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

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

Zedong Wu and Tariq Alkhalifah ,"A highly accurate finite difference method with minimum dispersion error for Helmholtz equation", Journal Of Computational Physics 365 (2017): 350-361. doi: 10.1016/j.jcp.2018.03.046
Zedong Wu, Tariq Alkhalifah
Acoustic wave equation, Anisotropic, Finite difference, Dispersion error
2018
​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.​
0021-9991