Towards topography in AWP-ODC

Ossian O'Reilly, Alexander N. Breuer, Yifeng Cui, Christine A. Goulet, & Kim B. Olsen

Published August 15, 2018, SCEC Contribution #8694, 2018 SCEC Annual Meeting Poster #293

A central component for reliable seismic hazard assessment is that models produce good agreements with observations. To match observations at high frequencies ( > 1 Hz) it becomes increasingly important to capture the interaction of seismic waves with topography. Therefore, we aim to bring topography support into future seismic hazard computations by adding new capabilities to the fourth-order finite-difference wave propagation solver AWP-ODC (Anelastic Wave Propagation, Olsen-Day-Cui). The AWP-ODC solver is extensively used for seismic hazard assessment within SCEC's Cybershake and High-F projects. The main difficulty that must be addressed here is how to ensure compatibility between the topography support and the AWP internal solver for practical purposes. That is, how to 1) roughly maintain the computational efficiency of the code, 2) limit geometric treatment to only cover the first few km of the upper part of the computational domain 3) deliver accurate computations at a tractable number of grid points per wavelengths (PPW, targeting ~ less than 15 PPW), 4) ensure stability, including at long simulation times, and 5) enable placement of point forces on the free surface (needed for reciprocity computations).

While there are many ways to incorporate topography in FD-based methods, such as immersed boundary methods, vacuum formulation methods, hybrid methods, we have chosen to focus on curvilinear coordinate transforms. Here, topography, in the form of elevation map data, is mapped to a curved grid by applying a 1D coordinate transform in the vertical direction. Our method is based on summation-by-parts (SBP) and is energy conserving. We have derived novel SBP interpolation operators for staggered grids. We investigate how the different formulations perform (e.g., solutions using covariant basis decomposition versus Cartesian), and how the coordinate transform influences accuracy (how deep the transform must reach before it can be coupled to a regular Cartesian grid block).

In a 2D point source simulation of the acoustic wave equation, featuring a Gaussian hill and canyon geometry, we find excellent agreement compared to EDGE (Breuer et. al 2017) at 10 PPW. We also demonstrate that the method is capable of simulating elastic waves in a challenging 2D geometry that samples a cross-section of the San Jacinto Mountains.

Breuer A., Heinecke A., Cui Y. (2017) EDGE: Extreme Scale Fused Seismic Simulations with the Discontinuous Galerkin Method. In: Kunkel J., Yokota R., Balaji P., Keyes D. (eds) High Performance Computing. ISC 2017. Lecture Notes in Computer Science, vol 10266. Springer, Cham

Citation
O'Reilly, O., Breuer, A. N., Cui, Y., Goulet, C. A., & Olsen, K. B. (2018, 08). Towards topography in AWP-ODC. Poster Presentation at 2018 SCEC Annual Meeting.

Related Projects & Working Groups
Computational Science (CS)