LONGTERM and PEAKSCAN: Neutron Activation Analysis Computer Programs 9780932206114, 9781951538453

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LONGTERM AND PEAKSCAN:

NEUTRON ACTIVATION ANALYSIS COMPUTER PROGRAMS

© 1972 by the Regents of the University of Michigan The Museum of Anthropology All rights reserved ISBN (print): 978-0-932206-11-4 ISBN (ebook): 978-1-951538-45-3 Browse all of our books at sites.lsa.umich.edu/archaeology-books. Order our books from the University of Michigan Press at www.press.umich.edu. For permissions, questions, or manuscript queries, contact Museum publications by email at [email protected] or visit the Museum website at lsa.umich.edu/ummaa.

ACKNOWLEDGEMENTS The authors thank Drs. Edwin N. Wilmsen and James B. Griffin of the Museum of Anthropology of the University of Michigan for their support and encouragement throughout the design and implementation of the entire activation analysis project, including the writing of the PEAKSCAN and LONGTERM programs.

Professors Griffin and Wilmsen also made available

the large amounts of computer time necessary for the development of the programs. Much of the basic development of the activation-analysis project was carried out by Professor Adon A. Gordus of the University of Michigan Department of Chemistry, and our initial attempts at programming, particularly those which led to the writing of LONGTERM, were carried out under his supervision. We thank Mr. Charles Sheffer of the Museum of Anthropology for his comments on and revisions of LONGTERM and for support in writing and debugging both programs.

The staff of the University of Michigan Computing

Center provided us with much assistance in debugging the programs and in mastering various aspects of data storage and retrieval under the Michigan Terminal System. This work has been supported by the National Science Foundation, grants, GS-1196, GS-3214, and GS-2242.

Funds were supplied by the College

of Literature, Science and the Arts of the University of Michigan to purchase computer time.

INTRODUCTION In 1966 the University of Michigan Museum of Anthropology began neutron activation analysis of archaeological materials including obsidian, chert, and pottery.

Under the direction of James B. Griffin and

Edwin N. Wilmsen, the Museum's activation analysis program has defined several important archaeological problems which it is solving by determining elemental compositions of prehistoric artifacts. Accounts of the program's early work with obsidian and pottery have been given by Griffin, Gordus, and Wright (1969) and by Gordus, Wright, and Griffin (1968).

Wright (1967) has briefly discussed a study he made

of Midwestern chert artifacts and sources.

These papers focus on the

problem of identifying the geological sources of the raw materials utilized by prehistoric peoples, and current neutron activation studies continue to concentrate on this problem. The initial work of the project, overseen primarily by Griffin and Gordus, resulted in the development of specialized laboratory techniques suitable for measuring many of the trace elements found in obsidians and cherts.

Also important at this stage were the acquisition and testing

of high-resolution spectroscopy devices used to collect gamma ray spectra from neutron-activated materials.

The most sensitive of our spectroscopy

systems includes a lithium-drifted germanium gamma-ray detector connected to a 2048 channel pulse-height analyser. Also developed during the initial stages of the program was a timedependent, single-channel spectrometer, which has been used to analyse obsidian specimens for the elements sodium and manganese.

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These elemental

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data are used an initial sorting device in distinguishing geological sources of obsidian. ·The system is automatic, and has been used to inexpensively analyse about 5,000 obsidian specimens.

Recent improvements

in our single-channel analysis system are described by Meyers (n.d.), and discussions of the results it has yielded are outlined by Farnsworth and Meyers (n.d.) and by Fires-Ferreira (n.d.). As the initial phases of the activation analysis program near completion, the program's task has shifted from development and testing of analytic techniques toward production of quantities of accurate analytic data.

A laboratory capable of analysing over 100 lithic specimens per

month has been established, and a program of analysis has been implemented to use the laboratory to its capacity.

This requires a large amount of

spectral analysis, and has as a by-product the production of great quantities of raw spectral data.

These data must be processed arithmetically

to yield quantitative information about the elemental composition of lithic materials. For a single chert specimen, quantitative elemental data are obtained by mathematical reduction of two 2048-channel gamma ray spectra.

A "first

count," made 7 days after the specimen has been irradiated, yields data for neutron-activated chemical elements with short radioactive half-lives. A "second count," made 2-4 weeks later, yields information for elements with longer half-lives.

The reduction of raw data from any individual

spectrum requires three steps:

1) identification of all radioisotopes

represented in the spectrum; 2) determination of the number of nuclear disintegrations recorded for each radioisotope represented in the spectrum; and 3) comparison of the spectrum with spectra from chemical standards

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of known composition in order to determine the exact amount of each chemical element represented by a detected radioisotope.

Using a desk

calculator, a technician could perform these three steps for a typical spectrum in 1 to 2 hours; hence, given 2 counts for each specimen, it would require 200-400 hours of technician labor to arithmetically process the raw output from the 100 specimens we analyse per month. this is an excessive amount of labor.

Clearly,

Wilmsen, as the current director

of the activation analysis program, thus requested that the authors develop the necessary computer programs to accomplish our data reduction automatically.

Two such programs have been written.

The first, called PEAKSCAN, is designed to "scan" entire gamma ray spectra in order to determine the locations, energies, and intensities of gamma ray photopeaks.

This information is then used to determine

qualitatively what chemical elements are represented in the spectra. LONGTERM, the second of the programs, is used to calculate the quantities of chemical elements represented in gamma ray spectra.

Data

input into the program include the locations and shapes of photopeaks (as indicated by PEAKSCAN), descriptions of the specimens being analysed, and information specifying the chemical compositions of the standards irradiated and analysed with the specimens of unknown composition.

The

final information output by LONGTERM is a quantitative determination of each chemical element measured in each specimen of unknown composition. Operation of these computer programs upon gamma ray spectra repre• senting an analytic specimen allows us to determine the trace element

composition of the specimen at about one-third the cost of hand-calcula-

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tion of the same information.

The added accuracy and precision of the

high-speed digital computer and the automatic production of punched cards containing the elemental data represent additional advantages over hand calculation. NEUTRON ACTIVATION ANALYSIS In nature, the atoms of any chemical element may exist as one or a very few isotopes.

All atoms of a single chemical element contain the

same number of protons in their nuclei, but atomic nuclei of the same element may contain different numbers of neutrons,

Atoms of a single

element containing different numbers of neutrons are termed different isotopes of that element. ral isotopes.

The element lithium, for example, has 2 natu-

All lithium atoms contain 3 protons, and 93 percent of

all lithium atoms have 3 neutrons. lithium atoms have 4 neutrons.

