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AbstractWe 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 that 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. © 2012 European Association of Geoscientists & Engineers.
CitationFomel S, Ying L, Song X (2012) Seismic wave extrapolation using lowrank symbol approximation. Geophysical Prospecting 61: 526–536. Available: http://dx.doi.org/10.1111/j.1365-2478.2012.01064.x.
SponsorsWe thank KAUST for partial financial support; Tariq Alkhalifah, Bjorn Engquist, Laurent Demanet and Paul Fowler for useful discussions; and BP for releasing benchmark synthetic models.