Mesh-free finite difference (FD) methods can improve the geometric flexibility of modeling without the need for lattice mapping or complex meshing process. Radial-basis-function-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 mesh-free 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 complex-frequency-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.

中文翻译：

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弹性波方程无网格有限差分解的PML和CFS-PML边界条件

无网格有限差分（FD）方法可以提高建模的几何灵活性，而无需晶格映射或复杂的网格划分过程。径向基函数生成的FD是最常用的无网格FD方法之一，它可以在非矩形计算域中准确地模拟地震波的传播。在本文中，我们为弹性波方程的无网格FD解提出了一个完美匹配层（PML）边界条件，该条件可以应用于非矩形速度模型的边界。但是，对于近掠入射波和低频波，PML的性能会大大降低。因此，我们还为弹性波方程的无网格FD解提出了复频移PML（CFS-PML）边界条件。对于两个PML边界条件，我们通过构造辅助微分方程来导出未分割的时域表达式，这两个方程都需要较少的内存并且易于编程。数值实验表明，这两个PML边界条件在无网格FD模拟中有效消除了人工边界反射。与PML边界条件相比，CFS-PML边界条件可更好地吸收近掠入射波和van逝波。