However, about 7 percent of natural

The 3 proton/3 neutron state is termed

lithium-6 (annotated 3Li 6 ), while the latter isotope is termed lithium-7 (3Li7). When a large number of atoms are placed in a nuclear reactor and bombarded with large quantities of free thermal neutrons (existing unattached to atomic nuclei), some of the atoms will absorb neutrons.

An

atom of any given element which absorbs a thermal neutron will typically be transformed into an atom of a different isotope of the same element. Thus, for example, an atom of 11 Na 23 (sodium-23), which has 11 protons 24 and 12 neutrons, will become an atom of 11 Na (with 11 protons and 13 neutrons) upon absorbing a free neutron. topes (including 11Na

24

Many artificially produced iso-

) are radioactive; that is, they are unstable and

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tend to disintegrate or decay to more stable nuclear states through time. An unstable radioactive atom may decay by emitting a subatomic par-

ticle called a beta-particle or by absorbing a free electron into its nucleus.

In either case, a nuclear photon, or gamma ray, may be emitted

by the decaying nucleus.

One-half the atoms in any group of atoms of a

single radioactive isotope will undergo decay within a predictable period, termed the half-life of the isotope.

The half-life of an isotope is

unique to that isotope. Decaying atoms of any radioisotope will emit photons of only one or, at most, a very few discrete energies. in electron volts.

Energies of photons are expressed

Gamma ray energies typically fall in the range between

100 and 2000 thousand electron volts (KeV).

Like its half-life, the

energies of the gamma rays emitted by a radioisotope are unique to the isotope. In order to determine the abundances of elements being measured in a neutron-activated specimen, it is first necessary to identify those isotopes which have been created by absorption of thermal neutrons within the specimen.

By collecting gamma ray spectra from specimens which have

undergone a neutron irradiation within a nuclear reactor, it is possible to identify many of the isotopes produced.

From the gamma ray spectra,

the energies of the gamma rays and the half-lives of the isotopes emitting them may be determined.

Tables of gamma ray energies, of the isotopes

represented by gamma rays of various energies, and of the half-lives of many radioisotopes are readily available in the literature (e.g., Lederer, Hollander, and Perlman, 1967; Dams and Adams, 1968).

Also available are

technical discussions of gamma ray detection, energy determination, and

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measurement of half-lives (e.g., Price, 1958). Besides its use for qualitatively determining the presence and absence of many elements, it is possible to use neutron activation techniques for quantitative elemental analysis (see, for example, Perlman and Asaro, 1969).

If a specimen of unknown chemical composition is ir-

radiated together with a chemical standard, and if their gamma ray spectra are collected under identical conditions, there is a perfect correlation between the specific activity of each radioisotope present in the stanAs

dard and the specific activity of the same isotope in the unknown.

an example of quantitative activation analysis, let us hypothetically irradiate a chemical standard and a specimen of unknown composition at the same time and position within a nuclear reactor. the same weight and shape.

Both samples have

After the irradiation, we collect gamma ray

spectra from the samples under identical counting conditions.

We observe

4,000,000 disintegrations of 11Na 24 atoms in the standard spectrum, and we observe 2,000,000 disintegrations of 11 Na 24 atoms in the spectrum from the unknown specimen.

We may determine from this information that If

the unknown contains exactly half as much sodium as the standard. we know the quantity of sodium present in the standard, we may then easily compute the quantity present in the unknown.

Thus, there are two basic principles upon which neutron activation analysis is based.

First, many chemical elements have natural isotopes

the atoms of which will absorb free neutrons, become radioactive, and emit gamma rays of fixed energies over specific periods of time,

Second,

the amounts of radiation emitted by two specimens containing the same

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neutron-activated isotope are exactly proportional to the quantities of the isotope's parent element present in each specimen (assuming that the specimens were irradiated and analysed under identical conditions). It is possible, then, to irradiate a few standard samples of known chemical composition with several samples of unknown composition and to compare their gamma ray spectra.

This allows experimenters to determine

the quantities of certain chemical elements present in the unknown specimens.

This elemental data may then by used for many purposes, depending

on the needs of experimenters.

In our case, we use data derived from

neutron activation analyses to determine the sources of the raw materials utilized by various prehistoric peoples. PEAKSCAN:

AN ALGORITHM TO LOCATE GAMMA RAY PHOTOPEAKS

An ideal gamma ray spectrum is made up primarily of three components

(see Fig. 1):

compton scatter (sometimes called background), which re-

sults from the partial absorption of gamma rays within a gamma ray detector (the unabsorbed gamma ray energy escapes from the detector); compton "edges," which are caused by the inability of a gamma ray to escape the gamma ray detector once a certain portion of its energy has been lost; and photopeaks, or total absorption peaks, which result from the complete absorption of the gamma rays by the detector. The relationships between these spectral components may be described mathematically in terms of the slopes of lines connecting adjacent channels in a digitally stored gamma ray spectrum (see Fig. 2).

When a

gamma ray spectrum is collected, it is stored as digital information within a series of core memory locations of the spectrometer.

Each memory

102

103

104

0

Fig. 1

Counts (Log)

11

s l

Backgrormd 11 0

0

indicated.

Valley region.

Examples of a Compton edge, a photopeak and a background region are

Gamma ray spectrum of a neutron-activated obsidian artifact from the Illinois River

Ere

Compton

+0

't

Photopeak

I

00 I

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:

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51·

~

"

E·:

'!.

a·:

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Fig. 2

40.00

60.00

100.00

)

lX 1Q-1 l

120.00

,

140.00

160.00

(

KGROUND"

180.00

) ""'

photopeak.

Abstracted from Fig. 1.

