Seismic wave extrapolation using lowrank symbol approximation

Published as Geophysical Prospecting, 61, 526–53 (2013)

Seismic wave extrapolation using lowrank symbol approximation

Sergey Fomel, Lexing Ying, and Xiaolei Song
Bureau of Economic Geology,
John A. and Katherine G. Jackson School of Geosciences
The University of Texas at Austin
University Station, Box X
Austin, TX 78713-8972
USA
sergey.fomel@beg.utexas.edu
Department of Mathematics
The University of Texas at Austin
1 University Station
Austin, TX 78712
USA
lexing@math.utexas.edu

Abstract:

We consider the problem of constructing a wave extrapolation operator in a variable and possibly anisotropic medium. Our construction involves Fourier transforms in space combined with the help of a lowrank approximation of the space-wavenumber wave-propagator matrix. A lowrank approximation implies selecting a small set of representative spatial locations and a small set of representative wavenumbers. We present a mathematical derivation of this method, a description of the lowrank approximation algorithm, and numerical examples which confirm the validity of the proposed approach. Wave extrapolation using lowrank approximation can be applied to seismic imaging by reverse-time migration in 3D heterogeneous isotropic or anisotropic media.

Seismic wave extrapolation using lowrank symbol approximation