviation, implies the concept of a sample which is taken from some underlying or object population that is the focus of interest ( Krumbein, 1960) . Any investigation

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GERARD V. MIDDLETON

into the "meaning" of such parameters must lead us to an attempt to clarify our basic geological concepts about what exactly we are trying to sample ( that is, the nature of the target population), and must also lead us to an investigation of natural distributions themselves. Are elements normally or lognormally distributed? The recent "log-normal controversy" has made geochemists study the nature of natural variation and experimental error (see the review by Shaw, 1961). Perhaps such analytical introspection can be carried too far, but since the normal distribution is the basic assumption of almost all of modern statistics, examination of the validity of this assumption is certainly in order. Probably the real problem is not to determine the fundamental law of the distribution of the elements, since it is scarcely credible that any such universal law exists, but to estimate the importance of the various sources of variation which give rise to any observed distribution, to verify the assumptions of the mathematical model which is used, and to improve the model. If it is true that in many cases the natural or experimental variation approximates to a logarithmic normal law more closely than to a normal law, then the use of a logarithmic data transformation might well be adopted as a regular matter of course. Problems of estimation become more pressing when we investigate the functional relationship between two or more variables. Geochemists are at present familiar with the elementary theory of regression and correlation for two variables. Considering only problems of estimation, such statistical techniques probably improve little, if any, upon the even more familiar graphical techniques. In many cases they may give a worse idea of the functional relationship than is given by graphical techniques, because we tend to forget one of the basic assumptions of regression analysis, namely that one variable is dependent upon the other, with the latter not subject to error. In most geochemical studies both variables are subject to error, so that the regression line does not correspond to what we would intuitively regard as the line which "fits" the data best. This is a problem which has long been familiar to palaeontologists, who have suggested as a solution the use of the so-called "reduced major axis" rather than the normal least squares method ( lmbrie, 1956). Examples of data which are not appropriately treated by ordinary linear regression are petrological and mineralogical variation diagrams ( such as Harker diagrams and those showing variation in refractive indices with composition). Figure 2 shows a variation diagram, with Fe20a ( total iron) plotted against Si02. Clearly both variables are subject to "error" (both analytical error and natural variation). Two different regression lines are obtained, depending whether the regression is of Fe20a on Si02 (assuming no error in Si02), or of Si02 on Fe20a ( assuming no error in Fe20a). In this particular example the regression of Fe20a on Si02 corresponds rather closely to the line which is fitted by eye by most observers, probably because most observers are over-influenced by the two high Si02 points. The reduced major axis is a unique regression line lying between the other two

10

~

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of''

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b 50

60

Si 0 2 °/o

70

--

80

FIGURE 2. Variation diagram: Fe 2 O 3 (total iron) vs SiO 2 (wt.%) in eugeosynclinal sandstones. Line (a) is the regression of Fe 2 O 3 on SiO 2 ; line (b) is the regression of SiO 2 on Fe 2 O 3 ; and line (c) is the reduced major axis.

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0

y

y 0

0

0

0

0

0

0

0

.

0 0 0

I

x,

Xz

X3

3(a), (b), (c). Y is a function of X 1 , X 2, X 3 . The scatter diagrams show the correlation of Y and X 1 (a) , Y and X 2 (b), Y and X 3 (c) for twenty randomly chosen values of X . Note that in figure 3(a) the value for the correlation coefficient should be r .58.

FtCURES

=-

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regression lines, and having the following attributes (lmbrie, 1956): "(i) it makes no assumptions of independence; (ii) it is invariant under change of scale; (iii) it is simple to compute; and (iv) results obtained from its use are intuitively more reasonable than corresponding results obtained from regression analysis ...." Hitherto the reduced major axis has been used mainly in palaeontology, but there seems to be no good reason why it should not be used in geochemistry in those cases where the assumptions of linear regression are not valid. It is probable that one of the main contributions of statistics will lie in the investigation of functional relationships between three or more variables. Application of ordinary two variate regression analysis or graphical plotting to a situation where more than two factors are important can lead an investigator to miss the true functional relationships. This is illustrated by the following imaginary experiment. Suppose a dependent variable Y is a function of three independent, mutually uncorrelated variables X1, X2, Xa . The relationship may be represented by the following "law": Y

= -2.70 -

0.35X1

+ 3.73X2 + 4.lOXa.

