Efficient Perfectly Matched Layer Implementation for Seismic-Wave Modeling in 3D Spherical Coordinate Sections

Abstract Perfectly matched layer (PML) has been successfully used in various wave propagation simulations in the Cartesian coordinate. But in cylindrical or spherical coordinates, the wave equations contain trigonometric terms, which make the PML equations derived by the complex stretching of the coordinate axes hard to transform back to the time domain for numerical solving. To use PML in 3D spherical sections for regional-scale seismic-wave simulation, we propose a trivial implementation of the PML in the spherical coordinate by implementing PML in a local Cartesian coordinate. The variables and spatial derivatives in the PML equations are directly expressed by the counterparts in the spherical coordinate, thus no interpolation or coordinate rotation is required during the time marching. Numerical simulations using a layered model and a slab model show that the proposed spherical-Cartesian PML implementation provides a stable PML on 3D spherical sections and can efficiently absorb waves at all the edges of the spherical section, including the convex bottom boundary.