SCEC Award Number 17192 View PDF
Proposal Category Individual Proposal (Integration and Theory)
Proposal Title Stable and Accurate Fault and Free Surface Boundary Conditions in Staggered Grid Wave Propagation Codes
Investigator(s)
Name Organization
Eric Dunham Stanford University
Other Participants Ossian O'Reilly
SCEC Priorities 4c, 4a, 2d SCEC Groups CS, GM, FARM
Report Due Date 06/15/2018 Date Report Submitted 06/15/2018
Project Abstract
 This work focuses on the development and testing of free surface boundary condition implementations for the elastic wave equation. In recent work, we showed how to extend the
so-called summation-by-parts (SBP) finite di fference method and simultaneous approximation term penalty method (SAT) to staggered grids for the acoustic wave equation. Here, we investigate how applicable this method is for solving the elastic wave equation. In particular, we study the accuracy of the method for some challenging problems featuring surface waves. We make a detailed comparison to the more conventional free surface boundary condition (FS2), which is implemented in SCEC's wave propagation code (AWP). We show that SBP-SAT delivers comparable accuracy to FS2, is capable of solving both forward and reciprocal problems (of particular relevance to Cybershake), is provably stable and energy conserving regardless of material properties, and is also extensible to other types of problems and methods. Among the latter are problems involving nonplanar surface topography. However, the implementation of the SBP-SAT approach is slightly more complicated and computationally expensive compared to FS2.
Intellectual Merit Seismic wave propagation simulations are central to many SCEC activities, including seismic tomography, earthquake source simulation, and ground motion simulation. One of the most challenging aspects of seismic wave propagation is resolving surface waves in the low-velocity layers near Earth's surface and in sedimentary basins. This project explores different numerical treatments of the free surface boundary condition, comparing a commonly used treatment (FS2, used in SCEC's AWP-ODC code) to a treatment utilizing SBP-SAT finite differences near the boundaries (elsewhere the methods are exactly the same). The SBP-SAT treatment is as accurate as FS2 and is always stable. Furthermore, unlike FS2, the SBP-SAT treatment can be extended to curvilinear meshes (vs. Cartesian meshes), thereby permitting simulation of wave propagation with nonplanar free surface topography.
Broader Impacts This project supported one postdoc, Ossian O'Reilly, at a critical time in his career as he transitions to being a SCEC postdoc at USC. The project has helped him understand SCEC's wave propagation and ground motion simulation needs, so that his future projects can be targeted to further advance SCEC's simulation capabilities. O'Reilly has also learned programming and scientific computing skills and will help teach these skills to others in the SCEC community. He will also help convey the importance of earthquake research to the applied math community in which he is active. The project will also help improve SCEC's ground motion modeling capabilities.
Exemplary Figure Figure 3: Reciprocity test in which the SBP-SAT method is used to solve the forward problem using reciprocity (dashed line). This solution is compared to the numerical solution of the forward problem (solid line). Credit: O'Reilly and Dunham, 2018, SCEC report.