In other words, if the data were plotted in four-dimensional space, all the points would lie on the same hyperplane. As in most geological situations, none of the independent variables can be controlled and it may, therefore, be assumed that they vary randomly from observation to observation; in actual fact, the values were picked from a table of random numbers. Twenty different sets of values were drawn, and the dependent variable was calculated for each sample. If we then proceed to investigate the effect of each independent variable on the dependent variable, we obtain the scatter diagrams and correlation coefficients shown in Figures 3 (a) , (b), ( c) . We might conclude that there is a significant correlation between each of the independent and the dependent variables but that the relationship between them is not very strong. In fact, the relationship is fully determinate, but it will never be revealed by plotting the results in two dimensions, even if we make use of a triangular diagram ( Fig. 4). The relationship would, however, be revealed immediately by using the technique of multiple linear regression. A real situation would probably be even more complicated: more than four variates would be involved, and they would nearly all be intercorrelated to some extent. There would be some experimental error and probably some of the significant variables would not have been determined, so that we could not expect to find a function which was a perfect fit to the data. But it should be clear that a functional relationship may be almost completely obscured unless we either hold all variables but two constant ( and this is practically never possible in the observational sciences) or take into account the effect of all variables at once. The appropriate techniques in statistics are those of multivariate analysis,

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3 7 II

13 23 29

28 28

33 :41

38

31 55 51

30

38

37 62

,40

X2

X3

FIGURE 4. The same points used in Figure 3, plotted in terms of the independent variables (summed to 100%), and with the values of the dependent variable ( Y) marked.

including factor analysis, multiple regression, and the discriminant function. Recent years have seen a sudden increase of interest in multivariate analysis, largely owing to the availability of large electronic computers which make feasible the extensive numerical calculations which are involved, and several techniques have already been applied to a variety of geological problems ( see bibliography). There is no doubt that application of multivariate techniques such as multiple regression and factor analysis is a complex procedure, even with the aid of automatic computing. The complexity of the mathematics, however, merely reflects the complexity of the real situation, which is inadequately or even erroneously treated by "simple" methods. Two examples of applications of multivariate methods will be given here. 1. Scapolite Composition and Refractive Index The relation between composition of scapolites and refractive index has been investigated by Shaw ( 1960) using graphical methods. The analyses of scapolites were recomputed in terms of the two principal endmembers, chloride-marialite ( NaAlSi3Os) 3 NaCl and carbonate-meionite

