Why another book?

I decided to write this book for five reasons. First, seismologists and explorationists, as well as many others in science and engineering, share the ability to synthesize the data implied by any physical model. They have much to learn, however, about ``inverse modeling,'' that is, given the data, the process of finding the most appropriate model. This task is also called ``model fitting,'' words that hardly hint at the ingenuity that can be brought to bear. There is no shortage of books about least-squares regression, also called ``inversion.'' These books provide a wide range of mathematical concepts--often too many, and often with no real examples. In my teaching and research I have found that people are mostly limited, not by lack of theory, but by failure to recognize where elementary theory is applicable. To cite an example, ``zero padding'' is a tiny bit of technology used nearly everywhere, but few people seem to recognize its mathematical adjoint and so are ill prepared to invoke $(\bold A'\bold A)^{-1}\bold A' \bold d$or set up a conjugate-gradient optimization. Therefore, a keystone chapter of this book shows how adjoint operators can be a simple byproduct of any modeling operator. In summary, the first reason I am writing this book is to illuminate the concept of ``adjoint operator'' by examining many examples.

The second reason for writing the book is to present the conjugate-gradient optimization algorithm in the framework of many examples. The inversion theory found in most textbooks, while appearing generally applicable, really is not. Matrix inversions and singular-value decompositions are limited in practice to matrices of dimension less than about one thousand. But practical problems come in all dimensions, from one to many millions (when the operator is a multidimensional wave equation). Conjugate-gradient methods--only beginning to find routine use in geophysics--point the way to overcoming this dimensionality problem. As in the case of inversion, many books describe the conjugate-gradient method, but the method is not an end in itself. The heart of this book is the many examples that are set up in the conjugate-gradient framework. Setting up the problems is where ingenuity is required. Solving them is almost routine--especially using the subroutine library in this book.

My third reason for writing the book is much narrower. Seismogram deconvolution--by far the largest use of geophysical inversion theory--is in a state of disarray. I see serious discrepancies between theory and practice (as do others). I believe the disarray stems from a tendency to cling to a large body of old quasi-analytic theory. This theory had a place in my first book, , but I have omitted it here. It can be replaced by a simpler and less restrictive numerical approach.

My fourth reason for writing the book is to illuminate the place of missing seismograms. Much data is analyzed assuming that missing data is equivalent to zero-valued data. I show how to handle the problem in a better way.

Finally, I am writing this book to illuminate the subtitle, Processing versus Inversion, by which I mean the conflicting approaches of practitioners and academics to earth soundings analysis.

This book should be readable by anyone with a bachelor's degree in engineering or physical science. It is easier for students to use than my first book, . It is written at about the level of my second book, .