Perfectly matched layers (PML) are a well-developed method for simulating wave propagation in unbounded media enabling the use of a reduced computational domain without having to worry about spurious boundary reflections. Using this approach, a compact three-dimensional (3D) formulation is proposed for time-domain modeling of elastic wave propagation in an unbounded general anisotropic medium. The formulation is based on a second-order approach that has the advantages of well-posedness, physical relationship to the underlying equations, and amenability to be implemented in common numerical schemes. However, many auxiliary variables are usually need to described second-order PML formulations. The problem becomes more complex for the 3D case modeling which would explain the dearth of compact second-order formulations in 3D. Using finite element method (FEM), 3D numerical results are presented to demonstrate the applicability of the formulation, including a highly anisotropic medium example.

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