An Invariant Rate‐ and State‐Dependent Friction Formulation for Viscoeastoplastic Earthquake Cycle Simulations

We present a 2-D numerical modeling approach for simulating a wide slip spectrum in a viscoelastoplastic continuum. The key new model component is an invariant reformulation of the classical rate- and state-dependent friction equations, which is designed for earthquake simulations along spontaneously evolving faults. Here we describe the methodology and demonstrate that it is accurate and stable in a setup consisting of a mature strike-slip fault zone. We show that the nucleation and propagation of an earthquake are well resolved, as supported by a good agreement with various analytical approximations, including those of the nucleation and cohesive zone lengths. Results generally converge with respect to grid size, time step, and other numerical parameters. The convergence rate with respect to grid size depends on the internodal averaging scheme, is influenced by wave reflections, and deteriorates for inclined faults. The simulated slip spectrum, ranging from stable sliding at the loading rate to periodic aseismic slip to periodic seismic slip as a function of nucleation size, is in general agreement with the literature. In this simple setup, dynamic pressure does not play a significant role. By analyzing the role of viscous deformation, we identify and confirm by our simulations a theoretical viscosity threshold below which earthquakes cannot nucleate. This threshold is shown to depend on the reference strength of rate- and state-dependent friction and the loading strain rate, which is in agreement with previous work on the brittle-ductile transition.