The combination of multi-element neutron activation analysis and multivariate statistics for characterisation in geochemistry

Ira. J. Appl. Radiat. lsot. Vol. 34. No. 1, pp. 407-416, 1983 Printed in Great Britain. All rights reserved

0020-708X~83/0104()7-10503.00/0 Copyright © 1983 Pergamon Press Ltd

The Combination of Multi-element Neutron Activation Analysis and Multivariate Statistics for Characterisation in Geochemistry J. I. W. W A T T E R S O N ,

J. P. F. S E L L S C H O P ,

C, S. E R A S M U S

a n d R. J. H A R T *

NIM-Wits Activation Analysis Research Group, Nuclear Physics Research Unit, University of the Witwatersrand, Johannesburg, South Africa

Instrumental neutron activation analysis provides an accurate method for the determination of some 20 to 40 elements in geological samples. This method has been combined with pattern recognition techniques to provide a powerful method for the study of geochemical differences and for the classification of unknown samples. Discriminant analysis, a statistical method of pattern recognition, was applied to the study of mineralisation in granites, to the classification of diamonds, to the identification of sedimentary units from the Witwatersrand and to the classification of coals from the Witbank Coalfield in South Africa. The results show that the methods can be used to identify and map the mineralised phase of the granite. In the case of the diamonds trace element signatures were found which were characteristic of the sources and these were used to classify very pure unknown samples with a high rate of success. In both the coal and particularly in the case of the Witwatersrand sediments these methods showed themselves to be a powerful tool for the identification of sedimentary units.

1. Introduction THE FUNDAMENTALconcept in pattern recognition is that a body of data obtained from a series of measurements on a universe of objects may have an underlying structure, and that features of this structure can be associated with particular categories or classes of interest. The recognition of these structural features or patterns can then be used for the classification of unknown objects. An additional important idea is that the structures underlying the data produce a great physical insight into the problem itself. Instrumental neutron activation analysis provides perhaps a unique method for the determination of a large number of chemical elements in geological samples. By following a standard procedure consisting of one or two irradiations in a reactor flux and the measurement of the resulting 7-ray spectrum at three or four decay times, the concentration levels of some 20-40 elements can be determined. These elements usually include seven or eight of the rare earths. sodium, potassium, rubidium, caesium, iron, scandium. cobalt, tantalum, thorium, uranium, antimony. hafnium, zirconium, as well as arsenic, tungsten, gold, iridium, zinc. copper and several other elements. Several of these elements or groups of elements show characteristic variations and the3 can be used as sensitive petrogenetic indicators. * On secondment from the South African Atomic Energy Board. 407

It is clear from this that the use of instrumental neutron activation analysis for the collection of data can be combined with pattern recognition techniques to provide a particularly powerful method for the study of geochemical differences and for the classification of unknown samples. Over the past decade we have been applying these two methods, to a number of geological and geochemical problems. In this article these results will be reviewed to illustrate the potential of the methods. In any pattern recognition problem there is a "series of measurement or data vectors x~. A linear classifier then consists of a set of transformations w~, that map the data vectors into the classification space, together with some way of defining regions in the classification space that are associated with the various classes. For example in the case of a two class problem w could be the vector joining the centroids of the classes, the mapping would be through the scaler product w-x. and the classification would be into class I (say) if w-x > 0~ where 0c is a critical value. Where more than two classes are involved the dimensionality of the classification space increases to n - 1 where n is the number of classes.~? ~ With ~7 classes there would thus be n - 1 different a~. There are two fundamentally different approaches to the classification problem. These use the methods denoted as sztperrised learni~Tg and unsupervised learni~g respectively. In the first method the classifier is designed [or "'trained") on a data set where the class membership is known and which is assumed to be

