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Efficient Implementation of CFS-CPML in FDTD Solutions of Second-Order Seismic Wave Equations

时域有限差分法 完全匹配层 有限差分法 波传播 波动方程 计算机科学 地球物理学 物理 数学分析 数学 光学
作者
Hanming Chen,Wenze Cheng,Lingqian Wang,Hui Zhou
出处
期刊:IEEE Transactions on Geoscience and Remote Sensing [Institute of Electrical and Electronics Engineers]
卷期号:62: 1-11
标识
DOI:10.1109/tgrs.2024.3386860
摘要

The complex-frequency-shifted convolutional perfectly matched layer (CFS-CPML) has been widely used in numerical simulations of the first-order seismic wave equations to avoid artifical reflections caused by truncated boundaries. However, numerically solving the second-order seismic wave equation is preferred for some large-scale geophysical algorithms, such as reverse-time migration (RTM). Extension of CFS-CPML to the second-order seismic wave equations has been realized by using a strict derivation approach in many literatures. However, the derived CFS-CPML formulations are complex, due to introduction of a large number of intermediate variables, which decreases overall computational efficiency, visibly. We present an efficient strategy to implement CFS-CPML in finite-difference time-domain (FDTD) modeling of the second-order seismic wave equations. We do not derive any continuous CFS-CPML formulations. Instead, we split the high-order centered-grid finite-difference (CGFD) stencil applied to approximate the second-order derivatives into two-level CGFD stencils. The inner stencils are viewed as the second-order CGFD approximations of the first-order derivatives at symmetric grid points. With this viewpoint, the convolution term related to CFS-CPML can be introduced to each inner CGFD approximation, naturally. The outer CGFD stencil is also viewed as CGFD approximation of a first-order derivative and it is augmented by a convolution term as well. By this way, CFS-CPML is incorporated into the FDTD simulations, efficiently. We take three-dimensional (3D) acoustic, viscoacoustic and elastic wavefields modeling for examples to verify the feasibility of the new implementation strategy of CFS-CPML.
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