Wave Equations and Wave Extrapolations in Seismic Imaging

Sergey Fomel, UT Austin
October 5th, 2011 at 4PM–5PM in 939 Evans Hall [Map]

Numerical solutions of the classic wave equation and its companion characteristic and bi-characteristic equations (the eikonal equation and ray equations) are widely used in the practice of seismic imaging. In reflection seismology, seismic data are collected on the surface in multiple experiments with moving sources and receivers. Exploring the geometrical nature of seismic wavefields and the physical connection between different experiments makes it possible to define common imaging tasks as imaginary wave propagation processes described by their own partial differential equations or pseudo-differential equations. A constructive way for defining numerical wave-extrapolation operators follows from a low-rank matrix approximation of Fourier symbols.