A High-Order Finite-Difference Method on Staggered Curvilinear Grids for Seismic Wave Propagation Applications with Topography
Ossian O’Reilly, Te‐Yang Yeh, K. B. Olsen, Zhifeng Hu, Alex Breuer, D. Roten, Christine Goulet
Abstract
ABSTRACT We developed a 3D elastic wave propagation solver that supports topography using staggered curvilinear grids. Our method achieves comparable accuracy to the classical fourth-order staggered grid velocity–stress finite-difference method on a Cartesian grid. We show that the method is provably stable using summation-by-parts operators and weakly imposed boundary conditions via penalty terms. The maximum stable timestep obeys a relationship that depends on the topography-induced grid stretching along the vertical axis. The solutions from the approach are in excellent agreement with verified results for a Gaussian-shaped hill and for a complex topographic model. Compared with a Cartesian grid, the curvilinear grid adds negligible memory requirements, but requires longer simulation times due to smaller timesteps for complex topography. The code shows 94% weak scaling efficiency up to 1014 graphic processing units.