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Mathematics of multidimensional seismic imaging, migration, and inversion. (English) Zbl 0967.86001

Interdisciplinary Applied Mathematics. 13. New York, NY: Springer. xxix, 510 p. (2001).
Migration technique improves largely the imaging of geologic structures within the Earth’s subsurface. The advancement of such technologies requires an increasingly sophisticated understanding of the mathematical physics of wave propagation. This textbook of mathematical-geophysics provides a unified approach to seismic imaging, formulated as an inverse scattering problem. It will help the reader to understand the classical results of seismic migration in a way that reveals the inherent assumptions were not explicitly stated. Fourier-like inversion formulas for migration are derived with one-dimension and multi-dimensions. This textbook can be seen as a bridge between the applied mathematics and geophysics communities.

MSC:

86-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to geophysics
86A15 Seismology (including tsunami modeling), earthquakes
86A22 Inverse problems in geophysics
35P25 Scattering theory for PDEs
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