Mathematics of Multidimensional Seismic Imaging, Migration, and Inversion

In the past 40 years geophysicists have discovered that they can construct images and even determine important physical characteristics of rocks that can yield information about oil and gas bearing structures in the earth. Doing this requires the application of advanced understanding of the mathematical physics of wave propagation. This collection of the necessary seismic data processing methods has been dubbed seismic "migration". This text ist the first to treat the many kinds of "migration" in a unified mathematical way. It serves as a bridge between the applied math and geophysics communities.

From the reviews:

PURE APPLIED GEOPHYSICS

"The presentation is exceptionally good, with a systematic progression from simpler to more sophisticated problems. This is very helpful to those readers not familiar with the subjectEvery seismological term and every necessary mathematical concept is explained so that the book is actually self-containedThe mathematics arekept are at a sufficiently low level of mathematical sophistication to make the book easy for its intended readershipAnother advantage of the book is a careful choice of the variablesExercises stimulate the reader's initiative and inquisitiveness. This is rather unusual in geophysical literatureEven for seasoned seismologists the book will provide an incentive to upgrade their know-how."

Inhalt
Preface.- Multi-Dimensional Seismic Inversion.- The One- Dimensional Inverse Problem.- Inversion in Higher Dimensions.- Large-Wavenumber Fourier Imaging.- Inversion in Heterogeneous Media.- Two-and-One Half Dimensional Inversion.- The General Theory of Data Mapping.- Distribution Theory.- The Fourier Transform of Causal Functions.- Dimensional vs. Dimensionless Variables.- An Example of Ill-Posedness.-An Elementary Introduction to Ray Theory.- Author Index.- Subject Index.