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Statistical analysis and data display at the Geochemical ProspectingResearch Centre and Applied Geochemistry Research Group,
Imperial College, London
Richard J. Howarth1,* & Robert G. Garrett21Dept. of Earth Sciences, University College London, Gower Street, London WC1E 6BT, United Kingdom2Emeritus Scientist, Geological Survey of Canada, 601 Booth St., Ottawa, Ontario, K1A 0E8, Canada
*Corresponding author: (e-mail: [email protected])
ABSTRACT: The Imperial College of Science and Technology, a constituent collegeof the University of London in the 1960s, had the good fortune to be one of the firstcolleges in the United Kingdom to have access to digital computing facilities. Thisreview traces the history of the application of computing in the GeochemicalProspecting Research Centre and its successor, the Applied Geochemistry ResearchGroup, as computing moved from being a frontier research area to becoming acommonplace tool. The three principal areas in which it was involved comprised: thequality control, and thereby assurance, of analytical data; the production ofpioneering atlases of regional geochemical variation in Northern Ireland ( 1973) andEngland and Wales (1978); and the application of methods introduced by workersin pattern-recognition and statistics to the interpretation of land-based and marineregional geochemical data.
KEYWORDS: computers, computing, applied geochemistry, history of geochemistry, history of statistics, history of cartography, regional mapping, spatial filters, geochemical atlas, SC4020,LGP2703, multi-element maps, data transformation, factor analysis, cluster analysis, discriminantanalysis, ridge regression, Kleiner-Hartigan trees, robust statistics, quality assurance
The Geochemical Prospecting Research Centre (GPRC ) wasestablished in 1954, under the direction of Professor JohnStuart Webb (19202007), in the Mining Geology section ofthe Royal School of Mines (RSM), Imperial College of Scienceand Technology (ICST), London. Initial studies were con-cerned with mineral prospecting using soil and drainage sam-pling in Northern Rhodesia (Zambia), Uganda, Sierra Leone,Bechuanaland (Botswana), Tanganyika (Tanzania), BritishNorth Borneo (Sabah, East Malaysia), Burma (Myanmar) andthe Federation of Malaya (West Malaysia), and extended in the1960s to Southern Rhodesia (Zimbabwe), the PhilippineRepublic, Borneo (now divided between Malaysia and
Indonesia), Fiji, East Africa, Australia, and the UnitedKingdom. By 1960, its studies had broadened into regionalgeochemistry, based on the analysis of stream sediments. In1963, Webb initiated the first of a series of investigationsconcerning the relationship between regional geochemistry andagricultural problems in livestock in Eire (Webb 1964; Webb &
Atkinson 1965). The application of geochemistry to marinemineral exploration began in 1964 (Tooms 1967). Conse-quently, by 1963, the Centres name was changed to the
Applied Geochemistry Research Group (AGRG ) to reflect theincreasing breadth of its applications.
The work of the GPRC and AGRG was underpinned bydevelopments in two complementary spheres: methods andinstrumentation for chemical analysis (discussed in the paper by
Michael Thompson (2010) and computing (Fig. 1). The latterfacilitated: (i) statistical quality-assurance in the analytical lab-
oratory; (ii) the display of large, multi-element, data sets in mapform; and (iii) the interpretation of such multi-element datasets.
First steps
Many of the early studies undertaken by research students inthe GPRC included simple, manually-based, statistical analyses.
Fig. 1.Annual numbers of GPRC/AGRG publications (total n=76)and theses (n=24) with a substantial computing and/or statisticalcontent over the years 195488.
Geochemistry: Exploration, Environment, Analysis, Vol. 10 2010, pp. 289315 1467-7873/10/$15.00 2010 AAG/Geological Society of LondonDOI 10.1144/1467-7873/09-238
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The situation in the early 1960s is summarized in Hawkes &Webb (1962 ). The use of histograms to display the frequencydistributions of element concentrations was commonplace,
while probability plots of cumulative frequency distributionswere less frequently prepared. In both cases, the data for therequisite plots were compiled by hand through the preparationof tally tables. At that time, analytical quality assurance wasbased on the use of statistical series samples. These were aseries of synthetic samples (each of which was composed ofknown proportions of two natural end-members, one having alow concentration of the element of interest, the other a highconcentration) which were included in analytical batches fol-lowing the procedure developed by the ex-RSM geologist andchemical engineer, Charles Alex Urton Craven (191893), withadvice from Professor George Alfred Bernard (19152002) ofthe Mathematics Department, ICST (Craven 1954), in order toestimate analytical accuracy and precision. For the largeamounts of photographic-plate spectrographic data generatedat the GPRC, bins for data concentration-ranges were selected(because of a tendency of operators to unconsciously interpo-
late values which were biased towards those of the analyticalstandards used), using a logarithmic concentration scale, andbin boundaries were placed mid-way between the knownconcentrations of the geochemical standards. A tick (the tally)
was placed in the appropriate bin for each analysis falling in thatrange, every fifth count being drawn as a horizontal linethrough the previous four ticks. This facilitated counting thetotal numbers of analytical results falling into each bin. A book,
widely used by students at the time, was Moroneys (1960 )Facts from Figures, which gave formulae for the calculation ofmeans and standard deviations from such grouped data, asaccumulated in the tally tables.
