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.

For more than 80 years, the oil and gas industry has used seismic methods to construct images and determine physical characteristics of rocks that can yield information about oil and gas bearing structures in the earth. This book presents the different seismic data processing methods, also known as seismic "migration," in a unified mathematical way. The book serves as a bridge between the applied math and geophysics communities by presenting geophysicists with a practical introduction to advanced engineering mathematics, while presenting mathematicians with a window into the world of the mathematically sophisticated geophysicist.

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.