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(CaAbSi20s)a CaCOa. Shaw recognized, however, that this procedure was only approximate in as much as many other end-members may be important. The author used Shaw's analytical data (nineteen reliable analyses and thirteen "dubious" analyses) to compute the multiple linear regression of the refractive indexes no, ne, and the difference dn on the ten variables Si02, AhOa, MgO, CaO, Na20, K20, H20, CO2, Cl, SOa. Some dangers in this procedure should be noted at once: (i) because the ten oxides add up to almost 100 per cent for any analysis, the matrix of sums and squares is close to being singular ( that is, its determinant is nearly equal to zero), and hence it is dangerous to invert the matrix ( a necessary step in obtaining the multiple regression) ; (ii) the oxides are not normally distributed, and (iii) some of the oxides are strongly intercorrelated. The intercorrelation of "independent variables," although it does not invalidate the techniques, makes the results very difficult to interpret. Finally, the technique of multiple regression is open to the same criticism as that of simple regression, namely that the independent variates are assumed to be without error. However, provided that the multiple correlation is high ( that is, the dependent variable is closely determined by the independent variables) the error 1s probably not too serious. Some of the pitfalls are illustrated by the regression of no on the ten oxides. Tests indicate that this regression is highly significant, but when the significance of each oxide is tested only one ( MgO) is found to be significant. Inasmuch as it is well known that the refractive indices of scapolites are principally influenced by the solid solution between meionite and marialite, this results is apparently erroneous. In fact, it is merely the naive interpretation that is erroneous. Because of the high correlation between such pairs as Na20 and Cl, CaO and CO2, Si02 and Cl, etc., the effect of chloridemeionite has been spread over at least four variables (Na20, AhOa, Si02, and Cl) none of which is significant by itself. It is doubtful, however, if it makes much sense to investigate the effect of say Na20, independent of Cl ( the correlation between them is r = .90). This problem may be partly overcome by progressively discarding the least significant variables and recomputing the regression until the most significant regression is obtained. 1 Thus, in the scapolite the second computation was a regression of no on the four most significant variables, Si02, MgO, Na20, and Cl. The regression is again highly significant, and the most significant variable is still MgO, followed by Na20, with Si02 and Cl being non-significant. When only two variables, Na20 and MgO, are considered it is seen that Na20 is the more significant by far. It is also seen that the regression with only two variables, while still highly significant, is not as good as the regression with four variables. These results are interesting because they reveal a hitherto unsuspected 1 Alternative procedures are given by Krumbein ( 1959) and Schultz and Goggans ( 1961).

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relationship between content of MgO and the refractive index of scapolites and because they indicate the very great caution which is needed in "causal" interpretation of the results of multiple regression. To illustrate yet another pitfall: it is by no means clear from the above results that Mg++ itself has any direct effect upon the refractive index of scapolites. It is observed that MgO is correlated ( in the reliable analyses) only with water. However, it is known that in the analysis of scapolite, the MgO value is much more reliably determined than that of H2O. Possibly, therefore, there is a scapolite "end-member" which contains Mg (OH) 2 and possibly it is really the ( OH)- ion which affects the refractive index. But because of the strong correlation between Mg and (OH) and the greater analytical error for (OH), H2O is rejected from the regression before MgO and the whole effect due to Mg(OH)2 is attributed to MgO. Probably the true role of Mg++ and (OHt could be elucidated only by study of synthetic scapolites; but at least the statistical approach has indicated a problem worthy of experimental investigation. 2. Geochemistry of Pelagic Muds 2 One of the problems in the use of multiple regression is that the "independent variables" are not truly statistically independent. In the scapolite example it can be recognized that the chemical oxides are not the "real" variables; the real variables are certain underlying combinations (end-members). In the scapolites, and in many other examples, it is not fully understood, a priori, what the underlying "factors" or combinations of variables are. The technique whereby such factors may be determined, by study of a matrix of correlations determined from a random sample, is known as factor analysis. Imbrie has calculated the matrix of correlations for analyses of deepocean muds collected from twenty-three locations in the Pacific Ocean. Analytical values for twenty-one chemical elements are given by Goldberg and Arrhenius ( 1958). Factor analysis of this matrix yields four linear combinations (factors) of the original variables. Each factor is statistically independent of the other three and the four factors together account for the greater part of the variation shown by the original variables. As originally determined ( by the centroid technique; see Harman, 1960) these factors may be a pure mathematical fiction and may not correspond to any grouping of elements which has physical significance. Techniques of "rotation of the factors" exist, however, which permit the determination of "rotated factors" which probably have physical significance. In this example Imbrie interprets his four factors ( rotated by the quartimax method; see Harman, 1960) as representing (i) chemical precipitation of Co, Ni, and Mn and associated elements on the sea floor, (ii) deposition of elements associated with clay, (iii) elements associated with influx of volcanic material, 2The author is indebted to Dr. John Imbrie for permission to discuss this example, taken from his unpublished work.