For those more interested in statistical analysis, Dixon &Massey (1957) was the text of choice. However, in the early-
and mid-1960s, textbooks written by geologist and statisticianco-authors started to be published on the topics of statisticaldata analysis and modelling, e.g. Miller & Kahn (1962) andKrumbein & Graybill (1965), and these, together with agrowing number of research papers, did much to exposestudents to the possibilities of the application of mathematicsand statistics to applied geochemical problems. In the early1960s such computations were carried out by means of tablesof logarithms and a six-inch (15 cm) slide-rule, with whichstudents were as adept as todays are with pocket calculators.
To assist in the calculations (based on a linear regressionmodel) required by Cravens (1954) method of estimation ofanalytical accuracy and precision, preprinted work-sheets wereused; one simply followed the steps and the results were arrived
at very much a black box approach. In order to meet therequirements of normality of residual errors in the regressionmodelling, and homogeneity of variance when the concen-tration levels in the statistical series samples spanned over anorder-of-magnitude, it was desirable to carry out these calcula-tions following a logarithmic transformation. This was thesubject of an MSc thesis by Stern (1959), but the routineapplication of his method was computationally complex, andessentially impractical for routine application, even using theMonroe electro-mechanical calculator available in the GPRC.Sterns supervisor in the Department of Mathematics, Dr. G.M. Jenkins (193382), who later became an expert in time-series analysis and systems engineering, appears to have begun
work on improving the deficiencies he recognised in Sterns
approach, in an unpublished manuscript A statistical problemin geochemical prospecting (1959?, recently found in oldAGRG files). In 1970, an ex-member of the GPRC staff,Clifford (Cliff) Henry James (19312003), published a version
of Cravens method still adapted to hand-calculation, on thegrounds that one of the difficulties of the method as originallydescribed is that the calculations involved require a computeror an electronic calculator with a memory unit . . . manylaboratories do not possess these facilities (James 1970, B88).
REGIONAL MAPPING
Following extensive fieldwork over several thousand squaremiles of Africa in the mid-1950s by Webb, Tooms and theirstudents, it became apparent that there was considerable scopefor regional geochemical surveys based on drainage reconnais-sance surveys. By 1960, this hypothesis was confirmed throughfurther studies in what was then Northern Rhodesia, elsewherein Africa, and in S.E. Asia. In 1960, a suite of drainage samplescollected for a base metal drainage reconnaissance survey over3000 mi2 (7770 km2) of the LivingstoneNamwala Concessionarea, Zambia, were made available to the GPRC by NamwalaConcessions Ltd. These were analysed spectrographically andchemically for 17 elements in 196162. Following a study of theassociation between trace element concentrations in the drainagematerials and the geology (Harden 1962), it was apparent thatthe
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Fig.
2.Portionofapoint-symbolmapoftheconce
ntrationofcold-extractablecopper(ppm)
inthe 0 and xi,i=1,k =100) to a new set of
variables y1, . . ., y(k1) where yj= loge[xi/x(k1)]; j=1, k1.In recent years, this transform has been widely promoted foruse in the earth sciences (most recently by Buccianti et al. 2006).Howarth tried on several occasions to apply the logratiotransform as a precursor to multivariate analysis of various
AGRG geochemical data sets but found that, in practice, the
results were often geochemically uninterpretable, and thatwhenever xi 0, the transform resulted in serious outlierproblems. More research, with a wide variety of data sets, isrequired on this subject.
