Description

Handbook of Exploration Geochemistry
VOLUME 2
Statistics and Data Analysis
in Geochemical Prospecting
Edited by
R.J. HOWARTH
Reader in Mathematical Geology,
Department of Geology,
Imperial College of Science and Technology, London, U.K.
ELSEVIER SCIENTIFIC PUBLISHING COMPANY
Amsterdam - Oxford - New York '1983

EDITOR'S FOREWORD
The objective of the Handbook of Exploration Geochemistry series is to
present specific aspects of exploration geochemistry in separate volumes in a
form that will be immediately useful to the field geologist practising geochemistry
and, at the same time, to provide a comprehensive review of the
subject that will be a source of reference for research workers. Other titles in
the series presently being prepared are: Rock Geochemistry in Mineral
Exploration; Drainage Geochemistry in Mineral Exploration; Soil Geochemistry
in Mineral Exploration; Biogeochemistry and Geobotany in
Mineral Exploration; and Volatile Elements in Mineral Exploration.
In the editor's foreword to the first volume of the Handbook of Exploration
Geochemistry - Analytical Methods in Geochemical Prospecting - I
stated that the greatest impetus for the progress of exploration geochemistry
had come from the contemporaneous development of rapid, cheap, and
reliable multi-element analytical techniques, coupled with the ready availability
of computers to handle the vastly increased flow of analytical data.
This, the second volume in the series, is devoted entirely to exploration
geochemical data processing and interpretation.
The processing and the interpretation of geochemical data is one of the
most difficult - and one of the most important - stages in the successful
application of exploration geochemistry. Although there are a bewildering
variety of statistical texts that catalogue a vast range of data treatment
techniques, the non-specialist is faced with making a decision concerning
which procedures are appropriate to an individual geochemical problem.
Furthermore, specific geochemical papers in various journals often assume
specialist knowledge, and detailed explanations of actual procedures are
limited. This volume - the only English language book specifically dealing
with exploration geochemical data processing and interpretation - is
intended to overcome these problems. I am pleased that Dr. Richard
Howarth agreed to undertake the rather awesome task of producing this
book, and I am delighted with his success in bringing together so many wellknown
experts in the field.
Adequate space is provided in this volume to digress upon procedures. The
chapters are necessarily of varying degrees of mathematical difficulty, but

VI
the book as a whole should be comprehensible to the modestly numerate
geologist. The step-by-step approach adopted in many chapters, with
extensive illustrations of the effects of various statistical treatments of data,
should allow the exploration geologist to choose an appropriate technique
for most situations.
The organization in Part I takes the reader logically and sequentially
through the normal data handling procedures - from data storage and
retrieval, through control procedures in analysis, univariate analysis, sampling
procedures, and mapping techniques - to the most complicated aspects
of multivariate analysis. Part II consists of reviews of specific techniques and
procedures currently used in various parts of the world. The use of the
computer, an essential practical aid to large data sets and complex statistical
manipulations, is described in detail, but simpler techniques are also
discussed. The graphical aids in the Appendix are unique.
Far too little attention has been devoted in the past to the interpretation
of the geochemical data produced during exploration surveys. This book
should overcome one of the major reasons for this deficiency - the geologist's
lack of the requisite knowledge to use the data. Its pUblication at a
time when microcomputers are becoming widely available should result in a
major increase in the scope and success of geochemical data interpretation,
hopefully with a consequent increase in the discovery rate of mineral
deposits through the use of exploration geochemistry.
G. J. S. GOVETT
Sydney, N.S.W., Australia

