Mathematical Geology, Vol. 8, No. 5, 1976

Renews Ratio Correlation by Felix Chayes The University of Chicago Press, Chicago and London, 1971, 99 p. This book is for those who are interested in correlating ratios of the type that arise for instance in modal analysis of rock samples. It is intended as a text for students of petrology and geochemistry, not as a work of reference. In the words of the author, "a working knowledge of elementary statistics, a good background in petrography, and an acute interest in ratio correlations" are presumed. The statistical methods are mainly based on large sample approximations. The mathematics is simple algebra with occasional recourse to matrix notation. Chapter 1 contains an introductory discussion of ratios in petrography and sets out in its simplest form the large sample approximation to the sampling behavior of a ratio of two quantities, both of which are subject to sampling error. The next two chapters contain applications of this approximation, for instance, to the derivation of estimates of correlations between ratios containing common elements. In Chapter 4, an expression for the correlation between two ratios is derived in terms of the parameters of a hypothetical set of quantities from which the ratios are conceived of as being formed. These latter quantities are defined to have zero covariances, and the expected value of the ratio correlation thus derived is termed the closure correlation. The remainder of the book, apart from Chapter 7 on regression, is concerned with the application of closure correlations to the testing of hypotheses about the nonexistence of correlation other than that due to closure, and with problems arising in the estimation of closure correlations. Some examples with real data are discussed in the text and many exercises are incorporated. A list of 32 references is given; there is no index. The book is clearly written and seems to me to be a useful contribution to the methodology of a rather difficult subject. The writer is clearly aware of the weak points of some of his treatment. For instance, the variances of the set of hypothetical quantities referred to previously have to be estimated from those of the ratios actually observed. In the data sets given in the book, 589 © 1976 Plenum Publishing Corporation, 227 West 17th Street, N e w York, N . Y . 10011. N o part o f this publication m a y be reproduced, stored in a retrieval system, o r transmitted, in any form o r by any means, electronic, mechanical, photocopying, microfilming, recording, o r otherwise, without written permission o f the publisher.

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the sample sizes are 15 (page 50) and 12 (page 56). With samples of this size, sampling errors may indeed be large, and the writer recognizes this as a possible source of trouble. I would like to have seen more discussion of the sampling contexts in which the problem of closure correlation arises. In modal analysis, the estimated proportions must sum to unity, but in chemical determinations of proportions by weight, the errors of analysis may not perhaps always be insignificant, calling in question the magnitude of the closure effect. On page 54, it is stated that it has been determined that Fisher's z transformation of the sample correlation coefficient yields a statistic the distribution of which "may be little affected by rather considerable departures from normality." A reference to the work in question would have been useful here, because its validity is central to the significance testing and interval estimation about which much of the book is concerned. For example I was doubtful about the use of confidence intervals based on bivariate normality with the skewed data of Table 2.5, page 23, though the warning given by the author at this point about the effect of sample size was relevant. The few textual errors found were the following. (1) In formula (2.1), page 11, the signs of the terms in the denominator containing a correlation coefficient should be negative. The correct form is used in deriving formula (2.15) on page 21. (2) In Table 2.3, page 18, the heading should refer to percentages, not proportions. (3) In line 6, page 77, Ni should read NI. R. H. Wimble

Statistics Department Rothamsted Experimental Station Harpenden ( UK) Geophysical Computer Programs edited by A. J. Rudman and R. F. Blakely Indiana Department of Natural Resources, Geological Survey Occasional Paper Series. The Indiana Geological Survey, Occasional Paper Series now includes Geophysical Computer Programs, a new and welcome addition to the growing array of practical geomathematical publications. Albert Rudman, associate professor of geophysics at Indiana University and Robert Blakely, geophysicist with the Indiana Geological Survey and associate professor in geology at Indiana University, are the editors. The stated purpose is to make readily

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available those programs that deal with established geophysical computations that are of interest to individual researchers and small establishments that do not have access to extensive program libraries. The $l.00 price of the initial program is right and the format is intentionally simple to encourage publication. If the initial contribution, " F O R T R A N Program for the Upward and Downward Continuation and Derivatives of Potential Fields" by the series editors, is indicative of things to come, they will be well received by both geologists and geophysicists. The approach is straightforward and understandable. The program is remarkably free of the fancy computational tricks that are so often machine dependent and difficult to decipher. Coefficients for the desired operation are read in from cards, the new map calculated and printed. Although changes could be incorporated to increase efficiency, the casual user could simply take the program, add his own JCL and expect it to run. IBM users also will have to change a few format statements. It is a ready-to-go program with sufficient comments for clarity of all operations. Publication format is familiar. There is an introduction, discussion of principles with references, program listing with coefficient tables, a test case, and examples of output. An estimate of running time is included. Future issues will present programs for the calculation of magnetic and gravity fields over both two- and three-dimensional bodies, depths to refraction seismic layers, and convolution filtering. Cross-correlation programs also are proposed and hopefully the editors will include their work on correlation of well logs. Also, the Indiana Survey will assume responsibility for the distribution of programs on cards or on furnished tapes. This is an excellent start on a new series and subsequent papers are eagerly awaited. J. E. Robinson Union Oil Co. of Canada Calgary, Alberta (Canada)

