Efficient anisotropic quasi-P wavefield extrapolation using an isotropic low-rank approximation

Zhen dong Zhang*, Yike Liu, Tariq Alkhalifah, Zedong Wu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


The computational cost of quasi-P wave extrapolation depends on the complexity of the medium, and specifically the anisotropy. Our effective-model method splits the anisotropic dispersion relation into an isotropic background and a correction factor to handle this dependency. The correction term depends on the slope (measured using the gradient) of current wavefields and the anisotropy. As a result, the computational cost is independent of the nature of anisotropy, which makes the extrapolation efficient. A dynamic implementation of this approach decomposes the original pseudo-differential operator into a Laplacian, handled using the low-rank approximation of the spectral operator, plus an angular dependent correction factor applied in the space domain to correct for anisotropy.We analyse the role played by the correction factor and propose a new spherical decomposition of the dispersion relation. The proposed method provides accurate wavefields in phase and more balanced amplitudes than a previous spherical decomposition. Also, it is free of SV-wave artefacts. Applications to a simple homogeneous transverse isotropic medium with a vertical symmetry axis (VTI) and a modified Hess VTI model demonstrate the effectiveness of the approach. The Reverse Time Migration applied to a modified BP VTI model reveals that the anisotropic migration using the proposed modelling engine performs better than an isotropic migration. The Author(s) 2017. Published by Oxford University Press. All rights reserved.

Original languageEnglish (US)
Article numberggx543
Pages (from-to)48-57
Number of pages10
JournalGeophysical Journal International
Issue number1
StatePublished - Apr 1 2018

Bibliographical note

Funding Information:
We thank Nabil Masmoudi and HuiWang for their helpful discussions, and Rene-Edouard Plessix, Samuel Gray and one anonymous reviewer for helpful reviews. We thank KAUST for its support and specifically the seismic wave analysis group members for their valuable insights. The published results are reproducible from the open source software Madagascar (www.ahay.org). The research was partly funded by the National Natural Science Foundation of China (Grant No. 41730425).


  • Numerical modelling
  • Seismic anisotropy
  • Wave propagation

ASJC Scopus subject areas

  • Geophysics
  • Geochemistry and Petrology


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