PML and CFS-PML boundary conditions for a mesh-free finite difference solution of the elastic wave equation

适于弹性波方程无网格有限差分数值解的PML与CFS-PML吸收边界条件（英文）

Mesh-free finite difference(FD)methods can improve the geometric flexibility of modeling without the need for lattice mapping or complex meshing process.Radial-basisfunction-generated FD is among the most commonly used mesh-free FD methods and can accurately simulate seismic wave propagation in the non-rectangular computational domain.In this paper,we propose a perfectly matched layer(PML)boundary condition for a meshfree FD solution of the elastic wave equation,which can be applied to the boundaries of the non-rectangular velocity model.The performance of the PML is,however,severely reduced for near-grazing incident waves and low-frequency waves.We thus also propose the complexfrequency-shifted PML(CFS-PML)boundary condition for a mesh-free FD solution of the elastic wave equation.For two PML boundary conditions,we derive unsplit time-domain expressions by constructing auxiliary differential equations,both of which require less memory and are easy for programming.Numerical experiments demonstrate that these two PML boundary conditions effectively eliminate artificial boundary reflections in mesh-free FD simulations.When compared with the PML boundary condition,the CFS-PML boundary condition results in better absorption for near-grazing incident waves and evanescent waves.

无网格有限差分法能有效提高数值模拟的几何灵活性,且无需网格映射或复杂的网格生成过程。RBF-FD(基于径向基函数的有限差分)是最常用的无网格有限差分法之一,可以准确模拟地震波在非矩形计算域中的传播。本文提出适于弹性波方程无网格有限差分数值解的PML(完全匹配层)吸收边界条件,可以应用于非矩形速度模型的边界。但是PML吸收边界对近掠射波、低频波的吸收效果不好。为此,我们继续提出适于弹性波方程无网格有限差分数值解的CFS-PML(复频移完全匹配层)吸收边界条件。本文所提两种边界条件均是通过构造辅助微分方程,得到不分裂时域表达式,具有存储量小、便于编程实现的特点。模拟结果表明,两种PML吸收边界条件都能有效地消除无网格有限差分数值模拟的人工边界反射。此外,本文所提CFS-PML相较PML对近掠射波和损耗波的吸收效果更好。