Using pseudo-spectral method on curved grids for SH-wave modeling of irregular free-surface

This paper uses curved grids in the context of a pseudo-spectral method to model 2-D SH-wave propagation in a medium with an irregular free-surface. A technique originally developed for computational fluid dynamics (CFD) is first used to generate curved grids following the irregular free-surface. Then the SH-wave equations in curved coordinates are derived, together with numerical boundary conditions at a free-surface are presented. Finally, a Fourier-Chebyshev pseudo-spectral method is used to simulate SH-wave propagation in curved coordinates and solutions in Cartesian coordinates are obtained. This numerical scheme is tested against the analytical solution for Lamb's problem in a uniform elastic half space with a sloping surface. An excellent agreement is found, which confirms the accuracy of the method present here. In addition, the scheme is applied to the model of topography with discontinuous derivative, and the results are compared with those obtained from the modeling on conventional curved grids by algebraic transform. It shows that the new scheme is more accurate than that on algebraic grids.