A new hybrid numerical scheme for simulating fault ruptures with near fault bulk inhomogeneities

The Finite Difference (FD) and the Boundary Integral (BI) Method have been used extensively to model spontaneously propagating shear cracks in a variety of engineering and geophysical applications. While FD has a large computational cost as it requires the discretization of the whole volume of interest, it can handle a greater variety of problems in comparison with BI, including bulk nonlinearities and heterogeneities. On the other hand, the BI method eliminates the necessity of simulating the wave propagation in the whole elastic medium by leveraging space-time convolutions with the source on the fault surface. The spectral implementation of the BI in particular is faster and much more computationally efficient than other bulk methods such as FD. However, the spectral boundary integral (SBI) formulation is restricted to linear elastic bulk and planar faults. This study proposes a new method, referred to herein as the "Hybrid Method", in which the two methods are combined. Benefiting from the flexibility of FD and the efficiency of BI, this method is capable of solving a wide range of problems in a computationally efficient way. In the Hybrid Method, nonlinearities or heterogeneities may be confined to a virtual narrow strip that includes the fault or the wave source. This strip, then, is discretized using a FD scheme in space and time while the virtual boundaries of the strip are handled using the SBI formulation that represents the two elastic half spaces outside the strip. Modeling the elastodynamic response in these two halfspaces needs to be carried out by an Independent Spectral Formulation before joining them to the strip with the appropriate boundary conditions. Dirichlet and Neumann boundary conditions are imposed on the strip and the two half-spaces, respectively, at each time step to propagate the solution forward. We illustrate the accuracy and efficiency of the method using several examples. This approach is more computationally efficient than pure FD and expands the range of applications of SBI beyond the current state of the art