In recent years, Dennis Helsel (Helsel & Hirsch 1992,357376; Helsel 2005), of the US Geological Survey WaterResources Division, has provided new approaches to theproblem of dealing with censored, i.e. below analytical detec-tion limit (dl), data. In the days of GPRC/AGRG, any such
values in a data set were routinely set to the appropriate dl/2for the purposes of statistical analysis and, in practice, it isdoubtful whether it brought any geologically significant biasinto the geochemical interpretations arrived at.
Robust methods
The deleterious effect of outliers present in a data set, leading tobias in calculation of the mean, inflated variances, spurious
Fig. 15. Trial KolomogorovSmirnov
filtered map for zinc concentrations(ppm) in the
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correlation coefficients, and so on, has long been recognised.However, it was only in the mid-1970s that methods whichcould automatically down-weight the effects of outliers to
obtain robust estimates of both univariate statistics (such asthe mean and standard deviation) and the covariance matrixor correlation matrix (which underpin principal components,
Fig. 16.Q-mode factor analysis maps for the geochemistry of the
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factor and classical linear discriminant analysis) began to bedeveloped (Andrews et al. 1972; Huber 1981), but it was a
while before their potential utility in applied geochemistry waspointed out (Campbell 1982; Garrett 1983; Howarth 1984).
Robust correlation matrices were calculated by Leech (1984),using software developed by the statistician Norman Camp-bell of the Commonwealth Scientific and Industrial ResearchOrganisation, Australia (Campbell 1980), who had taken hisdoctorate in the Statistics Department at Imperial College.
Turner (1986 ) implemented robust versions of both principalcomponents analysis and ridge regression software, whichproved immensely useful to AGRG research subsequently(e.g. Coward & Cronan 1987).
The extensive study of the application of robust principalcomponents and factor analysis by Turner (1986, 434548)concluded that factor analysis is preferable to principal compo-nents analysis because the use of a small number of factorsforces a grouping of the variables, reducing the dimensionality
of the problem and increasing interpretability. The greatestanomaly contrast is obtained using untransformed data; priorBoxCox transformation of the data is best if backgroundassociations and relationships are to be revealed.
Data displays
The arrival of the interactive statistical package MINITAB(Ryneret al. 1976) on the Colleges distributed terminal system
enabled routine data analysis to be used by both staff andstudents in AGRG and, because it embodied much of therecent thinking on graphics-based Exploratory Data Analysis(Tukey 1977), box-plots, quantile-quantile plots and othergraphical displays were soon taken up in AGRG work (Earle1982; Howarth 1984; Turner 1986). Earle (1982, 168183)developed a program (GIRAF) for the interactive dissection ofprobability plots into constituent sub-populations. Turner(1986, 166179) showed the utility ofmultivariate probabilityplots, based on the cube-root of the Mahalanobis distance(Healy 1968; Campbell 1979) for detection of multivariateoutliers.
Use of two new multivariate graphics to portray multi-element sample compositions for the purpose of comparison
were extensively investigated by Turner (1986), using theMorayBuchan data set: (i) Chernoff faces (Chernoff 1973),which assigns features of the human face ( e.g. position/style ofeyes, eyebrows, nose, mouth) to different variables to make
Fig. 17. Subtractive colour-combinedmap of the first three varimax rotatedfactors of the BoxCox transformedgeochemistry of the
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Fig. 18.Empirical discriminant classification map of the geochemistry of Pb, Ga, V, Mo, Cu, Zn, Ti, Ni, Co, Mn, Cr and Fe 2O3in the
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comparative displays, each face corresponding to a samplecomposition; and (ii) KleinerHartigan (KH ) trees (Fig. 23a;Kleiner & Hartigan 1981; Garrett 1983).
Turner found Chernoff faces to be unsatisfactory, in thatmuch work was required to find the best facial features to
which a particular element should correspond (which impliedthat the technique could be used to deliberately distort resultsby emphasis or suppression of any variable) and that, in orderto achieve the best visual emphasis for any anomalous samples,the analyst must have prior knowledge of which they are(Turner 1986, 346, 355). The KH trees were far moreeffective at portraying the multi-element sample compositions,using a tree morphology based on the hierarchical clusteranalysis of a robust correlation matrix; branch-lengths aredrawn proportional to the concentrations of the elements to
which each corresponds (Fig. 23a). It was likened to perform-ing a visual factor analysis. Although the physical size of theplotted trees made it difficult to use them in a spatial context
with a large data set by plotting them at their correspondingsample location on a map, nevertheless, side-by-side compari-son of the trees laid out as a graphic table, in numerical orderof sample numbers (Fig. 23b), proved quite satisfactory. KH
trees were also extensively used by Coward (1986).
