Simulation of elastic waves in the presence of topography using a curvilinear staggered grid finite difference method

Ossian O'Reilly, Alexander N. Breuer, Yifeng Cui, Christine A. Goulet, Kim B. Olsen, Daniel Roten, Guillaume Thomas-Collignon, & Te-Yang Yeh

Submitted August 15, 2019, SCEC Contribution #9882, 2019 SCEC Annual Meeting Poster #009

We are in the process of incorporating topography into the anelastic wave propagation code AWP. This code is used within SCEC’s Cybershake project and High-F simulation activities. AWP solves the elastic wave equation by staggering velocity and stresses using fourth finite difference approximations in space and second order time stepping. Topography is treated by a 1D curvilinear coordinate transform. A difficulty that arises when solving the elastic wave equation in curvilinear coordinates is that additional terms emerge that must be discretized using a combination of interpolation and differentiation. Unless carefully discretized, long term instabilities can develop that destroy the accuracy of the solution for certain types of grids. To overcome this issue, we present a provably stable method that leverages recent developments in summation-by-parts for staggered grids and curvilinear meshes. We compare our implementation against a finite-element discontinuous Galerkin code (EDGE) by simulating seismic wave propagation for a Gaussian hill geometry in 3D. We propagate surface waves over large distances (up to 50 km), an exercise that requires about 10 grid points per minimum desired wavelength to achieve good agreement with the reference solution. In order to understand the importance of incorporating topography into regional seismic wave propagation simulations, we compare simulations covering a region of the San Jacinto mountains against simulations with a planar free surface. In preparation for the integration of AWP topography into Cybershake, we are profiling and optimizing the code for the ORNL supercomputer Summit.

Citation
O'Reilly, O., Breuer, A. N., Cui, Y., Goulet, C. A., Olsen, K. B., Roten, D., Thomas-Collignon, G., & Yeh, T. (2019, 08). Simulation of elastic waves in the presence of topography using a curvilinear staggered grid finite difference method. Poster Presentation at 2019 SCEC Annual Meeting.


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