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representatite of that class in the universe of objects that may be classified. In the second method algorithms are used to find natural structures within the data set itself. The first approach is the basis for most "statistical" methods such as that of discriminant analysis while the second forms the basis for cluster analysis. Many arguments have been put forward as to the most appropriate of these methods. Obviously this will depend on the detailed nature of the problem to be tackled and of the relationship between the measurement and the underlying structure. For example, if differences between some of the variables are irrelevant to the structure then a supervised approach is much more likely to succeed. This is particularly important consideration in geochemistry where measurements must perforce be made on natural systems that have been subject to many different processes, only some of which are relevant to a particular study. Here a training set can, theoretically, be chosen as typical of a particular feature of interest e.g. mineralisation, provenance, differentiation index or stratigraphic location, and, if the set is properly chosen, features of the data due to other processes such as weathering or other secondary alterations can be averaged out. In the examples presented here we have chosen to use supervised learning and to apply the method of discriminant analysis. This method is one of those that is often grouped under the heading of statistical methods of pattern recognition. In pattern recognition it is necessary to obtain a similarity index or a generalised distance between sample points that can be used for comparison. In the example cited previously this was the projection of the measurement vector on to the classification vector. This generalised distance is in fact a distance in an n-dimensional space where the n dimensions represent the orthogonal element concentrations that are measured. One way of looking at the classification procedure is as a method of selecting the metric of this space to emphasise the relevant differences. This can be clarified by considering that one axis may represent, e.g. europium concentrations in ppm while another may represent sodium concentrations in per cent. A moment's reflection will show that the contributions of the differences in these element concentrations to a distance will depend entirely on the units in which they are expressed. The method of selecting the metric in discriminant analysis is simply to consider ratios of variances. The weight of the contribution of any element to the distance is hence the corresponding component of the w~ function defined previously and it is determined by the ratio of its variance within the groups or classes to its variance between the groups. We thus find that orthogonal transformation of the variables that will minimise the ratio of the within groups variance to the between groups variance. Say that the matrix of this transformation is Wso that: y=Wx

then it can be shown ~2b that the covariance matrix of the transformed variable y is related to the covariance matrix of the original data by Z{3) = W"~'(xl[{'i The variance of a particular component say y~ will then be given by the appropriate diagonal element of Z(yi}, O'2(yi} and

0"2(.1'i} = W'iY(X}W i where wi is the ith row of W. Now say that the between groups covariance matrix is denoted by B and the within groups covariance matrix is denoted by W then the quantity w'iBw i

w' Ww~

-~.

denotes the ratio of the between groups variance to the within groups variance in the direction defined b~ w~. This ratio, 2, represents the "'separability" of the groups in this direction and it is known as the discriminant criterion. It can be maximised by taking the partial derivative of ), with respect to w and setting the result equal to zero in the normal way. It is found (2) that the results are solutions to the equation

{W-I'B-

21)=0

This is an eigenvatue problem and when it is solved r non zero eigenvalues are found, with associated eigenvectors, where r is the rank of matrix B. The largest eigenvalue, 2. is then the largest value of the discriminant criterion and the corresponding eigenvector, w~, defines the direction in the u dimensional measurement space along which the dispersion between the groups is largest relative to the dispersion within the groups. So by a fairly elementary application of matrix algebra we have a method for finding patterns in the multivariate data obtained by neutron activation analysis that are typical of differences between geological classes, If the classes that are chosen have geochemically meaningful differences, then an examination of the eigenvectors wi, which are also known as discriminant fnnctions, will show up the relationships between the element concentrations that reflect these differences. The discrirainant functions found by this procedure are linear functions of the x~. If these are logarithms of the concentrations C~ then tile discriminant values w ' x will be of the form al log Co + a2 log C2 + ... + a, log C, = log {C'~'- Q - ' . . . C""I and this can be interpreted as the log of products or. if some of the ai are negative, of ratios of concentrations, These ratios of concentrations can be of direct geochemical significance. This process must however the regarded as heuristic rather than defini-

409

Geochemical cheracterisation

tive because the relationships found are limited by the procedure used. An unknown sample can then be classified into one of the groups b v simply considering its Euclidean distance from the various group means in the transformed space and assigning it to that group for which this distance is a minimum. It can be shown ~2~ that this distance is .just the so-called Mahalanobis distance between the point x and the group i given by d:(x.i) = (x - xi)' W - I ( x

-

xi)

