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 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.
|Original language||English (US)|
|Number of pages||11|
|State||Published - Apr 30 2012|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: We 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.