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either andesitic ( positive factor values) or basaltic ( negative factor values) , and (iv) Ba and Cu associated with high organic productivity. The relative influence of each factor at each locality is then easily calculated and illustrated by maps with contours representing lines of equal factor score. Factor analysis is thus a useful technique where large numbers of intercorrelated variables have been measured, and where it is suspected that the variables are actually determined mainly by relatively few underlying, mutually independent factors. SAMPLING AND EXPERIMENTAL DESIGN

Geologists are becoming increasingly aware of the errors which may be introduced into any investigation by faulty sampling. Problems of experimental design have hitherto been given most attention by students of sedimentary rocks, perhaps because with sedimentary rocks it is easy to obtain simple quantitative data (such as grain size, bed thickness, proportion of sandstone, and so on) which yet do not seem to be particularly meaningful. Careful sampling to obtain an unbiased estimate of regional trends, free from the disturbing effects of local sources of variation, has shown that much useful information may be obtained from such apparently meaningless measurements (Krumbein, 1955, 1956, 1960). As geochemical data become more abundant, and as geochemists become less sanguine about the possibility of clear and unequivocal solution of old geological problems, more attention will probably be given to experimental design in geochemistry. Many of the experimental designs which are elaborated in statistical texts have little pertinence for the geologist. It is important that the geologist or geochemist should come to learn, through trial and error and by consultation with statisticians, the types of designs which are appropriate to his own problems. Much work by geologists, and probably also by statisticians, remains to be done in this field. HYPOTHESIS TESTING AND CONFIDENCE INTERVALS

One great advantage of modern statistical methods is that they enable the experimenter to make precise statements about data that are subject to uncontrolled variation and to test hypotheses in a precise and strictly objective fashion. It must be admitted that in many cases precise methods merely confirm the results which have already been obtained by inspection of the data either in their original numerial form or after plotting in the form of a graph. Such tests as the t-test for comparison of two sample means are very useful where there is considerable overlap in the values exhibited by two samples, but are superfluous where there is a clear difference between the two samples; in other cases they serve mainly a negative purpose, that is, the negative result of the test warns us not to make inferences to which we might otherwise be inclined.

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A clear distinction must also be made between geological and statistical significance, and geologists should avoid too slavish an adherence to the "5 per cent level of significance" in testing. By taking a sufficiently large sample, it is almost always possible to establish that differences, significant at the 5 per cent level, do exist between two natural populations ( such as two igneous intrusions). If the differences are very slight, however, a statistically significant difference may be without any particular geological significance. A difference between means which is not significant statistically cannot, strictly speaking, be regarded as significant geologically; but if sampling is not extensive and if the geologist would prefer not to miss differences which do exist, even at the expense of thinking that differences between population exist, which in fact are merely due to sampling errors, then he should be careful not to set his significance levels too high. A different procedure must be adopted when the geologist is merely hunting for ideas from that adopted when he is attempting to prove or disprove some previously formulated hypothesis. To illustrate, consider the problem of establishing real differences in composition between two large igneous intrusions such as granite masses. A large volume of analytical data is available for the Mortagne granite in France ( Shaw, 1961 b), which permits a rather accurate estimate of the mean and variance of any major component. The average value for AbOa is about 15 per cent and the standard deviation is about 1 per cent. Table I shows the size of sample ( number of analyses of the second granite) which would be required to detect a difference in mean content of AbOs between the Mortagne and another intrusion showing comparable ( rather low) variability, at the 5 per cent confidence level. TABLE I Difference in means

5% 2% 1% 0.5% 0.2% 0.1% 0.05%

Size of sample

3 7

23 87

540

2180 8700

Various conclusions may be drawn from this table. First, it is obvious that, using a 5 per cent level of confidence and the ordinary "spot" sampling technique, it will be prohibitively expensive to attempt to detect differences between intrusions of less than 1 per cent AbOs. But if it is admitted that there will always be some small difference in composition between two major intrusions, then it is also clear that it will always be possible to show a "significant difference" by taking a large enough sample. More importantly, a difference of 2 per cent AbOs will be "significant" if seven samples are taken, but non-significant if six or fewer are taken. The proper procedure