CONTENTS
Editor's Foreword . ............. , ........ ~ . . . . . . . . . . . . . . . . . . . . V
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. VII
List of Contributors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX
PART 1. TECHNIQUES OF GEOCHEMICAL DATA PROCESSING AND
INTERPRETATION
Chapter 1. Data storage and retrieval. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 .
T. Mattiske
Introduction. . . . . . . . . . . . . . . . " . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Data storage and retrieval systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Data storage media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Punched cards. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Magnetic tape. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Disk and drum (mass or random access storage). . . . . . . . . . . . . . . . . . . . . . . 8
Mixed media. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Types of data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 10
Regional reconnaissance data . ....................... , . . . . . . . . .. 10
Local data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 11
Geological data. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .. 11
Data.organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12
Record types . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13
Data files. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 14
Sequential files. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 15
Direct or random access files. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 15
Indexed sequential files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 16
Inverted files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 17
Multiple-index files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 19
Structure of a data storage and retrieval system. . . . . . . . . . . . . . . . . . . . . . . .. 19
Data input and validation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 19
Data storage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 21
Data retrieval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 22
Programming considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 24
Programming languages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 24
Aspects of processing and programming. . . . . . . . . . . . . . . . . . . . . . . . . . .. 25
Generalized databa&e systems ... ...................... -. . . . . . . . . . .. 29
Elements of a database system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 29
The choice of a database package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 31
Database sytem examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 32

XIV
Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 37
Chapter 2. Control procedures in geochemical analysis . . . . . . . . . . . . . . . . . .. 39
M. Thompson
Introduction. • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Geochemical analysis and data quality. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 39
The statistical basis of analytical quality control. . . . . . . . . . . . . . . . . . . . . . . . 41
Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Deviations from the Normal distribution. . . . . . . . . . . . . . . . . . . . . . . . . .. 44
Variations of accuracy and precision. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 46
Laboratory control procedures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 48
Factors that need to be controlled .............................. 48
Control methods that utilize standards . . . . . . . . . . . . . . . . . . . . . . . . . . .. 50
The "statistical series" method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 52
A scheme for the use of standards. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 53
Methods that do not require special standards. . . . . . . . . . . . . . . . . . . . . . .. 54
Special problems in multi-element analysis. . . . . . . . . . . . . . . . . . . . . . . . .. 57
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 58
Chapter 3. Univariate analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 59
A. J. Sinclair
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 59
Central tendency and dispersion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 59
Histograms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 61
Density distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 62
Fitting a Normal distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 65
Confidence limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 66
Chi-square (X 2 ) goodness-of-fit test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 66
F- and t-tests. __ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 68
Analysis of variance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 69
Fixed analysis of variance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 69
Random analysis of variance (with hierarchical levels of variation) . . . . . . . . .. 71
Group separation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 74
Probability graphs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 75
References ............... : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 80
Chapter 4. Sampling methodology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 83
R. G. Garrett
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 83
Target and sampled populations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 83
Aims of the sampling programme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 84
Covariance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 85
Search techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 88
Grid search. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 88
Random stratified search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 89
Analysis of variance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 92
Balanced sampling designs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 93
Unbalanced sampling designs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 94
Computational methods for analysis of variance . . . . . . . . . . . . . . . . . . . . .. 95

xv
Strategies for optimum sampling design. . . . . . . . . . , . . . . . . . . . . . . . . . . . .. 100
Pseudo-stratified random sampling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 102
Map reliability factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 102
Number of samples required for anomaly detection. . . . . . . . . . . . . . . . . . .. 104
Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 105
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 107
Chapter 5. Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 111
R. J. Howarth
Introduction .............................................. " 111
Types of map ............................................. " 112
Class selection techniques ..................................... " 113
Externally controlled classes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 114
Data-specific classes ....................................... " 114
Serial classes ............................................ " 115
Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 119
Point-symbol maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 124
Contour maps ............................................. " 127
Trend surface analysis ..................................... " 130
Locally-fitted surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 135
Zone partitioning methods ............................. ' ..... " 136
Gridding methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . . .. 136
Three-dimensional views. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 167
Map filtering techniques ...................................... " 169
Low-pass filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 171
High-pass filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 174
Picture frame filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 175
Kolmogorov-Smirnov filter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 175
Comparison of filters ...................................... " 176
Example applications ...................................... " 178
Discussion ............................................. " 185
Cross-correlation maps ....................................... " 187
Multi-element maps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 190
Pie diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 191
Proportional line symbols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 192
Triangular diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 194
Colour theory ........................................... " 196
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 200
Chapter 6. Multivariate analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 207
R. J. Howarth and R. Binding-Larsen
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . •. 207
Case study data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 209
Cluster analysis. . . . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . .. 214
Partitioning into k groups ..................................... ' 218
Hierarchical clustering ....................................... ·220
Non-linear mapping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 222
Goodness of clusters ....................................... , 225
Correlation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 228
Principal components and factor analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 232
Principal components analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 234