"''""" 2oo·:oo

'i>tiA

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~ "

. :,~;:~ '

II 1,

II

II

~~~

ENERGY (IN KEVl

80.00

'""''"

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1

PHOTOPEAK

SRMPLE NUMBER 08-4898

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Schematic diagram of the slope values of a Compton edge, a background region, and a

20.00

I

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....._.~.;;< ;\. . . . .~

II I'

Jw,

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I

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SPECTRUM

I I

\0

-10-

location (or channel) represents a specific energy range, and each energy range is represented by an integral number of counts, representing nuclear disintegrations.

The entire spectrum may be visualized as a histo-

gram in which numbers of counts are stored on the basis of the energy range they represent.

A line drawn between any two channels in a spec-

trum represents the slope between the channels. Each of the components of a gamma ray spectrum has certain characteristics of slope which are unique to it.

A region of pure compton

scatter has a slope that averages zero -- there are no significant differences among the counts stored in any part of the region (see Fig. 1 for verification).

A compton edge, on the other hand, has a negative

slope; higher energy channels have progressively fewer counts.

At an

energy about 200 KeV higher than that of a compton edge, there is invariably a total absorption peak.

Gamma rays which have lost all but about

200 KeV of their energy within the gamma ray detector almost always lose the remainder of their energy, and are thus represented in the photopeak. The photopeak itself is represented by a region of sharply positive slope followed by a region of sharply negative slope.

Examples of each type

of region are noted on Figure 1. It is possible to design simple and inexpensive methods of computer processing to determine adjacent-channel slopes in gamma ray spectra. By performing a channel-by-channel analysis, a digital computer can determine which of the three spectral components is dominant at any point in a spectrum and report this information to the spectroscopist.

We have

written a Fortran-IV program, PEAKSCAN, to determine and report the locations of the photopeaks found in complex gamma ray spectra such as are

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generated in the activation analysis of lithic materials. Initial data fed to PEAKSCAN from punched cards identify the spectra to be scanned and define a maximum spectrum length.

Spectra longer than

the length specified are truncated, following which a brief error comment is printed. entirety.

Spectra shorter than specified are simply processed in their Following the definition of spectrum length, PEAKSCAN reads

the energies and approximate locations of up to ten "calibration" photopeaks from the punched cards.

The calibration peaks are used by the

program to normalize the channel versus energy relationship within each spectrum. After storing the length and calibration data, PEAKSCAN begins reading control cards, each of which specifies a sample name and an identification code for a spectrum to be scanned.

The control cards are

identical in format to the "SAMPLES" cards used to control LONGTERM (see below, p. 16). able.

The two card types are designed to be interchange-

Control cards are read one at a time; after PEAKSCAN reads a

single card, it searches an already mounted magnetic tape for the spectrum specified on the control card.

When the spectrum is located on the tape,

PEAKSCAN transfers it from magnetic tape to the computer's fast memory. The program then begins to scan the spectrum for photopeaks. The first step in scanning any spectrum is to assign a slope value to each pair of adjacent channels. I =

cx '

cx-1

1-

This is done by applying the formula:

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where C equals the number of counts in a given channel and x is the channel number of the first channel of interest. If I is positive, the slope of the pair of counts being considered (C

x

and C 1 ) is significant. x-

That is, it exceeds any slope which would

normally be produced by random variations in the count data.

When the

slope between any two channels is not significant (i.e., when I is negative or zero), the slope value for the channel pair is conventionalized to zero.

When I is positive, the slope for the interval between x-1 and

x is conventionalized to:

that is, simply to positive or negative 1. By assigning a conventionalized slope value of -1, 0, or +1 to each adjacent-channel pair, PEAKSCAN produces a "slope-map" of each spectrum it examines.

After completing this map for a spectrum, the program scans

the map, channel by channel, searching for photopeaks.

Each time PEAKSCAN

encounters successive slope values characteristic of a photopeak, it stores the location of the center channel of the peak.

The defining

characteristics of a photopeak are that it has at least two consecutive positively sloping channel pairs followed by at least two negatively sloping channel pairs.

The positive and negative regions of a peak may

be separated by a single nonsloping channel pair.

The center channel of

a photopeak is arbitrarily defined as the channel within the peak with the largest number of recorded counts.

Obviously, this value is accurate

only to the nearest integer channel number.

PEAKSCAN is capable of

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storing the locations of up to 100 photopeaks from any single spectrum. After determining the location of each photopeak, PEAKSCAN estimates the integral of the peak.

The integral corresponds to the number of

counts contained within the photopeak, and is directly proportional to The

the number of atoms of the mother element present in the specimen. photopeak integral is estimated by summing the contents of the seven

channels in the spectrum immediately adjacent to and including the center channel, then subtracting from this sum the "background per channel." The background per channel is determined by averaging the sums of the contents of the channels closest to each side of the peak.

This average

is multiplied by seven and subtracted from the peak sum to yield the estimated integral.

This is useful as a gross estimate of the quantity

of any individual isotope present in the specimen being examined,

A

more accurate though more expensive method for integrating photopeaks is used by the LONGTERM program (see below, p,l9 ).

In addition, we are

experimenting with techniques of fitting Gaussian curves to single photopeaks and overlapping multiple peaks.

This would yield a much more accu-

rate measure of the peak integral than either of the methods now in use. After an entire spectrum has been scanned and the locations and estimated integrals for all its photopeaks determined and stored, PEAKSCAN initiates a search for the calibration points specified during the program's initialization.