Before proceeding to an examination of different applications it is worthwhile considering some of the limitations of this method. One of the major dangers is that of developing a classifier that is tailored to the idiosyncracies of the sample set. This is known as over-design of the classifier. This tendency becomes very marked as the number of variables increases for a set of training samples of restricted size. This tendency is directly related to the number of degrees of freedom in the covariance matrix. Geometrically it is allied to the increased ease with which a projection plane that appears to group random sample points can be found as the number of dimensions increases. In regression terms it reflects the fact that a regression of order n can always be found to fit n data points. Ideally the classifier should be tested on an independent data set but the relatively small size of available data sets makes this impractical. The best solution in this circumstance appears to be the method of design with successive elimination originally proposed by KANAL and CHANDRASENKARAN.OI In this method the classification is designed with all the samples except the one to be tested. For a sample set of size n. this leads to a set of n classifiers each based on n - 1 samples and tested with the remaining sample. If the classification is stable then this will be shown by' the stability of the set of n - 1 classifiers. In the case of the Mahalanobis distance the distance with one data point omitted can be directly calculated by the so-called "Jack knife" technique without the need to recalculate and invert the covariance matrix. The restricted size of the data set makes it necessarx to restrict the number of variables that are used in the classification and this in turn leads to a requirement for a method to select a "'best" subset of elements. HOWARTH ~'~ has implemented a method which evalutes successively all the classifiers based on all the combinations of the variables and he has shown that this approach works well to evaluate the best subset of a group of 11 elements. However, in a typical neutron activation experiment with. say. 22 variables there are over 4 million combinations and it is not practicable to consider them all. The best way of accomplishing this that is presently' available appears to be to use stepwise discriminant analysis/5' This technique reduces exactly to stepwise regression in the case of only txvo groups.

Finally before we proceed with examples of applications it should be mentioned that the discrimmant analysis approach is effectively distribution free. It only depends on the very general assumption that the covariance matrix can be taken as a measure of the dispersion in the data set. There is however, clearly some loss of information if the dispersions within the various groups differ greatly. If on the other hand the assumption can be made that all the groups are normally distributed with similar covariance matrices then the probabilities of class membership can be deduced and it can be shown that a quantity related to the Mahalanobis distance d z, between two groups, n a m e l f ~ nln 2 nl + n2

(N-k-p+

1)d2

p ( N - k)

has that particular kind of statistical distribution known as an F distribution with p and N - k - p + I degrees of freedom, where n~ and n2 are the numbers of samples in the two groups respectively, N is the total number of samples, k is the number of groups and p is the number of variables in the analysis. This important relation can be used to compare the significances of different sets of elements. In the following sections several examples will be given of the combined application of instrumental neutron activation analysis and discriminant analysis to a variety of geochemical problems. In all cases the irradiations were carried out in the O R R type reactor, SAFARI I, of the South African Atomic Energy Board and the ";-spectra were measured on one of three Ge(Li) detector systems using specially constructed automatic sample changers. ~7~ The analytical methods used, which included irradiations in cadmium and short-lived irradiations, have been described in several papers3 8-~°~ The selected cases that will be described are the investigation of mineralisation in granites, the identification of horizons in" a sedimentary succession, the classification of diamond from different sources and the characterisation of coal seams in a coalfield. Various computer programmes have been used in this work but the principal ones were those developed by HAWKINS~1t) and the B M D ~12~ programme where the stepwise discriminant p r o g r a m m e s have proved particularly useful.

2. Mineralisation in Granite The Bushveld Complex is a large Pre-Cambrian layered complex and it is one of the most dominant features of South African geology. The mafic phase of this formation carries large deposits of platinum and chromite while the granitic phase is the site of significant tin mineralisation. This tin mineralisation is carried by one specific type of granite in the acid phase, and in the type area at Zaaiplaats. in the Northern Transvaal where there

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are very good exposures, this granite is known as the "'Bobbejaankop'" granite after a hill in the vicinity. In this area the tin-bearing Bobbejaankop granite and the associated phase known as the "'Lease" granite can easily be distinguished by texture, colour. mineral intergrowths and field relationships but in other areas with poor exposures or in drill hole cores it is not possible to identify the granites. It would thus be of great value if geochemical patterns could be derived that are characteristic of the miner;alised granite and that could then be used for exploration. In order to investigate this, instrumental neutron activation analysis method was applied to a suite of rocks from the type area at Zaaiplaats. These rocks included samples collected along a traverse that had good exposures of the different granite types and that included an area of the granites carrying economic tin mineralisation. An investigation of different neutron activation techniques including 14 MeV neutron activation and thermal and epithermal reactor activation showed that a total of 34 elements could be determined in the granites by these methods. Of these 34 elements. 25 could be determined by a procedure with a single reacto.r activation of 1 h and the measurement of the 7-ray spectrum at three different decay times: 7, 14 and 30 days. Of these elements 22 could be determined in all the samples and these were used for the discriminant analysis of the granites. (8'~3~ Three groups were chosen for the discriminant analysis. These were the mineralised granite (Bobbejaankop granite, B) the unmineralised Main granite (M) and a third group consisted of samples taken some distance away and which had been identified by different authorities as being similar to either the mineralised or the unmineralised granite (identified here as W). Initially a classification was carried out with all 22 elements (sodium, potassium, scandium, iron, cobalt, barium, lanthanum, cerium, neodymium, samarium terbium, ytterbium, lutetium, hafnium, tantalum, thorium, and uranium). A plot of the sample scores

B

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CANON. VAR.!

