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.

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.

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.

In the last 40 years geophysicists have found that it is possible to construct images and even determine important physical characteristics of rocks that can yield information about oil and gas bearing structures in the earth. To make these images and extract this information requires the application of an advanced understanding of the mathematical physics of wave propagation. The oil and gas industry labels a major collection of the necessary seismic data processing methods by the name seismic "migration".
This text ist the first to treat many kinds of migration in a unified mahtematical way. The audience is mathematically oriented geophysicists or applied mathematicians working in the field of "inverse scattering imaging". The text can serve as a bridge between the applied math and geophysics community by presenting geophysicists with a practical introduction to advanced engineering mathematics, while presenting mathematicians with a window into the world of the mathematically sophistiated geophysicist.