Numerical Modeling of Earthquake Cycles Based On Navier‐Stokes Equations With Viscoelastic‐Plasticity Rheology

Abstract

AbstractVisco‐elastic‐plastic modeling approaches for long‐term tectonic deformation assume that co‐seismic fault displacement can be integrated over 1000s–10,000s years (tens of earthquake cycles) with the appropriate failure law, and that short‐timescale fluctuations in the stress field due to individual earthquakes have no effect on long‐term behavior. Models of the earthquake rupture process generally assume that the tectonic (long‐range) stress field or kinematic boundary conditions are steady over the course of multiple earthquake cycles. This study is aimed to fill the gap between long‐term and short‐term deformations by modeling earthquake cycles with the rate‐and‐state frictional (RSF) relationship in Navier‐Stokes equations. We reproduce benchmarks at the earthquake timescale to demonstrate the effectiveness of our approach. We then discuss how these high‐resolution models degrade if the time‐step cannot capture the rupture process accurately and, from this, infer when it is important to consider coupling of the two timescales and the level of accuracy required. To build upon these benchmarks, we undertake a generic study of a thrust fault in the crust with a prescribed geometry. It is found that lower crustal rheology affects the periodic time of characteristic earthquake cycles and the inter‐seismic, free‐surface deformation rate. In particular, the relaxation of the surface of a cratonic region (with a relatively strong lower crust) has a characteristic double‐peaked uplift profile that persists for thousands of years after a major slip event. This pattern might be diagnostic of active faults in cratonic regions.