FIG. I. Discrimination between three granite populations,

B, M and W, with 22 variables and identical design and test sets.

o

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FIG. 2. Discrimination between three granite populations, B. M and W, with 22 variables, method of successive elimination.

for the first two eigenvectors (discriminant functions) produced the diagram of Fig. 1. The grouping was very tight and the classification appeared to be good. However in this case there were 30 samples and this proved to be a good example of an over-designed classifier. This is shown in Fig. 2, which illustrates the effect of applying the method of successive elimination. Although there was still some discrimination, the procedure was not stable and this was clearly a case calling for a reduction in dimensions. In this case this was accomplished by applying the stepwise discriminant analysis to the three groups taken in pairs and using the significance of the F value at each stage to judge the quality of the discrimination achieved. The results of this procedure applied to the two groups B and M are shown in Table 1. As can be seen it was possible to obtain a set of six variables with a significantly improved discrimination effect at step twenty. On the basis of similar analyses of the three groups in pairs, a "'best" set of eight variables was chosen. These were the concentrations of the elements tantalum, europium, barium. ytterbium, thorium, scandium, terbium and lutetium. Figure 3 shows the results obtained with these eight variables by the method of successive elimination and clearly the analysis was much more stable in this case. The analysis also showed that the geochemical pattern represented by the first discriminant function served to distinguish between the B granites on the one hand and the M and W granites taken together, on the other. Since the difference between the latter two was much smaller, the conclusion follows that the W granites are probably similar to the M and clearly different from the B granite. This conclusion has been confirmed by independent petrological assessments.~ l,,~ Before leaving the subject of the granites, one further topic merits discussion. If the discriminant functions are indeed reflections of real geochemical patterns in the granites then it should be possible to map them. That this can be done is shown in Fig. 4. This Figure shows the geology along the traverse according to STRAUSS(15) and the values of the six

Geochemical characterisation

411

TABLE 1. Stepwise discriminant analysis of two granites, mineralised, Bobbejaankop and unmineralised, Main Step Variables in the regression

no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

No.

Ba

Mahalanobis distance D

F-values for regression

5.8 7.9 9.5 11.4 13.3 16.4 20.5 21.1 23.7 25.6 25.2 24.8 24.4 25.9 27.4 25.9 27.4 25.9 24.4 21.9

150.3 131.7 118.1 129.5 130.5 153.8 192.1 165.5 168.8 160.5 184.3 226.0 271.7 248.9 225.4 216.6 225.4 248.9 271.7 276.0

1

Ba.Sc Ba.Sc.Th Ba,Sc.Th,Eu Ba.Sc.Th,Eu,Zr Ba,Sc.Th,Eu,Zr.Co Ba,Sc.Th,Eu,Zr,Co,Rb Ba.Sc.Th,Eu,Zr,Co.Rb, Fe Ba,Sc,Th.E u,Zr,Co,R b.Fe.Sm Ba,Sc.Th,Eu,Zr.Co,Rb.Fe,Sm,Sb Ba,Th,Eu.Zr.Co,Rb,Fe,Sm,Sb Th.Eu.Zr.Co.Rb,Fe,Sm,Sb Th,Eu.Zr.Co,Fe,Sm,Sb Th.Eu.Zr.Co,Fe,Sm.Sb,Ce Th,Eu.Zr.Co.Fe.Sm,Sb,Ce,Nd Th.Eu.Zr,Co,Fe, Sm.Sb,Ce,Nd,Hf Th.Eu,Zr.Co,Fe.Sm,Sb.Ce,Nd Th.Eu.Zr,Co.Fe.Sm,Sb,Ce Th,Eu,Zr.Co,Fe,Sm,Sb Th.Eu,Zr,Co.Fe,Sm

2 3 4 5 6 7 8 9 10 9 8 7 8 9 10 9 8 7 6

variable discriminant function plotted for all the sample points. This plot shows up remarkably the differences between the granite types and the similarity between the Bobbejaankop and Lease granites, althou,qh the latter samples were not used in the deriration of the discriminantfunction. It is apparent that a real structure in the data is being reflected here. The geochemical significance of the discriminant function in this case is that it is a differentiation index, t~3~ confirming the consanguinity of the Bobbejaankop and Lease granites and showing that these mineralised granites were formed at a significantly more advanced state of differentiation than the Main granites.

