Notes on modeling earthquake dynamics with the spectral element method

We provide a detailed presentation and discussion of a numerical modeling technique for earthquake dynamics based on the spectral element method. The problem of dynamic frictional contact along slip interfaces in elastic domains is formulated in a hybrid variational form, with Lagrange multipliers associated to the fault tractions. The problem is discretized in space by a spectral element method and in time by a second order finite difference time scheme. We investigate the convergence of the numerical error with grid refinement in canonical test cases. We study in detail the origin and nature of the high frequency numerical noise as well as different solutions to reduce it. Comparisons with other methods on a standard convergence test show that the spectral element method for fault dynamics is very accurate and competitive. The ability of the method to handle rupture problems with realistic geometries, fault zone structure and non-linear off-fault rheology is illustrated through several examples. ∗Institute of Geophysics, ETH Zürich, [email protected]