Siyang Wang: An efficient finite difference method for the elastic wave equation in layered media

Abstract: I will present our recent efforts in developing and analyzing an efficient finite difference method for wave propagation problems. We consider the elastic wave equation in a layered medium. The material properties are smooth in each layer but can be discontinuous at nonplanar material interfaces. The spatial discretization is based on high-order finite difference operators satisfying a summation-by-part property, and geometrical features are resolved by using curvilinear meshes. In addition, mesh sizes are adapted to the material properties to balance the number of grid points per wavelength. At material interfaces, we use the ghost point method and interpolation to impose physical conditions at nonconforming grid interfaces. With a predictor-corrector time integration method, the full discretization is provably energy-conserving with a favourable time-step restriction. The stability and accuracy properties are verified in numerical examples. In addition, we have performed tests on the benchmark problem LOH.1 in the geosciences by solving the 3D elastic wave equation, with results showing excellent agreement with the semi-analytical solution when using only 5 grid points per wavelength.

This is a joint work with Anders Petersson, Lawrence Livermore National Laboratory, USA, and Lu Zhang, Columbia University, USA