Compaction of Coarse-Grained Sediments, I edited by G. V. Chilingarian and K. H. Wolf Developments in Sedimentology, 18A: 1975, Elsevier, Amsterdam, 552 p., $54.25 (US). This volume, edited by the above two authors, but composed of contributions from other authors as well, to whit: D. R. Allen, A. H. Coogan, R. W. Manus, H. J. Bissell, L. F. Brown, O. G. Ingles, K. Grant, R. Raghaven, and F. G.

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Miller, comprises 8 chapters and an appendix, in addition to the literature references and an index. The introduction presents detailed definitions of the concepts used in the analysis of coarse-grained sediments, including an account of the statistical methods generally employed. Although well-established by usage, I cannot but utter, once again, my concern over the wide application of triangular classificationary diagrams, bearing in mind their statistical weaknesses. Such charts are clearly the outcome of a real need in the sedimentological world and one cannot help wondering whether the time is not ripe for a serious geomathematical assault on the problem. Rather suprisingly, the fundamental works of Matheron, Serra, and also Marsal seem to have been missed in this chapter, which takes up the subject of permeability and porosity in some detail. The second chapter is devoted to the mechanics of sand compaction. Experimental methods are described and the results discussed. Chapter 3 takes up the same subject for carbonate sands with the inclusion of information essential to the interpretation of the special nature of this type of sediment. Subsidence forms the topic of chapter 4. Partly historical, the subject is developed with reference to certain basins. There are no geomathematical parts in this chapter. Chapter 5 is concerned with the role of the compaction of sediments in determining the distributional geometry of fluvial and deltaic rocks, illustrated with reference to Carboniferous and Permian sequences of northcentral Texas. This chapter is purely descriptive. Chapter 6 is about the effect of compaction on various properties of coarse-grained sediments. Again, this is largely descriptive, although a few formulae occur in the text. In Chapter 7, the identification of sediments from well logs is studied. This chapter is introduced by means of a general account of the terminology of well logging. Chapter 8, on the mathematical analysis of sand compaction, is the one most likely to interest the readers of this journal. There is a general introduction to the field, followed by the basic concepts of the compaction process. Terzaghi's compaction model is presented in detail after which the subject of the compressibility of porous media is reviewed. Other topics taken up are the compaction and rebound of unidimensional porous columns, tridimensional deformation of porous media and developments, to mention a few of the main themes. The approach is in deterministic terms. Throughout this undoubtedly useful book, applications to the petroleum industry are kept well in mind. R. A. Reyment

Paleontologic Institute University of Uppsala Uppsala (Sweden)

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An Introduction to Bayesian Statistical Decision Processes

by Bruce W. Morgan Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1968, 116 p., not in print. Introduction to Bayesian Inference and Decision

by Robert L. Winkler Holt, Rinehart and Winston, Inc., New York, 1972, 563 p., $12.95 (US). It is a rarity indeed to find Bayesian applications in geomathematics, and the few that exist are mostly economics oriented. Almost all the statistical concepts and tools hitherto used in geomathematics have been borrowed from classical statistics where sample evidence plays a preeminent role in inferential procedures and decision processes. It can be argued that this state of affairs reflects mainly the statistical training of most quantitatively oriented geologists rather than the philosophical objections that geologists may raise in connection with the Bayesian approach. The Bayesian statistics allows an opportunity to combine, in a formal manner, past experience with the newly gained sample information. Furthermore, and perhaps more importantly, uncertainty about the past experience can be expressed in the form of personal or subjective probabilities. To many geologists such an approach, it seems, would have great appeal. An Introduction to Bayesian Statistical Decision Processes gives a brief and simple summary of the Bayesian statistics. The title would have been more appropriate if it had included a reference to the fact that the subject matter is discussed in the context of business problems. The book is written in a nontechnical language, with a bare minimum of mathematics. The emphasis in the book is on the structure and conceptual basis of the Bayesian analysis rather than on the precise techniques involved. The topics covered include Bayesian inference and decision in the context of binomial, rectangular, and normal distributions, and "preposterior analysis," whereby the value of additional information and the optimum sample size are assessed before sampling, both in the case of single-stage sampling and sequential sampling. In keeping with the main objective of the book, many subjects that have a direct bearing on applications have been left out of the discussions. The author has presumed that the reader has little or no statistical background. The book suffers from organizational weakness. Basic probability theory is dispersed throughout a large section of the book whereas its proper place would have been in an introductory chapter at the beginning. No clear distinction is made in the structure of the book between inference and decision making, which may well have been kept separate. More generally, some