Ridge regression
Linear multivariate regression analysis has long been used inapplied geochemisty to correct for the effects of elementinteraction (e.g. enhancement of element concentration levelsas a result of iron and manganese scavenging), and to empiri-cally explain the behaviour of an element in terms of others.Emphasis is often placed on the regression residuals (theobserved concentration minus that predicted by the fittedregression model) as a means of identifying anomalous behav-iour. For example, Moorby et al. (1987) fitted quadratic trendsurfaces (see above) to the residuals of Pb and Zn as predicted
by separate regression models fitted to the suite of elements{Ca, Mg, Al, Fe, Mn} in order to delineate broad trends ofbackground variation in carbonate-rich marine sediments (andhence the spatial setting of anomalous concentration values) in
two areas of the continental shelf of Greece. Stable anomalypatterns were shown to exist off the Sounion Peninsula, aknown area of mineralisation.
However, where it is crucial that the relative importance ofa number of elements in controlling the behaviourof another isdetermined, Hoerl & Kennard (1970) recognised that wheneverthe supposedly independent predictors in a linear regressionmodel are correlated (as is always the case where geochemicaldata are concerned) it will lead to the coefficients of somepredictors in the fitted regression equation which will be toolarge, and may even be of the wrong sign. Consequently, theyintroduced the ridge regression method to overcome suchundesirable features. The existence of their work was firstbrought to the attention of geologists by Jones (1972). It wasprogrammed for use in AGRG by Turner in 1979 (Turner1980), and the RIDGE11 program was subsequently extendedby Howarth in 198182, during work on the NURE contract
with the University of Georgia (see above; Howarth 1984;Howarth & Koch 1986) to include interactive selection of theridge parameter, choice of variables, progressive deletion of
outliers, and resubstitution of the entire data set, using the finalfitted equation, to obtain the residuals. The method wasextensively investigated in an exploration context by PhilipDavies (1983), and proved to be equally helpful in derivinginterpretational models in relation to the occurrence of bovinehypocupraemia (Leech et al. 1983; Leech 1984), and in theanalysis of a suite of marine mineral exploration data from thesouthwest Pacific (Coward 1986; Coward & Cronan 1987).
Turner (1986, 549593), using Ba, Pb and Zn as responsevariables for the 23-element MorayBuchan data set, demon-strated the efficacy of robust ridge regression, and showed thatanomaly (regression residual) contrast was maximised ifuntransformed data were used.
Other work
Miscellaneous applications have included: analysis of variance(ANOVA) to quantify variability attributable to both fieldsampling and analysis (Garrett 1969; Howarth & Lowenstein1971, 1972) and in the doctoral thesis by Richard Duff (1975),and the application of robust ANOVA by Ramseyet al. (1992);development of statistically-based criteria for the recognition ofuraniferous granitoids from NURE HSSR data (Koch et al.1981a,b; Howarthet al. 1981); and the application of numericalmodelling in vapour geochemistry by Ruan Tianjian (Ruan1981; Ruanet al. 1985a, b). In more recent years, GeographicalInformation Systems have been applied in studies ofenvironmental- and urban-geochemistry by workers in the
Environmental Geochemistry Research Group, the successorto AGRG at Imperial College (Tristan-Montero 2000; Tristan etal. 2000; Thums & Farago 2001; Thums 2003; Li et al. 2004;
Appletonet al. 2008).
ANALYTICAL QUALITY ASSURANCE
The development of analytical methods and related qualityassurance and interpretation methods in the GPRC and AGRGare discussed by Thompson (2010) but, for the sake ofcompleteness, brief details are also included here. As wasmentioned in the Introduction, Cravens statistical seriesapproach continued to be used into the 1970s (Stanton 1966;
James 1970), but it came to be recognized that the low- and
high-concentration end-members of a statistical series mightnot be representative, so far as their nature and matrix wereconcerned, of the field samples being analysed, and that themethod could only provide either an estimate of analytical
Fig. 20.Nonlinear mapping onto 2-dimensions of the geochemistryof manganese nodules from the Pacific Ocean on the basis ofnormalised Mn, Fe, Co, Ni, Cu, Pb and Ti. The compositionalcontinuum is divided into 6 classes for purposes of interpretation.(Redrawn from Glasbyet al. 1977, fig. 1).