XVI
Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 243
Factor analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . '. . . . . . . . . . . . . . . .. 245
Biplotting methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 250
Q-mode factor analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 253
Partial correlation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 254
Regression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 255
Canonical correlation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 271
Discriminant analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 276
Sources of programs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 283
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 283
PART II. A SELECTION OF GEOCHEMICAL DATA PROCESSING AND
INTERPRETATION METHODS IN USE IN VARIOUS PARTS OF THE
WORLD
Chapter 7. Regression analysis applied to interpretation of geochemical data at the
Geological Survey of Sweden. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 293
O. Selenius
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 293
Method ................................................... 293
Resulls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 294
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 301
Chapter 8. Use of pattern classification methods in till geochemistry . . . . . . . . .. 303
N. Gustavsson
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 303
Description of the problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 303
Choice of method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 304
Graphical methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 306
Example ............................................... : .. 308
Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 308
Acknowledgements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 309
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 309
Chapter 9. Geochemical characterization of tin granites in northern Thailand . . .. 311
S. Rehder and G. van den Boom
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 311
Selection of useful elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 311
The classification problem ..... ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 314
Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 314
Empirical discriminant analysis: PATREC1 ......................... 315
Determination of an optimal sampling design . . . . . . . . . . . . . . . . . . . . . . . . .. 317
The model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 317
Algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 319
Target map calculation in practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 321
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 322
Chapter 10. Statistical models for geochemical anomalies . ................. '- 325
R. I. Dubov
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 325

XVII
Types of models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 325
The simplest models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 325
Classification models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 325
Regression models ......................................... , 327
Rank approximation: basis of the method. . . . . . . . . . . . . . . . . . . . . . . . . . .. 329
Approximation of statistical distributions . . . . . . . . . . . . . . . . . . . . . . . . . . .. 332
Multi-dimensional regression analysis ............................... , 335
Additional remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 338
Conclusions ............................................... , 338
Acknowledgements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 338
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 339
Chapter 11. Mathematical and statistical activity in North America. . . . . . . . . . .. 341
R. J. Garrett
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 341
Data management. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 342
Search theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 342
Sampling and analytical variability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 342
Univariate statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ., 343
Distribution types. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 344
Background and threshold. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 344
Surface fitting .............................................. , 344
Multivariate analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 345
Regression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 345
Factor and principal components analysis . . . . . . . . . . . . . . . . . . . . . . . . .. 346
Cluster analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ., 347
Discriminant analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 348
Deterministic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 348
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ., 348
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 350
Chapter 12. Geochemical data processing in Western Europe. . . . . . . . . . . . . . .. 361
P. Le¥marie
Review. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 361
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 365
Chapter 13. Examples of geochemical data processing in Africa. . . . . . . . . . . . .. 369
K. A. Viewing
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . .. 369
Data processing and the interpretation of geochemical soil sampling results . . . . .. 375
Multi .. lement high·density drainage sampling. . . . . . . . . . . . . . . . . . . . . . . . .. 376
Multi-element drainage reconnaissance on a regional scale. . . . . . . . . . . • . . . . .. 378
Processing and interpretation of airborne geochemical survey data ........... , 383
Acknowledgements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 384
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 385
Chapter 14. Geochemical data processing in Eastern Europe. . . . . . . . . . . . . . .. 387
V. Nemec
Review ..............................................•.. '.' 387

XVIII
Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 388
Appendix. Graphical aids for some statistical tests. . . . . . . . . . . . . . . . . . . . . .. 393
R. J. Howarth
Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 393
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 401
References Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 403
Subject Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 417