SCEC Award Number 11083 View PDF
Proposal Category Individual Proposal (Integration and Theory)
Proposal Title Advanced Numerical Techniques for Dynamic Rupture Simulations
Name Organization
Eric Dunham Stanford University
Other Participants Kozdon, Jeremy (postdoc)
O'Reilly, Ossian (visiting masters student)
SCEC Priorities B1, A10, B3 SCEC Groups GMP, FARM, CS
Report Due Date 02/29/2012 Date Report Submitted N/A
Project Abstract
Our group has developed several novel numerical methods for dynamic rupture simulations. There have been two main thrusts, each targeted at specific outstanding scientific questions. Motivated by field and laboratory studies of fault roughness, we sought to develop a code capable of handling geometrically complex domains. Since one of the target research areas was the origin of incoherent high frequency ground motion, we needed a method free from the spurious numerical oscillations that plague many conventional codes. We also need high-order accuracy, both in the interior and also near faults. To accomplish this, we developed a method based on summation-by-parts finite difference operators with weak enforcement of boundary conditions and fault friction laws (both slip-weakening and rate-and-state). The method, including boundary treatment, is provably stable and accurate, as confirmed with rigorous convergence tests. We have also implemented Drucker-Prager plasticity to account for inelastic off-fault deformation. The code was parallelized and strong scaling tests show ideal scaling to 4096 cores (the most we have tested with thus far). This code was used in our published studies of high frequency ground motion from rough faults. We have also used it to study subduction zone earthquakes, a testament to its ability to handle extremely complex geometries.

A second thrust of our work has been on an adaptive mesh refinement (AMR) code for rupture dynamics. Here the motivating problem concerns the earthquake energy balance, in particular which physical processes explain the increase of fracture energy with propagation distance required by self-similarity. The AMR approach adaptively refines and coarsens the mesh to track sharp gradients in the velocity and stress fields, such as wavefronts and rupture fronts. The method is based on a low-order finite volume method, with high accuracy arising in this case from a dense mesh around the features of interest. The implementation is built on the CHOMBO AMR library from Lawrence Livermore National Laboratory. We have implemented slip-weakening and rate-and-state friction into our code, as well as continuum plasticity. The code is written in a dimension-independent manner, permitting both 2D and 3D simulations. We are currently adding thermal pressurization. After that is done, we will be able to study how much dissipation occurs on the fault (through thermal pressurization and frictional sliding) versus off the fault (in inelastic deformation).
Intellectual Merit Understanding earthquake physics and predicting strong ground motion requires development of stable and accurate rupture dynamic simulation codes. We have developed two such codes, one based on high-order finite differences and the other utilizing adaptive mesh refinement to hone in on regions of interest. These codes have enabled us to study rupture dynamics on nonplanar faults, the origin of incoherent high frequency ground motion, and to study the earthquake energy balance. These questions are fundamental to earthquake physics and seismic hazard assessment.
Broader Impacts This project led to a collaboration between SCEC PI Dunham and applied mathematician Prof. Jan Nordstrom of Linkoping University, Sweden. This collaboration initiated interest within the applied mathematics and scientific computing community on problems in earthquake simulation.
Exemplary Figure Figure 3: Comparison of our AMR code and our high-order finite difference
code, with strongly rate-weakening fault friction and Drucker-Prager off-fault
viscoplasticity. R0 is the characteristic size of the rupture front for quasi-static
crack growth. Plasticity occurs in a wedge-shaped region opening at a
very small angle with respect to the fault.