WEDMI: 4th-order Discontinuous Staggered-grid Finite Difference Method for Wave Propagation Simulations

Shiying Nie

Shiying Nie
MS Candidate
Advisor: Dr. Kim Bak Olsen

Monday, December 19th, 2016
CSL 422 – 11:30 am

In a realistic geological structure with large contrast in seismic wave speed between shallow and deep regions, the simulation of seismic wave propagation using a spatially uniform grid can be computationally very demanding due to over-discretization of the high-speed material. For this reason, numerical methods that allow for larger grid spacing discretizing the faster regions have the possibility to be much more efficient. Discontinuous mesh (DM) methods, operating by exchanging wavefield information between media partitions discretized with two different grid spacings, provide a convenient way to improve such efficiency issues. Unfortunately, DM methods typically suffer from inherent stability problems, in particular in strongly heterogeneous media, arising from numerical noise at the overlap of the two regions with different grid spacings. We have developed a 3-D fourth-order velocity-stress staggered-grid finite-difference DM method (AWP-DM) to model seismic wave propagation, using a weakly enforced discontinuous mesh interface (WEDMI) between fine and coarse meshes. WEDMI’s down sampling method from fine to coarse grids is related to the wavefield interpolation among coarse grid points by its matrix transpose operator. Benchmarks in models with realistic 3D velocity variations and finite fault sources across the grid interface show a stable result for a number of time steps exceeding the need dictated by current high-frequency ground motion simulations. The method requires a factor-of-three ratio between the coarse and fine grid sizes, and produces a level of accuracy comparable to that from the uniform fine grid scheme using at least 7-8 grid points per minimum S-wavelength inside the mesh overlap zone.