A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation

Zedong Wu*, Tariq Alkhalifah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media is crucial to seismic modeling, imaging and inversion. Actually, it represents the core computation cost of these highly advanced seismic processing methods. However, the conventional finite-difference method suffers from severe numerical dispersion errors and S-wave artifacts when solving the acoustic wave equation for anisotropic media. We propose a method to obtain the finite-difference coefficients by comparing its numerical dispersion with the exact form. We find the optimal finite difference coefficients that share the dispersion characteristics of the exact equation with minimal dispersion error. The method is extended to solve the acoustic wave equation in transversely isotropic (TI) media without S-wave artifacts. Numerical examples show that the method is highly accurate and efficient.

Original languageEnglish (US)
Pages (from-to)350-361
Number of pages12
JournalJournal of Computational Physics
StatePublished - Jul 15 2018

Bibliographical note

Funding Information:
We thank KAUST for its support and the SWAG group for the collaborative environment. We also thank BP for providing the benchmark dataset. The research reported in this publication is supported by funding from King Abdullah University of Science and Technology (KAUST). For computer time, this research used the resources of the Supercomputing Laboratory at King Abdullah University of Science and Technology (KAUST) in Thuwal, Saudi Arabia. We also thank the associate editor Eli Turkel and another anonymous reviewer for their fruitful suggestions and comments.

Publisher Copyright:
© 2018 Elsevier Inc.


  • Acoustic wave equation
  • Anisotropic
  • Dispersion error
  • Finite difference

ASJC Scopus subject areas

  • Computational Mathematics
  • Physics and Astronomy(all)
  • Applied Mathematics
  • Numerical Analysis
  • Computer Science Applications
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)


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