This is done by searching for already-identified photo-

peaks within eight

channel~

each calibration peak.

above and below the specified location of

If PEAKSCAN finds one or more peaks in this re-

gion, the one with the largest integral is accepted as the calibration

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peak, and its actual location and specified energy are used as data in a least-squares calibration curve fit.

If no photopeak is found within

a region where a calibration peak is supposed to be, the region is ignored in calibrating the current spectrum.

In either case, the program

attempts to find a calibration peak in each region specified by the user. If, after PEAKSCAN has search all specified calibration regions, three or more calibration peaks have been located, a linear least-squares regression is applied to the points found.

This yields a description of

the relationship between analyser channel numbers and gamma ray energies. The relationship determined is applied to each photopeak found in the current spectrum by PEAKSCAN, including the calibration peaks, to give the user an accurate measure of the energy of each photopeak. Finally, PEAKSCAN prints a summary of the operations it has performed and the results it has obtained for the current spectrum.

When this is

concluded, the program clears its memory and continues by scanning the next spectrum specified by a punched card. A short example of the operation and output from a single run of PEAKSCAN is given on pp. 58-63 of this report. LONGTERM:

A COMPUTER PROGRAM FOR QUANTITATIVE INTERPRETATION OF GAMMA RAY SPECTRA

LONGTERM is a computer program designed to determine the abundances of up to 40 chemical elements by interpreting the complex gamma ray spectra from up to 100 neutron-activated specimens.

The user may direct

the program to operate in any one of five ways, as follows: 1.

To sum specified gamma ray photopeaks, calculate constants from data read for up to 20 chemical standards, and calcu-

~15-

late abundances of specified elements in parts-per-million (ppm). 2.

To sum specified peaks, store the summations for later reduction to ppm, calculate constants from the standards, and stop.

3.

To sum specified peaks, store the summations, and stop.

4.

To read summations from a previous execution, calculate constants from the standards, and then calculate abundances of specified elements.

5.

To read previous summations, read a set of constants, and calculate abundances.

Except where noted, the following explanation describes the first method of program operation.

The latter four methods are essentially sub-

sets of the first. To initialize a run of LONGTERM, information is read which describes the photopeaks to be summed and identifies the spectra to be processed. First read are the names of the photopeaks, their gamma ray energies and half-lives, the number of analyser channels included within each peak, and either one or two methods of integrating the peak with respect to the background.

If a given peak is to be used in determining the energy-to-

channel-number relationship (calibration) of the spectra, the user specifies the channel at which it is expected.

A maximum of ten calibration

peaks can be given. It frequently happens that two photopeaks are located in such close juxtaposition that they partially overlap; these are termed "interfering"

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peaks.

Up to ten sets of interfering peaks may be corrected.

One iso-

tope of each set must have a second gamma ray peak which can be precisely integrated (i.e., which is not interfered with), and the size of which is a fixed percentage of that of the first peak of the isotope.

As an ex-

ample, assume a spectrum in which sodium-24 and copper-64 are the only isotopes represented.

Na

24

yields three gamma rays, with energies of

2751 KeV, 1369 KeV, and 511 KeV. with an energy of 511 KeV.

cu 64 gives off only a single gamma ray,

If the user desires to analyse the Cu 64 511

KeV photopeak, the contribution due to the 511 KeV gamma ray from Na 24 must be subtracted.

Let us assume that in the example we are using, the

511 KeV Na 24 peak is 0.83 times the size of the 1369 KeV Na 24 peak.

To

correct the interfering Na and Cu peak to Cu only, LONGTERM is told to sum the 1369 KeV Na peak, to multiply the sum by .83, and to subtract the result from the combined Na-Cu peak at 511 KeV. After storing the data for interfering peaks, the program is given a reference time (called "T-zero") to which all peak data will later be normalized.

Because gamma-ray-emitting radioisotopes decay, (and because

any spectrum from an irradiation is collected at a different time along the decay curve of each isotope than any other spectrum,) T-zero is used to arithmetically correct all spectra to the same arbitrary point in each isotope's decay curve. After storing T-zero, LONGTERM reads the sample name, spectrum number, "slot" number, weight, starting time, and count duration of each specimen which is to be analysed.

The slot number is an arbitrary measure of the

distance from the gamma ray detector to each sample counted.

For example,

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in any given set of samples, some are more radioactive than others.

The

more radioactive samples should be placed further from the detector, to avoid electronic pulse pile-up and loss of peak resolution.

In such a

case, samples counted in a given slot can only be compared to standards counted in the same slot, if comparison to the standard is to be valid. A maximum of ten counting slots may be specified. LONGTERM's initializing step is to read the name of each standard and its slot, followed by a weight-percent figure for each element being determined by that standard.

A maximum of twenty standards may be

specified. SPECTRUM READ-IN AND DATA REDUCTION:

LONGTERM, as currently imple-

mented, requires that spectra to be processed be stored on nine-track magnetic tape in "IBM-standard" formatted, labeled blocks.

This means,

in effect, that there is an identifying label placed before and after each spectrum, identifying the spectrum's number, size, and giving other information needed by the Michigan Terminal System to read the tape.

Once

the MTS magnetic tape software is given the spectrum's number, it automatically positions the tape to the beginning of that spectrum.

The pro-

gram then reads the spectral data into core storage. The first operation performed on each spectrum is calibration.

In

calibrating a spectrum, LONGTERM first scans an area from eight channels below each specified calibration channel to eight channels above it, in order to find the channel containing the largest number of counts.

LONG-

