A complex frequency-shifted perfectly matched layer method for particle-based seismic wave modeling in anisotropic media

The dynamic lattice model (DLM) is a particle-based approach for simulating seismic wave propagation in heterogeneous anisotropic media, notable for its intuitive physical representation. The DLM allows particles to interact micromechanically through springs, providing a unique perspective on understanding wave propagation. To reduce artificial reflections caused by truncated boundaries, incorporating an absorbing boundary condition (ABC) is crucial in seismic wave modeling. Among the various ABCs, the perfectly matched layer (PML) is a widely used and effective technique in wave-equation-based numerical methods, such as the finite difference method (FDM). While PML techniques can easily handle partial spatial derivative terms in the FDM, their application to particle-based methods is challenging due to the absence of explicit spatial derivatives in the DLM. Moreover, the PML implementation in particle-based methods often suffers from significant spurious evanescent reflections caused by near-grazing incident waves. In this study, we apply the complex frequency-shifted PML (CFS-PML) to the DLM to reduce boundary reflections for wave propagation in anisotropic media. The CFS-PML introduces two additional scaling and frequency-dependent damping factors in the stretching function to address the issues encountered with the PML. By shifting the pole to a non-zero value, these factors enable the CFS-PML to effectively absorb both traveling and evanescent waves. We divide the simulation domain into two regions: an interior domain where the DLM is used to simulate seismic waves, and an exterior PML domain where the CFS-PML is implemented by the FDM. Numerical experiments demonstrate the effectiveness of this hybrid implementation scheme and the absorption capabilities of the CFS-PML in complex anisotropic media.