Spectral-infinite-element simulations of coseismic and post-earthquake deformation

Accurate and efficient simulations of coseismic and post-earthquake deformation are important for proper inferences of earthquake source parameters and subsurface structure. These simulations are often performed using a truncated half-space model with approximate boundary conditions. The use of such boundary conditions introduces inaccuracies unless a sufficiently large model is used, which greatly increases the computational cost. To solve this problem, we develop a new approach by combining the spectral-element method with the mapped infiniteelement method. In this approach, we still use a truncated model domain, but add a single outer layer of infinite elements. While the spectral elements capture the domain, the infinite elements capture the far-field boundary conditions. The additional computational cost due to the extra layer of infinite elements is insignificant. Numerical integration is performed via Gauss-Legendre-Lobatto and Gauss-Radau quadratures in the spectral and infinite elements, respectively. We implement an equivalent moment-density tensor approach and a split-node approach for the earthquake source, and discuss the advantages of each method. For postearthquake deformation, we implement a general Maxwell rheology using a second-order accurate and unconditionally stable recurrence algorithm. We benchmark our results with the Okada analytical solutions for coseismic deformation, and with the Savage & Prescott analytical solution and the PyLith finite-element code for post-earthquake deformation.