Perfectly matched layer-absorbing boundary condition for finite-element time-domain modeling of elastic wave equations

时域有限元弹性波模拟中的位移格式完全匹配层吸收边界(英文)

The perfectly matched layer （PML） is a highly efficient absorbing boundary condition used for the numerical modeling of seismic wave equation. The article focuses on the application of this technique to finite-element time-domain numerical modeling of elastic wave equation. However, the finite-element time-domain scheme is based on the second- order wave equation in displacement formulation. Thus, the first-order PML in velocity-stress formulation cannot be directly applied to this scheme. In this article, we derive the finite- element matrix equations of second-order PML in displacement formulation, and accomplish the implementation of PML in finite-element time-domain modeling of elastic wave equation. The PML has an approximate zero reflection coefficients for bulk and surface waves in the finite-element modeling of P-SV and SH wave propagation in the 2D homogeneous elastic media. The numerical experiments using a two-layer model with irregular topography validate the efficiency of PML in the modeling of seismic wave propagation in geological models with complex structures and heterogeneous media.

完全匹配层是地震波方程数值模拟中一种高效的吸收边界条件,本文目的在于将这种技术用于时域有限元弹性波数值模拟中。但时域有限元法是基于二阶位移格式的波动方程的数值模拟方法,所以一阶速度-应力格式的完全匹配层不能直接用于该数值模拟方法中。本文推导了二阶位移格式完全匹配层的有限元矩阵方程,实现了完全匹配层在时域有限元弹性波模拟中的应用。在二维均匀弹性介质P-SV波和SH波传播的有限元模拟中,完全匹配层对体波和面波具有近似零反射系数;不规则地表双层介质模型的数值实验验证了完全匹配层在复杂构造非均质地质模型中地震波传播模拟的效果。