TERM then determines if the number of counts in this channel is more than two standard deviations greater than the number of counts in the preceeding

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channel.

If this condition is satisfied, the program assumes the peak to

represent a Gaussian distribution of points, and finds its centroid by bisecting a line at one-third of the peak's height.

To do this, the pro-

gram estimates the height of the second channel before the largest channel as one-third of the peak height, and bisects a line from this point to the equivalent point on the downward slope of the peak. A least-squares fit is performed using all points found by the calibration search; any calibration point falling more than two channels to either side of the fitted curve is rejected from further consideration. LONGTERM prints the locations of all of the calibration points found and of all the points which remain valid after testing.

A final calibration

is performed using the remaining points, and a slope/intercept calibration curve is calculated and printed.

However, if fewer than three

"good" calibration points remain after the first curve fit, LONGTERM does not compute a calibration curve but uses the calibration calculated from the previous spectrum.

If it has not yet successfully calculated a cali-

bration curve, the current spectrum is not processed, and processing continues with the next spectrum.

If five spectra in a row cannot be

calibrated, LONGTERM indicates that it has executed improperly and stops. When LONGTERM has determined a calibration curve for a spectrum, it can predict the center channel of each of the photopeaks to be integrated; the center channel of a peak equals the calculated calibration-curve slope times the specified peak energy plus the "zero-channel energy".

The pro-

gram will look one channel to either side of the calculated center channel of each peak for the channel containing the larger number of counts.

For

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photopeaks which have an odd number of channels, the channel with the largest number of counts is considered to be the center of the peak.

If

an even number of channels is to be summed, the program searches for the second larger count within one channel of the center channel, and sets the center channel either one-half channel higher or one-half channel lower than the highest channel. Two methods of determining the background may be specified on each "PEAKS" card.

Normally, each PEAKS card specifies simply a background

area before the peak and an area after the peak. if the user. desires. can be used:

Either may be omitted

In calculating a background, one of two procedures

1) all the channels from x channels before (or after) the

peak to y channels before (or after) the peak can be averaged, or 2) the lowest n consecutive channels from x to y channels before (or after) the peak can be averaged. A primary and a secondary background area may be defined for each peak.

There are two reasons for specifying alternate methods of choosing

the background:

1) if an unexpected peak appears in the middle of the

background area specified by one method, the program will be able to use the alternate method; 2) if a peak is small in some spectra but quite large in others in a single run, it is advantageous to calculate the background close to the centers of the small peaks, but necessary to calculate it further away from the larger peaks' centers.

Thus, if two methods are

given, the program will calculate a tentative background with each, and choose the one which gives the lower number of background counts per channel.

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To determine the integral of a photopeak, LONGTERM first sums the channels within the specified peak region.

From this sum LONGTERM sub-

tracts the calculated background, determined as the average background per channel times the number of channels in the photopeak. The standard deviation for each peak is determined as the square root of the sum of all channels used in calculating the peak integral and the background per channel.

It represents the range of values within which

the calculated integral would be expected to fall about 67 percent of the time. Once the summations and their standard deviations have been determined, LONGTERM subtracts any intefering peaks.

Sums of peaks are then corrected

for decay since T-zero and divided by specimen weight and count duration to determine "corrected counts per minute per milligram." After all the spectra in a run have been integrated and corrected, LONGTERM prints the corrected counts per minute per milligram (CPM/MG) and the standard deviation (in CPM/MG) for each spectrum and peak.

Then all

the CPM/MG data, along with much of the information stored at the beginning of the program, is written to device 8 (a sequential mass-storage device such as a disk file or magnetic tape).

Using intermediate storage to save

the summation information prevents the user from having to rerun the expensive initial stages of the program should he want to add, delete, or alter parameters describing the chemical standards.

After the summation-data

output (if the control code is 1 or 2), LONGTERM continues with the next step in processing the data, calculation of "R-values" {CMP/MG/PPM) for each standard.

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"Counts per minute per milligram per part-per-million" are called R-values in order to distinguish them from the "constant" which is either calculated later as the average of all statistically valid R-values for each peak, or may be supplied by the user on cards.

R-values are calcu-

lated for each slot, and those calculated for one slot are considered separately from those of other slots.

For each standard, the R-value of

a particular peak is determined by dividing the corrected counts-per-minute per milligram by the parts-per-million value the user has supplied for that standard, peak, and slot.

The calculated error in CPM/MG is likewise

divided by the ppm value to determine an initial error estimator.

When all

the R-values have been determined for a peak, their sum is divided by the number of R-values to determine the initial estimator of the average R-value or constant for the peak and slot. Ideally, the randomness of radioactive decay would account for all the variation observed in the activation analysis of a set of chemical standards, and their ranges of variation (expressed by the error estimate) would overlap. overlap.

However, observed ranges of R-values frequently do not

Reasons for this include the effects of neutron flux-gradients

across the irradiation positions in nuclear reactors, errors in measuring the weights of the chemical standards, errors in determining the actual chemical compositions of the standards, and inhomogeneity within batches of standard material.

Such errors are difficult to assess or correct.

Thus,

