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

Visco‐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. The numerical modeling method for long‐term tectonic deformations averages out the co‐seismic fault displacement into thousands to tens of thousands of years, and neglects near‐fault damages of earthquakes; therefore, it may not be able to decipher fault activities in detail. Software simulating earthquake rupture dynamics may not have a good estimation of background stress due to long‐term tectonic deformations. In this study, we develop a numerical framework that embeds earthquake rupture dynamics into a long‐term tectonic deformation model by adding inertial terms and using highly adaptive time‐stepping that can capture deformation at plate‐motion rates as well as individual earthquakes. The inertia term, which is neglected in long‐term large‐scale modeling methods, is considered to simulate the dynamic rupture processes. The rate‐and‐stat