This textbook is a pleasant surprise. It is an excellent introduction to multivariate analysis, much better than I have encountered elsewhere. As the title indicates, the examples are geological such as analysis of spatial distribution of geological features, geochemical analysis, sediment transportation problems, paleontological sampling issues, stratigraphic sequence comparisons, fluvial pattern analysis, etc.Davis provides a chapter on matrix algebra, emphasizing the mathematical operations that underlie trend surface analysis, principal components, and discriminant functions. I found his geometric approach to eigenvalues and eigenvectors to be more intuitive than traditional algebraic approaches found in most linear algebra texts. I also like the discussion on determinants. I suspect that a reader unfamiliar with matrices and linear algebra might find this introduction to be too concise and a bit overwhelming. But as a review, the chapter was really quite good.
More than 350 pages are devoted to the final three chapters - Analysis of Sequence Maps, Map Analysis, and Analysis of Multivariate Data. These three chapters provide an exceptional discussion of advanced statistical techniques. The mathematics are well explained and the techniques are described in detail, including pitfalls in the mis-application of the various statistical methods.
My copy (14th printing, first edition) includes a section on Fortran IV programming and scatters some Fortran examples across various chapters. While this feature somewhat dates the text, it is at most a distraction and can easily be skipped without any loss of understanding of the statistical methods. The Fortran sections may not have been retained in the second edition (1986). This newer edition apparently provides updated coverage on probability, non-parametric statistics, and Fourier analysis and adds coverage of kriging methods.
In recent years more books on geostatistics have appeared and some are quite good. However, I have noted that the Davis text is invariably included on a short reading list for graduate geostatistics courses. My only concern is that this text has become increasingly difficult to locate. I give it five stars.
