A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation
Alkhalifah, Tariq Ali
KAUST DepartmentEarth Science and Engineering Program
Physical Science and Engineering (PSE) Division
Seismic Wave Analysis Group
Online Publication Date2018-04-05
Print Publication Date2018-07
Permanent link to this recordhttp://hdl.handle.net/10754/627484
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AbstractNumerical 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 is highly accurate and efficient.
CitationWu Z, Alkhalifah T (2018) A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation. Journal of Computational Physics 365: 350–361. Available: http://dx.doi.org/10.1016/j.jcp.2018.03.046.
SponsorsWe 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.
JournalJournal of Computational Physics