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topics are in unexpected places in the book, and as a result the reader is sometimes lost as to which subject he is following. Also, the book's didactic value would have greatly increased if it had contained illustrations on probability distributions and utility functions. For the reader who would like to have a mere synoptic view of the Bayesian analysis, this book would be no disappointment. The reader whose interest goes deeper, however, would do well to save his money for a more advanced book. Introduction to Bayesian Inference and Decision is such an advanced introductory book. It is well written, well organized, with a proper balance between the concepts and methodology. The Bayesian approach is treated in a logical sequence, starting with basic probability concepts, then proceeding to inferential procedures and decision processes, and finally concluding with an overview. Early in the book a distinction is made between the subjective and frequency interpretations of probability, and procedures are described formally defining subjective probability. The Bayesian inference for discrete and continuous probability models is first discussed in general framework, next followed by a discussion of special situations where the data-generating (sampling) process is of the Bernoulli, the normal, and the Poisson type, or where the prior distribution is diffuse. Decision theory is developed in moderate detail, and the various inputs to the decision-making problem are elucidated with extensive examples. An entire chapter is devoted to preposterior analysis, which should be of great interest to any cost-conscious researcher engaged in statistical sampling. The book ends with a discussion of the relationship between "classical" inference, Bayesian inference, and decision theory; this concluding chapter is highly illuminating and thought-provoking. The book contains many examples and illustrations, a rich bibliography, and a large number of exercises. Certain statistical tables that are relevant to Bayesian statistics are included at the end of the book. The requisite mathematics is college algebra, though a knowledge of calculus would be a definite advantage. The book is self-contained, and does not presume a prior statistical background on the part of the reader. It is difficult to find faults with this book. It is highly recommended as an introduction to Bayesian statistics for teachers, students, and researchers alike. F. Demirmen Shell International The Hague (Netherlands)

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A Decade of Digital Computing in the Mineral Industry

edited by Alfred Weiss Am. Inst. of Min., Metall., and Petr. Engineers, Inc., New York, New York, published 1969, reprinted 1971, 952 p. Order from: Society of Mining Engineers, P.O. Box 8800, 540 Arapeen Dr., Salt Lake City, Utah 84108; $23.00 (US). This remarkable 952-page publication on the state-of-the-art was put together in just 10 months by the editor and his helpers. The short time was achieved by directly offsetting typewriter-prepared manuscripts. This publication technique has the advantages of quickness and economy, but lacks the polish of a volume of well-edited, typeset papers. Although some of the papers are rough in places, the advantages of such a production greatly outweigh the disadvantages. The symposium was the 8th in a series sponsored by the University of Arizona, Stanford University, Colorado School of Mines, and Pennsylvania State University (the consortium is now known as APCOM). This meeting was held in Salt Lake City, Utah on 17-19 September 1969, under the sponsorship of the Society of Mining Engineers of AIME. Forty-seven papers by authors from 14 countries are presented in seven sections. The subjects of the different sections are: 1. Computer applications in exploration 2. Computer applications in property appraisal and investment decisions 3. Data storage and retrieval 4. Computer applications in mining 5. Computer applications in pyrometallurgical processes: the state-of the-art 6. Analysis and simulation of concentrating operations 7. Developing on-line process control--state-of-the-art in data automation, computer procedures, and on-line computer control Each section is prefaced by "an introduction, thus providing the reader with an in-depth review of the state-of-the-art and establishing cohesiveness within the respective application areas. These 'Introductory Reviews' also contain bibliographies of references to acknowledge other important workers within the subject specialities who were unable to participate." Most of the papers of interest to quantitative geologists are in sections 1 and 3 and to some extent in section 2. Papers in section 1 on exploration, following an introduction by D. T. O'Brian, are:

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"Computer graphics," L. M. Kaas "Time sharing," M. O. Halverson "Analysis of solutions," J. R. Sturgul "Financial analysis," D. T. O'Brian "Extension variance," M. David "Mineral potential appraisal," D. P. Harris P. 1. Eimon and D. B. Morris introduce section 3 on data storage and retrieval which includes the following papers: "Geological information," C. J. Dixon "GIPSY," J. W. Sweeney, C. H. Addison, and R. W. Shields "Information center," J. J. Lloyd "Geological data," S. C. Robinson "Earth science information," R. E. O'Dette and J. T. Dichman Readers may find individual papers in other sections of interest also. One of the interesting items is the large number of people from industry who participated in the symposium. The proceedings include a glossary of computer terms, a reference and general index, and an appendix of abstracts of papers not submitted in time for inclusion in the publication. Although it is almost time for a similar symposium on the decade of the 70's, this publication contains much of interest today. Those who like sets of publications will want it for completeness, others will want it for historical reasons, and some will find it valuable for the scientific content even though much has developed on the subject since 1969. D. F. Merriam

Department of Geology Syracuse University Syracuse, New York (USA)