Numerical methods for 3-D Dynamic Rupture

Percy Galvez (ETHZ), Dr. Luis A. Dalguer (ETHZ), Dr. Tarje Nissen-Meyer (ETHZ), and Prof. Dr. Jean-Paul Ampuero (CalTech, USA)

My research project focuses on developing a numerical method to accommodate realistic dynamic earthquake rupture for complex 3D fault geometries and heterogeneous velocity structures. Previous efforts have come a long way, but an efficient solver to simultaneously tackle complex faults and rupture models as well as 3D velocity variations and large-scale wave propagation in an efficient, parallel sense is an active research topic.

We port previously developed ideas for implementing dynamic rupture using a spectral-element method to a new comprehensive solver which relies on external meshing such that complex fault geometries can easily be handled. We will run a series of realistic numerical experiments to show the influences and benefits of modeling such structures. This will involve the task to specifically mesh these 3D structures using the meshing software CUBIT, and adding dynamic rupture to the flexible, open-source, and widely-used SPECFEM3D software (available here). We expect significant insights into the behavior of rupture models for such realistic settings, which may help discriminate between these different empirical constitutive relationships.

However, the spectral-element method as well as the finite-difference method suffers from spurious high-frequency oscillations of the slip-rate function that commonly occur on numerical solution o dynamic rupture problems. Up to now, these artifacts have been damped a posteriori using artificial viscosity models in the bulk. To overcome such artificial patchwork, we will adopt ideas presented within the framework of discontinuous Galerkin methods, in which a discontinuous so-called Riemann problem is solved around the fault, free of any spurious noise. The challenge lies in redefining the theory for a second-order partial differential equation as usually used in spectral elements. Using these ideas, the resultant approach will be a comprehensive tool for any earthquake modeling efforts, in that it combines the efficiency of the spectral-element method with flexible geometry and discontinuous solutions around the fault. A successful implementation is very beneficial as it combines the most intriguing properties of these numerical methods, solves the discontinuous problem in a well-posed manner, and will furthermore pave the way to other applications of discontinuous modeling using spectral elements.