we use two methods for determining the error estimate for any standard constant.

First, the mean of the R-values, or the constant, is computed.

Each R-value is then compared to the constant.

If any R-value varies from

-22-

the constant by more than its

~

estimated error (derived by the first

estimating method), this variation replaces the first estimation as the measure of error for that R-value.

The final error estimator around the

constant is equal to the square root of the sum of the square of the error estimators for the R-values divided by the number of R-values, or:

E

c

=~L:E 1 r n

where E is the error estimator, c represents the constant, r the R-values, and n the number of R-values.

After the final error estimate is calculated,

the R-values are again compared to the constant, and any of them which varies from the constant by more than 1.5 times E use.

c

is rejected from further

If any R-values are rejected at this point, LONGTERM uses the

remaining ones to calculate a new constant and a new E . c In certain cases, the user will provide LONGTERM with constants (and error estimators) of his own.

One such case would occur when all the

standards in an irradiation were deficient in one or more elements which were present in the other irradiated specimens.

By combining information

describing the thermal neutron flux of the reactor, the neutron absorption cross-section of the parent isotope, the activity and gamma ray intensities of the daughter isotope, and the efficiency of the gamma ray detector used, the user may generate a synthetic constant and plug it into the input data (if the program is being run under control codes 1, 4, or 5). LONGTERM divides the observed CPM/MG for each peak in each spectrum by the final constant for that peak (which is actually a CPM/MG/PPM value) to

-23-

determine the parts-per-million of the element represented by the peak. This product is output as a list of values computed for all spectra in a run, and as an individual punched card for each spectrum and peak. A complete run of LONGTERM, following the steps described above, for 20 photopeaks and 45 spectra costs about 35 to 40 cents per spectrum using the Michigan Terminal System.

An example run of LONGTERM follows page 64

of this monograph. PROGRAMMING CONSIDERATIONS LONGTERM and PEAKSCAN, though designed and implemented in the standard Fortran IV programming language, make use of a number of hardware and software features peculiar to the IBM System-360 series computers and to the Michigan Terminal System, the executive monitor system operated on the University of Michigan's IBM 360/67.

LONGTERM and PEAKSCAN have rather

different logical designs than might normally be the case for programs of their length and complexity. A reader carefully examining either LONGTERM or PEAKSCAN will note two major steps that have been taken to improve their efficiency.

First, both

arithmetic expressions and subscripts for variable storage arrays have been kept as simple as possible.

Extremely complex equations have been broken

into relatively simple components, and each component is recomputed only as often as it changes.

Thus, for example, in the decay correction formula in

LONGTERM, such items as the count period of each spectrum divided by the weight of the specimen being counted, the time from T-zero to the start of the count period for each spectrum, and the half-life of each isotope times e· 693 are calculated immediately upon reading, and only the results are

-24-

stored.

Although it would be possible to store each of these parameters

as a single variable and to combine all of them into a single massive decay correction formula, this would require much longer execution times by LONGTERM, since the program would recalculate each relationship each time it computed a decay correction.

Similarly, where complex array

subscripts are used more than once without changing, we instruct the programs to compute the complex subscript explicitly and to place this result in an intermediate storage buffer.

The content of the buffer is then used

as the subscript, saving the expense of recomputing the subscript itself. As a second step toward efficiency, we avoid using external (explicitly defined) subp_rograms and subroutines.

Thus, it would be possible

to call a subroutine with a name such as CALBR8 which would apply a series of user-supplied parameters to each spectrum and return to the main program only the calibration-curve slope and intercept for each spectrum.

This

would allow us to treat the CALBR8 subroutine as an independent module which we could alter, replace, or delete without affecting the remainder of the program.

This would make revision of the program simpler, and would

simplify interpretation of program flow by removing the complexities of certain operations from the user's view. However, we have chosen to use "in-line" subroutines, written within the structure of the main program, for several reasons.

We are willing to

pay the relatively small extra cost of writing in-line routines in order to avoid the large extra cost of operating external subroutines.

External

subroutines are more expensive to operate than in-line routines because they must perform many bookkeeping tasks which in-line routines avoid,

-25-

including temporary storage of the addresses and buffers being used by the main program, transfer and storage of addresses and buffers to be used by the subprogram, and retrieval and restoration of main program parameters when the subprogram has completed its task.

We feel that the advantages of

in-line routines far outweigh the advantages of external subroutines for a program such as LONGTERM, which will be used to operate on large quantities of information over a period of several years. Anyone who may wish to use or adapt LONGTERM or PEAKSCAN must note that the programs use certain conventions of the Michigan Terminal System and of IBM computing systems in general which may not be available at other computing installations.

We have avoided, by not using them at all, some

of the peculiarities of IBM Fortran systems (such as NAMELIST input and output, complex subscripting, etc.).

Therefore most of the problems which

would arise in adapting the programs concern handling of input and output files and devices.

The three features we used and will discuss are magnetic

tape data storage, interchangeability of files and devices, and the use of the MTS READ and WRITE data-transfer routines. We noted above that our spectral data was stored on "IBM standard labeled" magnetic tape.

This means, we stated, that each spectrum we

analyse is stored as a physically distinct block of data at both ends of which are character strings, 'or labels, uniquely identifying the name and location of the data.

To locate a spectrum, the user passes a "data-set

name" to an MTS label-searching routine.

The searching routine auto-