3. T h e Identification o f D i a m o n d The use of these techniques to classify diamonds as to source represents a far more difficult problem. The

o o

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D

o a

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I I I

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x

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FIG. 3. Discrimination between three granite populations. B. M and W. with 8 best variables, method of successive elimination.

Degrees of freedom 1 2 3 4 5 6 7 8 9 10 9 8 7 8 9 10 9 8 7 6

19 18 17 16 15 14 13 12 11 10 11 12 13 12 11 10 II 12 13 14

Significance ratio (99.9';/0) 9.97 12.68 13.53 16.31 17.24 20.70 25.64 21.47 20.80 18.35 22.69 29.33 36.28 32.28 27.8 24.8 27.8 32.8 36.28 37.2

levels of concentration of the trace elements in diamond are far lower than those in rock. In this case irradiation times of 15 rain, 90 rain and 90 h and a total of 10 different counts were used to determine the trace element contents. ~9~ A total of 28 elements were determined in the diamonds and in many cases the sum total of all these element concentrations was < 1 ppm. A suite of 96 samples from known sources (Premier, Finsch and Jagersfontein) were used as the training set and a set of six samples of unknown origin was used as the test set. One of the problems of this data set was that, as a result of the low concentrations, some of the elements were below the detection limit in several of the samples. This was a major problem as only 13 of the 28 elements were observed in all the samples of the training set. These missing values were therefore predicted by a multiple regression technique. Many elements that occasionally had missing values were found to be strongly correlated with, and therefore predictable from, those elements that were actually observed.~ ~6~ In the case of the unknown samples this procedure could not be followed and in this case the unknown concentration was set equal to the detection limit. The classification achieved with all 28 elements is shown in Table 2. This classification was tested by the method of successive elimination and a very high success rate of 89.6Yo was obtained. However in terms of these discriminant functions the unknown samples were outliers and a reduction was effected in the number of variables used in order to find a sub-space that would span both the training and the test sets more effectively. The fact that this was necessary highlighted the

J . I . W . Watterson et al.

412

F. HILLSI 10 .

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OISTANCE ALONG TRAVERSE,

0 METRES

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2(30

FIG. 4. Section through the granites showing the mapping of the best six element discriminant function compared with the best ratio.

TABLE 2. Discriminant analysis of three diamond populations for 28 elements. (a) Accuracy of back classification Source Premier Finsch Jagersfontein

Sample U U U U U U

10 I1 12 13 14 15

Premier

Finsch

Jagersfontein

30 3

2 3 22

34 2

Accuracy o; 94.5 90.9 81.5 89.6 Average

(b) Classification and test probabilities for unknowns Closest source Classification test probability Finsch Jagersfontein Finsch Jagersfontein Jagersfontein Finsch

importance of sampling in this type of analysis. For the analysis to be meaningful the training set must be representative of the universe of objects that contains the unknowns. In this case the training set was chosen to cover various intrinsically interesting categories, such as colour, inclusion content and boart occurr e n c e s . f r o m one m o n t h ' s production at the three mines, Premier, Finsch and Jagersfontein, and as such was not truly representative of the population that the u n k n o w n were drawn from. For example, four of the six u n k n o w n samples had an impurity content lower than that of 85';~ of the training set. A technique k n o w n as "interrelationship analysis ''~v) was used in this case as an aid in the selection of a variable subset. By the use of this method 16 elements were selected. With these elements in the analysis the results shown in Table 3 were obtainedJ ~6~ Although the M a h a l a n o b i s distance between the populations decreased, the back-classifi-

0.017 0.266 < 0.001 <0.001 <0.001 0.070

cation success rate was only slightly reduced from 89.6~0 to 84.4~o. The most i m p o r t a n t effect of this dimensionality reduction is however shown in Table 3 which shows the aposteriori probabilities for group membership for the u n k n o w n samples with 16 variables.

TABLE 3. Discriminant analysis of three diamond populations with 16 elements. Test probabilities for unknowns Sample U U U U U U

l0 11 12 t3 14 15

Closest source Premier Jagersfontein Premier Finsch Jagersfontein Finsch

Classification test probability 0.597 0.863 0.350 0.062 0.124 0.561

Geochemical characterisatiml

413

The success rate of four or five out of six is creditable considering the obviously subtle nature of the differences between the populations and the resulting difficulty of the classflication problem. 0

0

4. The Identification of Stratigraphic Horizons in a Sedimentary Sequence

t-i

FIG. 5. Discrimination between three diamond populations for 16 best variables.