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would be to decide beforehand what difference in composition will be considered geologically significant, what probability of error may reasonably be tolerated, and whether it is more important not to assert that there are differences which are not present ( Type I error) or not to miss differences which are present (Type II error) and then design the sampling plan accordingly. In order to design such a sampling plan, it is, of course, essential that the variability be roughly known, and this is one reason why studies of the extent and nature of chemical and mineralogical variability m geological units of various types are of considerable importance. CLASSIFICATION

Two main classes of problems arise in classification. In the first class, we have already established two or more groups, forming a classificatory system, and we wish to assign unknown items to one or more of the groups. For example, we may wish to assign unknown rock specimens to a petrographic classification. So long as the classification which is used is purely arbitrary and is constructed according to proper operationalist principles, no problems should arise. As soon as something more than a purely arbitrary classification is devised, however, problems of assignment will arise. Thus it may be possible to divide shales into two main categories, marine and non-marine, and to devise a number of criteria for distinguishing between the two classes. Inevitably borderline cases will arise: certain specimens of unknown origin will show some characteristics (say, content of certain trace elements) in common with the marine shale group and others in common with the non-marine shale group. The questions arise, how can we make the best possible assignment to one or other group and how can we assess the probability of misclassification ( in general and in any particular instance)? A multivariate statistical method, known as the discriminant function, is appropriate to this first class of problems and has recently been applied, for example, to the problem of discriminating on the basis of chemical analyses between economically valuable refractory quartzite and quartzite which has no economic value (Wood, 1961 ) . A more interesting application has recently been made by Potter, Shimp, and Witters ( 1963, in press). They set up a discriminant function for distinguishing marine from fresh water shales on the basis of trace element content. The initial investigation was of thirty-three modern argillaceous sediments whose environment of deposition was known. A discriminant function was set up, based on the content of B, Cr, Cu, Ga, Pb, Ni, and V. After rejection of variables which contributed little to the discrimination, it was found that the best discrimination was possible using only the two elements Band V. The actual function was found to be X = 5.3415 (log B) 5.6928 (log V) and the probability of misclassification estimated to be about 19 per cent ( as compared with a probability of misclassification of 50 per cent for random assignment). The

+

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GERARD V. MIDDLETON

function was then used to classify thirty-three ancient shale samples, whose environment of deposition was known from geological and palaeontological criteria. Twenty-eight out of the thirty-three were classified correctly, thus providing an empirical test of the predicted efficiency of the function. A similar efficiency should not necessarily be expected to hold if this function is used on samples whose environment of deposition is unknown. Potter's function was set up using only marine and fresh-water samples, whereas an unknown sample might also have been deposited in brackish or strongly saline waters. A rather large frequency of misclassification might well be expected with the brackish group. This problem could have been avoided by including a third group ( and possibly others) in the original sample. Another problem which might be approached through the discriminant function is the following: suppose we have established several classes of objects ( for example, rock analyses), can we determine which classes are most closely related to each other, and what the nature of the relationship is? As an example, the author has calculated discriminant functions for three tectonic groups of sandstones ( eugeosynclinal, taphrogeosynclinal, exogeosynclinal and others; Middleton, 1960). It might be expected theoretically that the eugeosynclinal and exogeosynclinal groups would be relatively closely related, the exogeosynclinal, and taphrogeosynclinal groups less closely related, and the eugeosynclinal and taphrogeosynclinal groups least closely related. This is confirmed by calculating a statistic ( called Mahalanobis' D 2 ) based upon eight variables, which measures the "distance" between the groups. The values of D 2 are shown in Table II, and TABLE II VALUES OF

D2

FOR SANDSTONE GROUPS

No transformation "Eu" vs. "Exo,, "Exo" vs. "Taph" "Eu" vs. "Taph"

5.08 2.80 8.51

Logarithmic transformation

3.70 4.85 9.50

demonstrate the antithesis between eugeosynclinal and taphrogeosynclinal sandstones and the relative similarities of the eugeosynclinal and exogeosynclinal, and the exogeosynclinal and taphrogeosynclinal pairs. Further tests are available (Rao, 1952) if it is desired to investigate whether or not the "centres" of the populations lie in a straight line, or on a plane ( if there are more than three groups). Since problems such as these are common in petrology, the discriminant function may well prove to be of great value to the petrologist and geochemist. The second class of problems is perhaps more common than the first, and is certainly a much more difficult problem mathematically. In this class there are no a priori groups, but from a random sample of the over-all