matically finds the correct spectrum ahd positions the tape so that thereafter the data may be read as if they were located in a card reader, on a

-26-

disk file, or in any other MTS input device.

Other computing systems may

not have similar labeled-tape handling conventions, and the user may be forced to adopt an alternative means of data storage and transfer. We noted that magnetic tapes may be read exactly like information from any other file or input device. logically interchangeable.

In MTS all input/output devices are

Thus, our input data could be read from punched

cards, paper tape, magnetic tape, a remote teletype terminal, a disk file, or even from a touch-tone telephone.

Similarly, our output could be on

punched cards, on paper or magnetic tape, or on printed sheets.

By

specifying "logical" device numbers (e.g., "5" in "READ (5) DATA") in the source codes for LONGTERM and PEAKSCAN, and assigning a device to each logical number at the time the object programs are executed, we may use any device or combination of devices available in MTS as our input/output media. As with tape-label processing, this degree of flexibility may not exist on computing systems other than MTS. Another input/output option used by LONGTERM is the binary data transfer invoked by calling the MTS routines WRITE and READ.

WRITE is invoked after

the corrected counffi have been calculated by a code 1, 2, or 3 start.

It

stores the count data for each spectrum and peak, and the identification data needed to interpret the counts, on a disk file or other large-scale output medium.

The data are output as 2 records, one about 130,000 bits

long and the other about 17,000 bits long.

A code 4 or 5 start of LONGTERM,

using the same file or device as an input device (specified as device 8), will recall intermediate data previously stored and continue operation of the program.

This saves the cost of rereading, resumming, and recorrecting

-27-

the raw count data.

Again, to be used on computing systems other than MTS,

there must be the capability to read and write large blocks of binary-coded data. CONCLUSION To date, we have used PEAKSCAN to examine over 1500 gamma ray spectra. LONGTERM has been used to resolve over 1000 of these into their constituent elemental compositions.

The programs are being continually modified as we

improve and refine our methods of spectral analysis.

However, both PEAKSCAN

and LONGTERM as described in this monograph offer highly efficient algorithms for spectral analysis.

LONGTERM in particular has proven both

inexpensive to operate and adaptable to the analysis of a wide variety of lithic materials. Specifically, our lithic analysis project program has been divided into three phases:

obsidian analysis, analysis of cherts from Colorado and

Wyoming, and analysis of cherts from the lower Illinois River Valley. Obsidian analysis to date has been largely a c~ntinuation of Griffin's and Gordus' work with Hopewellian materials.

Farnsworth and Meyers (n.d.)

outline an investigation strengthening Griffin's

hypothesis that Hopewellian

obsidians were derived (by mechanisms yet undetermined) from natural sources in and near what is now Yellowstone National Park, Wyoming.

In particular,

they discuss the continuation of work defining the source of the "Hopewell 90" obsidians described by Griffin, Gordus, and Wright (1969), and model social mechanisms for distribution of obsidian within the lower Illinois Valley region.

We plan to continue work with Illinois and Midwestern

obsidians, and hope to expand and refine Wright's work with obsidians from the Near East (Wright, 1968) and Fires-Ferreira's (n.d.) studies of Meso-

-28-

american obsidians.

We are investigating methods of inexpensively analysing

obsidians for up to fifteen elements after only a short thermal neutron irradiation. Our investigations of chert sources and artifacts, begun by Wilmsen, Barbara Luedtke, and Meyers, are also being continued and expanded.

Work

done to date by Luedtke and Wilmsen has allowed sorting of artifacts from the Lindenmeier sire in Colorado into several source groups, and more importantly has allowed the investigators to conclude that many chert sources are geochemically so dissimilar to Lindenmeier artifact cherts that they could not have been used by the occupants of the site. Meyers has begun intensive investigation of geochemical variation within cherts of the Burlington Limestone in the lower Illinois Valley, which were probably used in the manufacture of over 95 percent of the stone artifacts found in the region.

He has been able to distinguish Burlington

cherts from those of other geologic formations in the region, and to assess tentatively the chemical effects of postdepositional weathering on chert artifacts. Future work with chert will include initial studies of materials from Michigan and from the Mexican state of Oaxaca, refinement of the methods we now use to determine the quantities present of 20-25 elements in chert specimens, and development of techniques to determine the abundances of elements for which we do not now routinely analyse. Beginning with Gordus' development of techniques for neutron activation analysis of artifacts in the mid-1960s, the staff of the Museum of Anthropology's neutron activation analysis project have assembled a massive store

-29-

of information concerning the geochemical composition and variation of stone artifacts and their natural sources; concerning techniques of lithic sample preparation, neutron irradiation, and gamma ray spectroscopy; and concerning techniques of data storage and manipulation.

This report, a description of

the computer programs PEAKSCAN and LONGTERM, is designed to present some of our experience for the benefit of other archaeologists who may be interested in elemental analysis of artifacts, but who lack experience in methods of chemical analysis.

More specifically, it describes the structures and uses

of PEAKSCAN, a Fortran-IV computer program designed to locate gamma-ray photopeaks in neutron-activated materials, and of LONGTERM, a Fortran program designed to routinely analyse gamma-ray photopeaks in order to determine the abundances of neutron-activated chemical elements. and LONGTERM are straightforward, efficient programs.

PEAKSCAN

They are simple and

inexpensive to operate, and are quite adaptable to a variety of digital computers and to the analysis of many types of neutron-activated materials.

-30-

References Dams, R. and F. Adams

1968

Gamma-ray Energies of Radionuclides Formed by Neutron Capture Determined by Ge(Li) Spectrometry.

Radiochimica Acta Vol. 10:

1-14. Farnsworth, Kenneth B. and Thomas Meyers n.d.

Reconsideration of Sources for Lower Illinois Valley Obsidians. American Antiquity, in press.

Gordus, AdonA., Gary A. Wright, and James B. Griffin

1968

Obsidian Sources Characterized by Neutron-Activation Analysis. Science Vol. 161:382-384.

Griffin, James B., A.A. Gordus, and Gary A. Wright

1969