In this case the reason for dimensionality reduction is not only to achieve a more stable classification but also to find a variable subset in terms of which the training set appears to be representative of the test set. Fig. 5 shows the discriminant functions for the case of 16 variables. However it should be noted that the method of successive elimination was not used in this case. A further reduction of the number of variables to a total of 10 was made on the basis of interrelationanalysis. In this case the accuracy of back-classification was 77.1°o. The classification of the unknown samples on the basis of 16 and l0 elements is shown in Tables 3 and 4 and compared with the actual sources in the last column.

TABLE 4. Discriminant analysis of three diamond populations ~vith 10 elements, la) Accuracy of back classification Source

Accurac3 "~

Premier Finsch J agersfontein

72.2 84.8 74.0 Average 77.1

Ib} Classilication and test probabilities for unknowns Actual Classification test Sample Closest source source probabilities

U 10 U U L L U

11 12 13 14 15

x ~1 ",4 I

Premier Premier Premier Finsch Jagersfontein Finsch

2"

Premier Premier Premier Finsch Finsch Finsch

0.511 0.587 0.227 0.352 0.506 0.429

Mine geologists often orientate themselves with respect to a sedimentary succession by the use of certain "'marker" horizons that are easily recognisable. A series of investigations were carried out to establish whether instrumental neutron activation and discriminant analysis could be used to lind geochemical patterns typical of particular quartzite, shale and conglomerate horizons in the Witwatersrand sediments." 8.19~ Such geochemical patterns could be used in the same way to identify particular horizons. These patterns could be of great practical value in mining and exploration where faulting can easily produce serious uncertainties. The upper division of the Witwatersrand is up to 3000 m thick. It is composed almost entirely of quartzites and conglomerates and it is in these conglomerates that the gold mineralisation is found. There are two divisions of the Upper Witwatersrand, a lower division known as the Main-Bird Series and the Kimberley-Elsburg Series in turn contains conglomerate rich zones one of which is known as the Kimberley Reef Group. It is this G r o u p that was investigated. The samples for this study were collected from the Durban Roodepoort Deep Mine on the West Rand. In this region the Kimberley Reef is some 200m thick, and it is extensively folded and faulted. Approximately 50 m of the reef surrounding the horizon of economic interest, the pay band, were sampled at four different locations from a total of six borehole cores. Three of these were at one location while the four different locations covered the mine over a distance of some 6 kin. A total of 40 samples were used for the analysis covering a total of 12 geologically distinct horizons. All of these horizons were not developed in any one of the boreholes. The samples were irradiated in a neutron flux of 101an.era . -2 s-~ for 4 h and their induced activity was measured with a Ge(Li) detector at four different decay periods, i.e. after 5, 11, 32 and 54 days. A total of 26 elements were determined in the samples. Some of the elements e.g. gold and uranium showed differences within zones that were much larger than differences between zones. Other elements were remarkably constant both within and between zones.

The 24 elements that were determined in all of the samples were used for the discriminant analysis. These were iron. lanthanum, scandium, chromium. arsenic, gold. tantalum, nickel, uranium, hafnium. cesium, cerium, europium, thorium, neodymium.

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J. 1. W. Wutterson et al.

Io0

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• Known X Unknown

i i i i i i Fe Lo, ScCr AsAuTa

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FiG. 6. Stepwise discriminant analysis of Witwatersrand sediments--accuracy of classification of test samples (unknown) and training samples (known).

ytterbium, cobalt, terbium, lutetium, titanium, sodium, zirconium, antimony and barium. The classification achieved by the discriminant analysis was tested by using the three cores at one location as a test set and the other three as the training set. The classification of the six zones developed at this location was therefore tested. There were a total of 14 samples available in the training set for these six zones. This was a very small number of samples, particularly where 24 variables were available for the classification, and an interesting technique was employed to increase the number of degrees of freedom in the covariance matrix. Each of the samples was analysed in triplicate and each of the individual results obtained was entered as a separate data vector into the discriminant analysis. Mathematically the effect of this procedure was probably to stabilise the inverse of the covariance matrix with an effective minimum of the withingroups variances related to the reproducibility of the experimental results. The efficiency of this method was shown by the results obtained. Once again the stepwise discriminant procedure was utilised in order to select a subset of the variables for the optimum discrimination. The results of this procedure are summarized in Fig. 6. The accuracy of the classification assessed on the separate test set as described above is shown in the crosses in this figure while the dots show the accuracy achieved when back-classifying the training set. Confining the discussion to the first method of testing the results only. the classification accuracy rose from _~'~0"~,,with iron alone to 80~; with the four el-

