A novel hybrid numerical finite element-spectral boundary integral scheme for modeling earthquake cycles

Mohamed Abdelmeguid, Xiao Ma, & Ahmed E. Elbanna

Published August 15, 2018, SCEC Contribution #8676, 2018 SCEC Annual Meeting Poster #198

Modeling earthquake ruptures is a complex challenge due to the eclectic sources of nonlinearities, such as friction law, plasticity, and material damage. In addition to the nonlinearities, another challenging aspect of earthquake dynamic is the multiscale nature of the problem, both spatially and temporally. Spatially, principle slip surfaces can be several orders of magnitude smaller than the fault rupture. Temporally, stress accumulation and instability initiations occur on a much larger time scale than the sudden energy release of a rupture episode. Accordingly, novel numerical approaches are required to resolve both temporal and spatial scales, as well as account for the nonlinearities accurately.

Here, we present a hybrid scheme that combines finite element method (FEM) and spectral boundary integral method (SBIM) to simulate earthquake cycles with rate and state fault subjected to slow tectonic loading processes of long duration intermitted by episodes of dynamic fracture in the presence of near-field heterogeneities or nonlinearity. On a spatial level, regions of small-scale heterogeneities and complex fault geometry are handled using a FEM approach, while the linearly elastic bulk with a known Green’s function is modelled using SBIM. Accordingly, we benefit from the flexibility of FEM in handling nonlinear problems, while retaining the superior performance and accuracy of SBIM. We handle the intricacies associated with this time evolution using an alternating explicit-implicit scheme, such that during dynamic rupture an explicit time integration is utilized for computational efficiency, with the implicit time integration being specific only to inter-seismic periods where larger time steps are required. The presented approach is validated using a benchmark problem from the Southern California Earthquake Center’s dynamic rupture simulation validation exercises. We further demonstrate the capabilities of this computationally- efficient scheme by modeling earthquake cycles for a 2D in plane problem with different parameters and settings. Finally, we discuss the potential of our approach in modelling a wide class of problems in geophysics and engineering.

Citation
Abdelmeguid, M., Ma, X., & Elbanna, A. E. (2018, 08). A novel hybrid numerical finite element-spectral boundary integral scheme for modeling earthquake cycles. Poster Presentation at 2018 SCEC Annual Meeting.

Related Projects & Working Groups
Fault and Rupture Mechanics (FARM)