A hybrid finite-difference/low-rank solution to anisotropy acoustic wave equations

Zhen Dong Zhang*, Tariq Alkhalifah, Zedong Wu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


P-wave extrapolation in anisotropic media suffers from SVwave artifacts and computational dependency on the complexity of anisotropy. The anisotropic pseudodifferential wave equation cannot be solved using an efficient time-domain finite-difference (FD) scheme directly. The wavenumber domain allows us to handle pseudodifferential operators accurately; however, it requires either smoothly varying media or more computational resources. In the limit of elliptical anisotropy, the pseudodifferential operator reduces to a conventional operator. Therefore, we have developed a hybrid-domain solution that includes a spacedomain FD solver for the elliptical anisotropic part of the anisotropic operator and a wavenumber-domain low-rank scheme to solve the pseudodifferential part. Thus, we split the original pseudodifferential operator into a second-order differentiable background and a pseudodifferential correction term. The background equation is solved using the efficient FD scheme, and the correction term is approximated by the low-rank approximation. As a result, the correction wavefield is independent of the velocity model, and, thus, it has a reduced rank compared with the full operator. The total computation cost of our method includes the cost of solving a spatial FD time-step update plus several fast Fourier transforms related to the rank. The accuracy of our method is of the order of the FD scheme. Applications to a simple homogeneous tilted transverse isotropic (TTI) medium and modified BP TTI models demonstrate the effectiveness of the approach.

Original languageEnglish (US)
Pages (from-to)T83-T91
Issue number2
StatePublished - Mar 1 2019

Bibliographical note

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© 2019 Society of Exploration Geophysicists. All rights reserved.

ASJC Scopus subject areas

  • Geochemistry and Petrology


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