β Scribed by G.S. Watson
No coin nor oath required. For personal study only.
Dr. Agterburg won his Dutch Ph.D. studying the structural geology of the Dolomites but since 1962 he has been with the Geological Survey of Canada where he now heads the Geomathematics Section. This book is essentially a text book on statistics for Geologists, preceded by a 115 page review of caIculus and matrix algebra. The calculus will be familiar to all engineers but the matrix algebra may not be except perhaps in its three dimensional form used sometimes for elasticity theory.
This reviewer is a statistician who has, on occasion, helped geologists and geophysicists. The articles in this Journal seem to make surprizingly little use of statistics. Surprizingly, since so many of the topics discussed use physical methods on very variable material. Thus measurements must surely be discussed statistically. Further it would seem that probabilitistic (or statistical) models might be better descriptions of the phenomena of interest than deterministic ones. If any reader cares to take up this challenge, Agterburg's book is a good way to start.
Chapter 1 is a brief comment on models in Geology, and Chapters 2, 3,4 the mathematical review. Chapters 6, 7, 8 give a 130 page introduction to probability theory and statistics. Chapters 9 to 14 apply these ideas to various types of statistical problems, as does Chapter 5 in a slightly different way. The book is very difficult for a statistician to read because it is illustrated at every point by geological applications that are non-trivial. While it is possible for statisticians to point out very minor blemishes, the treatment is really very solid and sensible. Many references are given to both the theoretical bases and the practical applications.
No doubt the best way to provoke engineering geologists to look at this book would be to give an example of its use here. Failing that one might mention the sorts of problems dealt with. Chapter 5 discusses methods for exploring the relationships between a number of variables when little is known theoretically.
Chapter 9 is the classical approach (trend analysis) to describing the variation of some quantity in space by fitting functions, usually polynomials. This is a standard problem in economic geology. Chapter 10 is another, and more general, approach to the same problem which has been developed at the Paris School of Mines by Matheron and his colleagues. It rests on the idea of a random function. To describe such functions, one needs to know, or to estimate, their autocovariance function. These ideas are well known to electrical engineers who, however, usually think in terms of the frequency content of the signal and its power spectrum This is discussed in Chapter 11. It is easier this way to understand the effect of smoothing data to get interpolated or predicted values. Chapter 12 gives
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