A discontinuous Galerkin method for sequences of earthquakes and aseismic slip on multiple faults using unstructured curvilinear grids

Simulations of sequences of earthquakes and aseismic slip (SEAS) including more than one fault, complex geometries and elastic heterogeneities are challenging. We present a symmetric interior penalty discontinuous Galerkin (SIPG) method accounting for the complex geometries and heterogeneity of the subsurface. The method accommodates two- and three-dimensional domains, is of arbitrary order, handles sub-element variations in material properties and supports isoparametric elements, i.e. high-order representations of the exterior and interior boundaries and interfaces including intersecting faults.

We provide an open-source reference implementation, Tandem, that utilises highly efficient kernels, is inherently parallel and well suited to perform high resolution simulations on large scale distributed memory architectures. Further flexibility is provided by optionally defining the displacement evaluation via a discrete Green's function, using algorithmically optimal and scalable sparse parallel solvers and preconditioners. We highlight the characteristics of the SIPG formulation via an extensive suite of verification problems (analytic, manufactured and code comparison) for elasto-static and seismic cycle problems. We demonstrate that high-order convergence of the discrete solution can be achieved in space and time for elasto-static and SEAS problems.

Lastly, we apply the method to realistic demonstration models consisting of a 2D SEAS multi-fault scenario on a shallowly-dipping normal fault with four curved splay faults, and a 3D multi-fault scenario of instantaneous displacement due to the 2019 Ridgecrest, CA, earthquake sequence. We exploit the curvilinear geometry representation in both application examples and elucidate the importance of accurate stresses (or displacement gradients) representations on-fault. Our results exploit advantages of both the boundary integral and volumetric methods and is an interesting avenue to pursue in the future for extreme scale 3D SEAS simulations.