Identification of the Sources of Hopewellian Obsidian in the Middle West.

American Antiquity Vol. 34, No. 1:1-14.

Salt Lake

City. Lederer, C.M., J.M. Hollander, and I. Perlman

1967

Table of Isotopes, Sixth Edition.

John Wiley and Sons.

New

York. Meyers, Thomas n.d.

Dual Element Activation Analysis of Obsidian to Determine Artifact Sources.

Unpublished manuscript.

Ann Arbor.

Perlman, I. and F. Asaro

1969

Pottery Analysis by Neutron Activation.

21-52.

Archaeometry Vol. 11:

Oxford.

Pires-Perreira, Jane Wheeler n.d.

Obsidian Trade in Mesoamerica 1200 B.C. to A.D. 1500. in press.

Science,

-31-

Price, W.J. 1958

Nuclear Radiation Detection.

McGraw Hill.

New York.

Wright, Gary A. 1967

The Study of Chert Sources and Distributions by Activation Analysis.

Unpublished paper presented at the 1967 annual

meeting of the Society for American Archaeology. 1968

Ann Arbor.

Obsidian Analysis and Early Trade in the Near East: 3500 B.C. Arbor.

Ph.D. dissertation.

7500 to

University of Michigan.

Ann

-32~ICHlGA~

rERMINAL

S~STEct

c c c

FORTRAN G(41336)

P tAKSCAN

.:' o- 19-7 2

J?EAKSCAK GAMMA-RAt fUCiOEBAKS AND GIVES THEiR IPJ?ROIIMATE ENERGIES AND IN'TEGRALS,

~OCATES

c c c c

~ICHIGAN

TEdMINAL SlSIEB JEVICE ASSIG~ctENTS: 5=*SINK* 6=(MAG)*IAPE* 7=*1APE*wCC

4=*SOu~CE*

c

c c

THIS J?BOGEAct MUST BE fFECELED B~ AN ~RUN OF THE MIS l?ROGBAM *MOUNT, ~ITH *fAPE* SJ?ECIPIEC AS THE PSEUDO-DEVICE-NAME FCR THE MAG TAPE !10UNTED,

c c

c c c c c

NRGY(1C0) ~ITA SP!C;2060*C,0/ £LEAD (4,U0) LENGTH EURMAT (IS) HEAD (4,85,END=87) (UFilLL(KI), CHANL(KI), KI=1, 10) FURMAI (6X,F9,4,'I65,F1C.S) GO TC 88 KI = KI-1 ~i:!ITE (5 ,89) (KK, ENHHIL (KK), CHANL {KK), KK= 1,KI) fORMAT ('CALIDRATION PCIN1~:',j,10(l3,F8,2,F8.2,/)) ilEAD (It, 1C~,END=200C) NAI1EA, NAt1EB, NAMEC, ITAJ?EN FOR11AT (3Alt,11X,.l5) Dl!H~NSICN

2

c

c c

100

1

PCSIT.ION THE MAGTAPE ANC rlEAC IN TEE SPECTRUJ.'I, EHE SPECTRUM lS ASSDM!C IU BE IN RECORDS OF 8(16,11) ON DEVICE (wHICH NvRMALLY Will liE A MAG TAPE), THE FIRST LENGTH/8 HECORDS wiLL BE READ, AhL THEN AN END-OF-filE CONDITION IS SOUGHT (EG,, 256 RECORDS WCULC El READ FOR A 204€ CHANNEL SPECTRUM, AFTER ~HICH AN END-UF-FILE MAEK IS THE NORMAL BECORD), IF AN END-OFfiLE IS NCT FOUND, IT IS ~OTED THAT THH SPECTRUM EXCEEDS THE SPECIFLED LENGTH, AND C~lt THE NUMBER OF CHANNELS S~ECIFIBD B~ THE O~ERATCR ARE PRCCISSEU, THE VARIABLE LEN ENDS AS 1HE ACTUAL NUMBER OF CHANNELS PBCCESSED, 7

WRITJ:: {7,12-::J) ITAPEN 120 FCliMAT ( 1 fCSN 1 , 16) DUMMY = -2, BEAD (6,140,END=150) (SP:EC(LEN), 140 FORMAT (7(F6,0,1X), F6,nj

LEN=1,LENGTH), OUM1H

TilE PEAK SEARCHING BCG1INE STAHTS HERE,

c

EIRST, ASSIGN SLOPE VALUES TC

c c

NUMPEK IS raE NUJ.'IBEE CF 1HE LAST PEAK FCDND, AND ENDS AS THE TOTAL NUMBER OF PEAKS IOUND IN ThE SPECTRUM,

c

~ACH

CHANNEl IN THE SPtCTRDM,

11:53,36

-33-

MICHIGAN

TEHAINA~

C

SiSTEM FORTRAN G(41336) KFACTR(X)

c 150 NUMPEK

0018

0019

GO 26

oc 27

002!l

0029 0030

c C C C C C

c

(033 00 34 0035 00 36 oc 37 0038

0039 0040 00'11 co 42

1)6-19-72

IS THE SLOEE VALUE CALCULATED FCR ANY GIVEN CHANNEL.

0

LEN = LEN-1 DO 30G I=1,LEN II = I + 1

00 20 0021 00 22 00 23 oc. 24 00 25

0031 00 32

=

PEAKSC AN

c

c c c c c c c

DELTA= SPEC(II) - SEEC(I) !!DELTA = S\;RT ((SPEC (I) +SHC (II)) /2.) IF (DEl.T A , LE. PDELIA) GC ·ro 22') KFACTE(I) = 2 GO TO 300 .220 DELTA = AES (DELTA) H (DJ::LTA ·.LE, PDELIA) GC TO 240 KEACTR(I) =-2 GO TO 31)0 240 KFACTR (I) = 0 300 CONTINUE NOi CHICK EACri CHANKEI 1C SEE IF IT IS THE CENTER OF A PEAK. THE SLOPE FOR A~Y CHnhNEl WILL BE EITHER PLUS, MINUS, OR ZERO. THE CONDITIONS INDICAIING A PEAK ARE EITHER: (1) 2 PLUSSES FOLLO>IED BY 2 MINUSES; CR (~) 2 PLUSSES FCLICWED lH A ZERO FOLLOWED BY 2 MINUSES 1\PEAK = 0 CO 400 I=5,LEN IE (KFACTR (I) , GE, C) GC 10 4CO II = 1-1 IE (KFACTE(II) .GE. 0) GC 'L'O 400 r;: = I-2 I3 = I-3 14 = I-4 U ((KFACTB(I2) .GT.O ,AND, KFAC'Td(I3) .GT.O) .oa. (KFAC1R(L2) .EQ.O 2 .AND. KFACTR(IJ),GI.C .AND. KFACTR(l4).GT.(j) GO TC 320 GC TO 400 I£ A PEAK IS FOUND IE! CfNTEB IS DETERcliNED AS THE HIGHE~T POINT WITHLN ONE CHANNEL CF THE APPROXIMATE CENIER POUND ABOVE. LPEAK(NUMP~K)

ENDS AS 1Hf LOCATION Of THE CENTER CHANNEL Of THE

CU6HENT PEAK. KSUct(NUMP~K)

ENDS AS jhE THUNCATED INTEGRAL CF PEAK AREA.

c

c c c c c c c 'JO 4 3 oc 44 oc 45 0046

THE BACKGROUND PER CHAINE~ IS TAKEN AS THE AV8RAGE OF CHANNELS 4 - 5 BEFORE AKD AFIER 1HE PEAK CENTER. THE APPROXIMATE INTEGRAL IS THE SUM OF TiE 7 CHANbELS CENTERED ABOUND THE CENTER OF THE PEAK MINUS 8*(BACKGhCLND ~ER CHANNEL). THIS CALCULATION IS INTENDED ONLY AS AN ESTl~AIE OF PEAK SIZE, AND MAY BE INACCURATE wHERE PHOTOPEAKS ARE CLOSElY SfACED OR NEAR A CCSPTON EDGE. 320 NUMPEK = NUMPEK + 1 IF (NUMPE.K • LT. 101) NUMPEK = NUMPEK - 1 GO TO 410

GC TC 340

11:53.36

-34dlCHIGAN TERRINAL S[STEM FORTRAN G(41336}

PEAKSCAN

06-19-72

340 U (Si'EC(l2) ,LT. SPEC(l3)) I2 = I3 KPEAK = I2 LPEAK (NOf1PEt\) = KPEAII 360 BKG = (SPEC(KPEAK-4)+SEEC(KPEAK-5)+SPEC(KPEAK+~ +SPEC(KPEAK+4))/8. KSUl1 (NUl'!PEK) = (SPEC (HEAK-3) +SPEC(KPEAK-2) +SPEC (KPEAK-1) +SPEC (KPE +aK)+SPEC(KPEAK+1)+SPEC(KPEAK+2)+SPEC(KPEAK+3})-BKG*7.C 400 CONTINUE

00 47 0048 0049 0050 0() 51

()0 52

c

c

c c c c c c

c c c c c c

oc 53 0054 (I~ 55 '1056 0057 cc 58 00 59

or 60

~( 61 0062

OOE3

0064 00 65 0066 0067 0068

cc 69

cc 7'1

0011 0072 ('( 7 3 OCI4 0075 0076 0017 CC78 or: 79 00 dO

oc a1 0082 00 E3

0{ 64

CCcS

c

ALL PEAKS HAVE EEEN fCUND, CALIBRATE TEE SPECTRUM BY FINDING THE HIGHEST PEAK WITHIN E CHANNELS ON EITHER SIDE OF EACH SUSPECTED PEAK LOCATION, IF NC flAB IS FOUND IN THE REGION OF A GIVEN CALIBRATION POINT, THAT POINT IS IGNORED, IF LESS THAN 3 PEAKS REMAIN AT THE E~D OF TEl~ SEARCH, NO CALIBRATION IS MADE, AND ~NEBGIES FOR THIS SPECTRUM ABE SET TO '****'· OTBERiiSE, THE lOCATED PEAKS AND ThE SUEPLIED CALIBRATION ENERGIES ARE USED TO liT A LINEAR LEAST S~UAEES REGRESSION LINE TO THE ENERG~-CHANNEL EELATIONSHIP,

IS THE NUMBER OF TEE COhRENT PEAK BEING EXAMINED, AND IS VARIED FROM 1 TO NUMfEK, KI IS THE rOTAL NU~EEr CF CALIBRATION POINTS BEAD IN,

J

41.:, J = 1 NPEK1 = NUMPEK + 1 NPEK2 = NU~PEK + 2 NPEK3 = NUMPEK + 3 Lf'EAK (NPEK 1) = 2('000 LPEAK (NPEK2) = 2C\JOC LPEAK (NPfl\3) = 20000 KSUl'!(NPEK1) 0 KSUM (NPEK2) 0 KSUM (NPEK3) = 0 N = 0

SUMCH = ,~, SUMEN = 0, SUMCH2 = 0, SUMUL'I = 0, DO 6 C Q 11 = 1 , KI UC = CHHL(M) - 8 LHI = LLO + 16 425 IF (LPEAK (J) , GT. LHI) GG TO 60~· 1.f (LPEAK (J) • L 1, LLO) GC TO 500 NUM = I) IF (L.l'EAK(J+1) .GT, lHI) GO TO 1~ILl EE THE NUMBER OF CHANNELS FROM THE CENTER Of' Tti.li PEAK TO START SUI\MltjG THE EACKGROUND 1 . AND IN IBKG3 (X,Y) wiLL ~E ONE LESS THAN Ih.li NUMBER OF Tl.ffES CONSECUTIVE SETS OF CHANNELS WILL BE SUMI\ID. EACH TiffE A NEW SET OF CONSECUTIVE CHANNELS IS CHECKED, THE ~IAH1ING CHANNEL NUME.IiR IS INCREMENTED BY 1.

220 IBKG1 {I,J) = INO (J)-1 IiKG2~ 1 J) = -ILAST{J) ll:lKG3(1 1 J) = HAST(J)-INC(J)-IFST{J)+1 IBKG1 (l,JJ) INC(JJ) -1 IBKG2(l,JJ) IFST{JJ) l.BKG3 (I, JJ) = !LAST (JJ) -INO (JJ) -IFST {JJ) + 1 23') CONTINUE

co 73 0074 0075