Diffuse thick fault representation in 2D SEM for earthquake dynamic rupture simulations

Natural fault system observations feature complexity that includes damage variation from the outer damage zone to the fault core and associated rheological degradation (e.g. variation in the frictional strength and spatio-temporal slip localisation). In earthquake dynamic rupture simulations, faults are typically treated as infinitesimally thin interfaces with distinct on- versus off-fault rheologies. Commonly, such faults are explicitly represented in the discretisation of the computational domain.

Here we present a diffuse interface approach for dynamic rupture modelling. We introduce a 2D spectral element method (SEM) with an embedded smeared discontinuity representing volumetric fault slip. Our diffuse fault SEM is inspired by the stress-glut method of Andrews, 1999. In our approach, a subdomain in which the tangential stresses are limited by a critical shear strength and an empirical friction law is embedded in a purely elastic domain, resembling classical discrete fault representations. Our approach is implemented on a structured quadrilateral mesh within an SEM framework for elastic wave propagation, with PETSc (Balay et al. 2019) as a linear algebra back-end.

Our method collapses volumetric complexities onto a distribution within a compact support instead of the traditional interface approach, making it a flexible inelastic zone alternative for mesh-independent fault representation in dynamic rupture simulations. We conduct 2D numerical experiments, including a kinematically driven Kostrov-like crack and spontaneous dynamic rupture as defined in SCEC community benchmarks (Harris et al., 2018) of increasing complexity. We extract the spectral response from seismograms at different receivers normal and along the fault. We also analyse the capacity of flexible fault representation by including mesh-independent fault geometries. 

Our approach will allow us to incorporate volumetric failure rheologies in SEM dynamic rupture simulations and is part of the TEAR ERC project (www.tear-erc.eu).