An efficient Helmholtz solver for acoustic transversely isotropic media

Zedong Wu, Tariq Alkhalifah

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


The acoustic approximation, even for anisotropic media, is widely used in current industry imaging and inversion algorithms mainly because P-waves constitute most of the energy recorded in seismic exploration. The resulting acoustic formulas tend to be simpler, resulting in more efficient implementations, and they depend on fewer medium parameters. However, conventional solutions of the acoustic-wave equation with higher-order derivatives suffer from S-wave artifacts. Thus, we separate the quasi-P-wave propagation in anisotropic media into the elliptic anisotropic operator (free of the artifacts) and the nonelliptic anisotropic components, which form a pseudodifferential operator. We then develop a separable approximation of the dispersion relation of nonelliptic-anisotropic components, specifically for transversely isotropic media. Finally, we iteratively solve the simpler lower-order elliptical wave equation for a modified source function that includes the nonelliptical terms represented in the Fourier domain. A frequency-domain Helmholtz formulation of the approach renders the iterative implementation efficient because the cost is dominated by the lower-upper decomposition of the impedance matrix for the simpler elliptical anisotropic model. In addition, the resulting wavefield is free of S-wave artifacts and has a balanced amplitude. Numerical examples indicate that the method is reasonably accurate and efficient.

Original languageEnglish (US)
Pages (from-to)C75-C83
Issue number2
StatePublished - Mar 1 2018

Bibliographical note

Publisher Copyright:
© 2018 Society of Exploration Geophysicists.


  • Acoustic
  • Anisotropy
  • Fourier
  • Vti
  • Wave propagation

ASJC Scopus subject areas

  • Geochemistry and Petrology


Dive into the research topics of 'An efficient Helmholtz solver for acoustic transversely isotropic media'. Together they form a unique fingerprint.

Cite this