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population ( for example, all igneous rocks) we wish to discover whether any natural subgroups occur. The usual way to approach this problem is to plot up scatter diagrams for two measured variables, and by inspection to determine whether there is any tendency for the points to be grouped into two or more clusters. This is obviously a somewhat subjective procedure, and is also a very inadequate one if more than two variates have been measured on each sample. Until recently no solution had been proposed to this problem, but within the last two years lmbrie has suggested that a variety of factor analysis ( the Q-technique) may provide an acceptable solution. lmbrie and Purdy ( 1962) have used the technique to construct a natural classification of Bahama Banks sediments. It would appear that the technique is also suitable for detecting natural groupings in geochemical and petrographic data. CONCLUSIONS

The purpose of this brief and non-mathematical review of statistical methods has been to indicate the types of problems in geology and geochemistry to which such techniques may be applied. Geochemical and modem petrographic techniques provide large volumes of quantitative data, suitable for statistical treatment. Computational techniques which were previously very laborious and time-consuming may now be performed very quickly, reliably, and easily by automatic computers, so that geochemists should be prepared to make use of established techniques and experiment with some of the more recent developments, particularly in multivariate analysis. ACKNOWLEDGMENTS

My sincere thanks are due to Paul Potter and John lmbrie for permitting me to make reference to their unpublished work, and to Denis Shaw and my other colleagues at McMaster for many fruitful discussions. REFERENCES The following list of references is not intended to be comprehensive, but merely to draw attention to prominent papers in the field or to papers which exploit new techniques. For an extended review, refer to R. L. MILLER and J. S. KAHN ( 1962), Statistical Analysis in the Geological Sciences (New York: John Wiley & Sons). Applications of statistics to geochemistry BATEN, W. D., and DEWITT, C. C. ( 1944). Use of the discriminant function in the comparison of proximate coal analyses. Ind. Eng. Chem. Anal. Ed. 16 : 32-4. CHAVE, K . E., and MACKENZIE, F. T. (1961) . A statistical technique applied to the geochemistry of pelagic muds. J . Geol. 69: 572-82. (Applies to geochemistry a technique of correlation analysis developed for use in paleontology by E. C. Olson and R. L. Miller.) CHAYEs, F. ( 1949). On ratio correlation in petrography. J . Geol. 57 : 239-54. - - - (1960) . On correlation between variables of constant sum. J. Geophys. Research 65 : 4185-93. ( Some pitfalls of variation diagrams, and the statistical treatment of rock analyses) .

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FAIRBAIRN, H. W. ( 1953). Precision and accuracy of chemical analyses of silicate rocks. Geochim. et Cosmochim. Acta 4: 143-56. HEY, M. H. (1956). On the correlation of physical properties with chemical composition in multivariate systems: Mineral. Mag. 31: 69-95. KRUMBEIN, W. C., and TuKEY, J. W. (1956). Multivariate analysis of mineralogic, lithologic and chemical composition of rock bodies. J. Sediment. Petrol. 26: 322-37. (An extension of analysis of variance, especially designed for variables of constant sum) MIDDLETON, G. V. ( 1960). Chemical composition of sandstones. Bull. Geo!. Soc. Am. 71: 1011-26. - - - ( 1962), ( in press). A multivariate statistical technique applied to the study of sandstone composition. Trans. Roy. Soc. Can. (The second of the two papers discusses the application of the discriminant function technique to data analysed non-statistically in the first paper.) POTTER, P. E., SHIMP, N. F., and WITTERS, J. (1963, in press). Trace elements in marine and fresh-water argillaceous sediments. Geochim. et Cosmochim. Acta. SHAW, D . M. ( 196 la). Element distribution laws in geochemistry. Geochim. et Cosmochim. Acta 23: 116-34. ( Reviews the "lognormal controversy"; bibliography) - - - and BAN KIER, J. D. ( 1954). Statistical methods applied to geochemistry. Geochim. et Cosmochim. Acta 5: 111-23. ( Applications of the t-test, F-test, and linear regression) STEVENS, R. E., ed. ( 1960). Second report on a cooperative investigation of the composition of two silicate rocks. U .S. Geo!. Survey Bull 1113. (Gives much information on analytical error in geochemistry) WINCHELL, H. ( 1961). Regressions of physical properties on the compositions of clinopyroxenes. II. Optical properties and specific gravity. Am. J. Sci. 259: 295-319. - - - and TILLING, R. (1960). Regressions of physical properties on the composition of clinopyroxenes. I. Lattice constants. Am. J. Sci. 258: 529-47 . WooD, G . V . ( 1961). Discriminating between refractory and non-refractory quartzite by quantitative petrography. J. Sediment. Petrol. 31: 530-3. General references