ements iron. lanthanum, scandmm a n d chromium. With the inclusion of arsenic, gold and tantalum it rose to 9000 and 100°o was achieved ~vith ten elements in the discrimfnant functions. Thus the most important single element appears to be iron. This element separated the quartzites from the conglomerates and it is probably an indicator lbr the heavy minerals in the conglomerate matrix. '~*~' The second most important element was lanthanum which represented the light rare earths. As an example the data for this element are shown in Table 5. As can be seen from the table this element serves to identif3 Zone 4, the quartzite hard bar and Zone 6. a conglomerate, both of which have significantly lower lanthanum concentrations. The consistency of the values in Table 5 is remarkable when it is borne in mind that the cores were spread over a lateral distance of 6 km. The element scandium helped to identify Zone 3 while chromium, arsenic and tantalum were important for Zones 3, 7 and 2 respectively. ~t~ The great advantage of the multivariate pattern recognition technique is that it enables all of these elements and the relationships between them to be taken into account in the identification of the stratigraphic horizons. An extremely important aspect of such a study is the division of the stratigraphic succession into sedimentary units. In some instances the decisions by the geologist are of necessity highly subjective. One way to overcome this problem is to utilise statistical methods to establish a stratigraphical subdivision on the basis of the element concentrations as determined by instrumental neutron activation analysis. This has been done by Rasmussen and proved to be remarkably successful. (2°~

5. T h e G e o c h e m i c a l C h a r a c t e r i s a t i o n of C o a l S e a m s Coal provides an ideal matrix for instrumental neutron activation analysis and a number of trace elements originating in both the ash and the organic component can be determined by this method. The instrumental neutron actiwLtion method has been applied to a suite of 147 samples from a large coalfield in South Africa. the Witbank Coalfield. ~2~

TABLE 5. Lanthanum values for six cores in ppm C o r e no.

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2

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17 17 II 21 14 22

16 14 -22 16 --

18 20 8 20 -19

16.1 16.2 8.8 21.5 14 19.2

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Fi(;. 9. Discrimination between three main coal seams of the Witbank coalfield.

The relationship between the structure and the geochemistry of the maior seam of this coalfield was studied in detail and compared with that of two other seams. Up to six layered units occur in the major seam, three of these are mined preferentially and the geochemistry of these was also studied, A total of 16 elements were determined in the coal. Most of these were associated with the inorganic or ash content but two of them. bromine and antimony, had organic associations. The individual elements could not be used to classify the coal seams or the layered units between them, although geochemically interesting trends emerged for example in the variation of the bromine concentrations. The techniques of discriminant analysis were applied in this case in different ways. In the first case they were used to investigate the three layered units within the major seam. This analysis is shown in Fig. 7. It showed that the three units are very similar with some slight difference between the two units, B and D, which are mainly bright coal, on the one hand and C which is a dull shaley coal, on the other. Much more interesting was the fact that where the middle seam C, was absent the samples showed a very distinct difference from the normal B or D pattern. Discriminant analysis was applied to the same set of samples to examine areal variation by a study of

the differences between samples from different localities or regions. This analysis is shown in Fig. 8 and it produced a distinct grouping illustrating a significant areal variation. This is thought to be mainly due to a variation in bromine reflecting a slow change from a fresh water to a more brackish depositional environment. <22) This change is also related to changes in the quality of the coal across the basin. In this case the samples from the different areas could be classified back into their groups with a success rate of 99°,0 using a discriminant analysis based on all 16 elements. Finally the discriminant method was applied to a suite of samples representing the three major seams of the Witbank Coalfield sampled at one colliery. Although the trace element concentrations of these seams are superficially very similar, the discriminant functions clearly separated the seams into three groups. These results are shown in Fig. 9. The success rate of the classification was 98% in this case.