Statistical analysis and data display at GPRC and AGRG 309
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precision ( repeatability) at a particular concentration, or anaverage precision value over the concentration range.
Thompson & Howarth (1973, 1976, 1978), Howarth &
Thompson (1976 ), and Thompson (1978, 1981, 1983), devel-oped an alternative approach, based on duplicate analysis ofrandomised splits of routine field samples in which it was
Fig. 21. Spatial disposition in thePacific Ocean (Lambert equal-areaprojection) of the 6 classes from thenonlinear mapping of Fig. 20. (Redrawnfrom Glasbyet al. 1977, fig. 3).
Fig. 22. Comparison of the BoxCoxtransform in reducing skewness (s) andkurtosis (k; shown ask) for a data set
with the same parameters for theuntransformed and log-transformed data
values (Howarth & Earle 1979, fig. 8).
R. J. Howarth & R. G. Garrett310
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assumed: (i) that analytical error could generally be wellmodelled by the normal distribution (Thompson & Howarth
1980); and (ii) that analytical precision varied as a linearfunction of concentration in the analytical system (Thompson1988) which, it turns out, was also assumed by Jenkins in hisunpublished (1959?) manuscript mentioned p. 290. The dupli-
cate analysis method rapidly became established within AGRG,alongside the use of classical Shewhart ( 1931) control charts to
control analytical batch performance through the monitoring ofanalyte concentration levels in splits of long-term house refer-ence materials (Thompson 1981, 1983). The ThompsonHowarth chart, as it became named, was subsequently adopted
Fig. 23. (a) KleinerHartigan ( KH)tree morphology for theMorayBuchan, Scotland, streamsediment data set based on Wards(1963) agglomerative clusteringalgorithm applied to a robustcorrelation matrix of BoxCoxtransformed data (redrawn from Turner1986, fig. 7.76); (b) Examples of KHtrees for actual samples from theMorayBuchan data set (portion of
Turner 1986, fig. 7.102).
Statistical analysis and data display at GPRC and AGRG 311
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by the wider geochemical and chemical community (e.g. Ana-lytical Methods Committee 2002) and their approach continuesto be extended in scope (e.g. Stanley 2006; Stanley & Lawie2008).
In other applications, simulation and regression techniqueshave been applied to evaluation of matrix correction andinterference effects (Howarth 1973d; Thompson et al. 1979)and to the comparison of analytical accuracy between analyticalmethods (Thompson 1982). More recently, robust ANOVAhas been used to determine the magnitude of analytical variancein relation to other sources of variance in geochemical data(Ramseyet al. 1992).
When John Webb initiated the pioneering series of multi-element multi-purpose geochemical atlases in the mid-1960s,there was inevitable trade-off between the analytical methodused, expected analytical precision, and rapidity of turn-round;this was not what traditional geochemists were used to, and thematter proved controversial. AGRG staff had to justify thisnew approach (Howarth & Lowenstein 1971, 1972; Webb &
Thompson 1977; Webb et al. 1978). Even today, despite
considerable advances in analytical methods, such a fitness-for-purpose approach to analysis requires explanation (Thompson& Fearn 1996; Fearn et al. 2002).
Looking back now, it is probably impossible for youngergeochemists to realise just how difficult it was, not only toimplement many of the statistical techniques, where we werebreaking new ground in applied geochemistry, but to convincepotential users of the utility of the results. In a broaderperspective, Garrett et al. (2008) reviewed the development ofinternational geochemical mapping to date; it is pleasing tothink that AGRG pioneered many of the methods that subse-quently became adopted.
The development and implementation of the computer-basedmethods over the years described here was enabled by many bodies.
We principally have to thank the Department of Scientific andIndustrial Research and its successor, the Natural EnvironmentResearch Council in Britain for their support to AGRG over manyyears; other contributions have come from the Anglo AmericanCorporation (South Africa) Ltd.; the Institute of GeologicalSciences/British Geological Survey; Roan Selection Trust TechnicalServices; Sierra Leone Geological Survey; Ministerio de Economia,Industria y Comercio de Costa Rica; Wolfson Foundation; and theU.S. Department of Energy, National Aeronautics and Space
Administration, and Rome Air Development Center (New York).We are grateful to them all for their assistance, whether throughresearch contracts, support for studentships, or other help. Theauthors are most grateful to the Editor, Gwendy Hall, and the
Association of Applied Geochemists for their assistance with thefunding of the colour illustrations in this paper.
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