1. ESTIMATION GRIFFITHS, J. C. ( 1961). Measurement of the properties of sediments. J. Geo!. 69: 487-98. HARMAN, H. H. (1960). Modern factor analysis. Chicago: University of Chicago Press. lMBRIE, J. (1956) . Biometric methods in the study of invertebrate fossils . Bull. Am. Museum Nat. Hist. 108: 211-52 . KENDALL, M. G. (1957). A course in multivariate analysis. New York: Haffner. KRUMBEIN, W. C. ( 1959). The "sorting out" of geological variables illustrated by regression analysis of factors controlling beach firmness. J. Sediment. Petrol. 29: 575-87. SCHULTZ, E. F., and GOGGANS, J. F. (1961). A systematic procedure for determining potent independent variables in multiple regression and discriminant analysis. Agri. Exp. Sta., Auburn Univ., Bull. 336. 2. SAMPLING AND DESIGN OF EXPERIMENTS W. C. ( 1955). Experimental design in the earth sciences. Trans. Am. Geophys. Union 36: 1-11. - - - ( 1956) . Regional and local components in facies maps. Bull. Am. Assoc. Petrol. Geologists 40 : 2163-94. - - - ( 1960). The "geological population" as a framework for analysing numerical data in geology. Liverpool Manchester Geo!. J. 2: 341-68. ( Gives annotated bibliography) KRUMBEIN,

3. SIGNIFICANCE TESTING QuENOUILLE, M. H. (1958). The fundamentals of statistical reasoning. London: Charles Griffin & Co. SHAW, D. M., and BANKIER, J. D. (1954). Statistical methods applied to geochemistry. Geochim. et Cosmochim. Acta 5: 111-23.

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4. CLASSIFICATION

I MBRIE, J. ( 1962). Factor analysis in geology. Bull. Am. Assoc. Petrol. Geologists 46:

269 (abstract), and unpublished ms. - - - and PURDY, E. G. ( 1962). Classification of modern Bahamian carbonate sediments. In Classification of Carbonate Rocks, Special Publication Am. Assoc. Petrol. Geologists. KENDALL, M. G. (1957). A course in multivariate analysis. New York: Haffner. PoTTER, P. E., SHIMP, N. F., and WITTERS, J. ( 1963, in press) . Trace elements in marine and fresh-water argillaceous sediments. Geochim. et Cosmochim. Acta. RAo, C . R. ( 1952). Advanced statistical methods in biometric research. New York: John Wiley & Son. Other references GOLDBERG, E. D., and ARRHENIUS, G. 0. S. ( 1958). Chemistry of Pacific pelagic sediments. Geochim. et Cosmochim. Acta 13: 153-212. SHAW, D. M. ( 1960). The Geochemistry of scapolite. Part I. Previous work and general mineralogy. J. Petrol. I: 218-60. - - - ( 1961b). Manipulation errors in geochemistry: a preliminary study. Trans. Roy. Soc. Can., 3rd Ser., 55: 41-55.