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6. D i s c u s s i o n and C o n c l u s i o n s Instrumental neutron activation is a remarkably powerful method for the determination of trace elements in geological samples. In some cases more than one third of all the stable elements can be determined in this way by one irradiation and three or four measurements of the ~'-ray spectrum. The data yielded by this method are also of an almost unique standard of accuracy and consistency for many elements at the trace element level. There are few methods that can compete for example in the determination of the rare earths or gold. One of the problems in the past has been how to use this wealth of information. We have tried to show here that the combination of this method with statistical methods of pattern recognition can give a profound insight into a variety of geological problems. These have ranged through the development of mappable functions for a mineralised granite., trace element signatures for diamond, the characterisation of sedimentological units and the investigation of a

416

J. I. I#( Watterson et al.

coalfield, but these are only a few of the many problems awaiting investigation and even in these cases much work remains to be done in practical applications to realise the full promise of the method. Up to now one of the major reasons for the relative paucity of the work is that instrumental activation analysis, although simple in principal, is logistically complicated when large numbers of samples are handled. Reliable data reduction also demands sophisticated computer programmes. It is only recently with the development of disc based ;'-spectroscopy systems that the method has become capable of handling many samples simply and at a reasonable cost. But with these developments the time is right for a wide use of these two methods to make major contribution to the o p t i m u m usage of our mineral resources and our understanding of geochemistry.

Acknowledgements--The authors wish to acknowledge the major part played by Dr D. M. HAWKINS, Mr S. E. RASMUSSENand Mr R. H. LEAHY in the development of the methods and some of the results described here. Two of the authors, WATTERSOY and ERASMUS,wish to express their appreciation to the President of the National Institute for Metallurgy of South Africa for permission to publish this paper and Dr R. J. HART wishes to express his thanks to the South African Atomic Energy Board for their support.

References 1. NAGY G. Proe. IEEE. 56, 836 (1968}. 2. TATSUOKAM. M, Multivariate Analysis (J. Wiley, New York, 1971 ).

3. KANAL L. and CHANDRASENKARANB. Proe. Xam. E/e~iron. ConI~ 24. 2 (1968). 4. HOWARTH R. J. Proc. 4th lilt. Geochem. E.vptor. Syrup. [Ed. JONES M.} pp. 259 (Institute of Mining & Metallurgy. London. 1973). 5. MCCASE G. P. Teelmometrics 18. 47 (1976). 6. KOCH G. S, and LINK R. F. Statistical 4mt/vsis ol GeoIo~tical Data (J. Wiley, Ne~v York. 1971 ). 7. ANDEWEGA. H. and WATTERSON J, I. W. IEEE Tra~ls. Nuel. Sei. NS-27, 728 (1980t, 8. WATTERSON J. I. W, and SELLSCHOPJ. P. F. J, Radtoanal. Chem. 38, 301 {19771. 9. FEso H. W.. BIBB.YD. M., SELLSCHOPJ. P. F. and WxTTERSON J. I. W. J. Radioanal. Chem. 17, 195 119731. 10. ERASMUSC, S.. FESQ H. W.. KABLE E. J. D., RAS:qtSSliX S. E. and SELLSCHOPJ, P. F. J. Radioanal. Chem. 39. 323 (1977). 1I. HAWKINSD. M. and RAS,X,IUSSEN S. E. J. ),lath. (;eolo~t~ 5, 163 (1973). 12. BMD Statistical Package. Health Science Computing facility. U.C.L.A. (1977). 13. WATTERSON J. I. W. Unpublished Ph.D. Thesis. University of the Witwatersrand. Johannesburg (1975). 14. DE WAAt S. A, Trans. Geol. Soc. S..4Ii'. 75, 135 11972). 15. STRAL'SS C. A. S. All'. Geol. Surv. Memoir No. 46 (S. Afr. Dept. of Mines. 1954). 16. ERASMUSC. S., HAWKINS D. M.. KABLE E. J. D.. FIiSQ H. W. and BmaY D. M. S. Afr. Nat. Inst. for Metall.. Report No. 1652 {19751. 17. HAWKINS D. M. J. R. Slat. Soc. 3 11973}. 18. RASMUSSENS. E. and FESQ H. W. S. AfT. Nat. Inst. I\~r Metall. Report No. 1563 (1973). t9. RASMUSSENS. E. S. Afr. Nat. Inst. for Metall, Report No. I874 (1977). 20. RASMUSSENS. E. Nuclear Physics Research Unit. University of the Witwatersrand. Johannesburg, Report NPRU 774(1977). 21. HART R. J., LEAHY R. and FALON R. M. J. Radioanal. Chem. 71,285 (I 982). 22. HART R. J. and LEAHY R. M. Proc. hit. ConL Appl. Mineral. in the Mineral Industry, Johannesburg, South Africa, June 11981).