A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation
A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation
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DOI：
10.1016/j.jcp.2018.03.046
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发表时间：
2018-07
期刊：
影响因子：
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通讯作者：
Zedong Wu;T. Alkhalifah
中科院分区：
文献类型：
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作者：
Zedong Wu;T. Alkhalifah
各向同性或各向异性介质中声波方程的数值模拟是地震模拟、成像和反演的关键。实际上，它代表了这些高度先进的地震处理方法的核心计算成本。然而，传统的有限差分方法在求解各向异性介质中的声波方程时，存在严重的数值色散误差和S波伪影。我们提出了一种通过比较有限差分系数的数值色散与精确形式来获得有限差分系数的方法。在色散误差最小的情况下，找到了具有精确方程色散特性的最优有限差分系数。将该方法推广到求解横观各向同性(TI)介质中无S波伪影的声波方程。数值算例表明，该方法具有较高的精度和效率。
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.