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

Abstract

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 infinite-element 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 post-earthquake 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.