Geophysical Inverse Theory

In many physical sciences, the most natural description of a system is with a function of position or time. In principle, infinitely many numbers are needed to specify that function, but in practice only finitely many measurements can be made. Inverse theory concerns the mathematical techniques that enable researchers to use the available information to build a model of the unknown system or to determine its essential properties. In Geophysical Inverse Theory, Robert Parker provides a systematic development of inverse theory at the graduate and professional level that emphasizes a rigorous yet practical solution of inverse problems, with examples from experimental observations in geomagnetism, seismology, gravity, electromagnetic sounding, and interpolation. Although illustrated with examples from geophysics, this book has broad implications for researchers in applied disciplines from materials science and engineering to astrophysics, oceanography, and meteorology.

Parker's approach is to avoid artificial statistical constructs and to emphasize instead the reasonable assumptions researchers must make to reduce the ambiguity that inevitably arises in complex problems. The structure of the book follows a natural division in the subject into linear theory, in which the measured quantities are linear functionals of the unknown models, and nonlinear theory, which covers all other systems but is not nearly so well understood. The book covers model selection as well as techniques for drawing firm conclusions about the earth independent of any particular model.

Students in my class found the presentation too theoretical, and couldn't relate the material in the book to their own research projects. In particular, many of them found that the book made use of too much advanced mathematics without adequate explanation. Many of the exercises in the book are extremely challenging, but there aren't enough relatively simple exercises to help students build confidence in their understanding of the material. In order to be prepared for this text, students need to have a strong background in linear algebra, numerical computing, and some understanding of basic ideas in functional analysis.

On the other hand, I've found this book to be a useful reference in my own research.


Delightful mix of theory and practice   October 28, 1999
 6 out of 8 found this review helpful

This book presents inverse theory in gradual steps with practical problems presented at each level. Chapter 1 provides a good theoretical basis for what follows so that the book is (reasonably) self-contained.

What I like most is the way the author reaches into the heart of the problem at each level before going into the nitty gritty math (which is well presented too). The philosophical discussions (especially in chapter 4) are particularly enjoyable.