FEM simulations of seismic cycle along a complex normal fault

In the assessment and prediction of seismic hazards, developing numerical methods capable of accurately simulating long-term earthquake cycles in complex fault systems is of critical importance. We developed a fully dynamic numerical method for simulation of earthquake cycle based on the Newmark implicit time integration scheme in finite element method (FEM). This method employs an adaptive time-stepping strategy to accurately capture the entire earthquake cycle, including earthquake preparation, rupture nucleation and rupture propagations, and post-seismic adjustments. To investigate long-term earthquake cycles, we developed a geometrically complex normal fault model with depth-dependent dip angles. This model, governed by the rate- and state-dependent friction law (RSF), was used to simulate 1,100 years of seismic activity under a tectonic loading rate of 15 mm/year. The calculation process is stable, and the model is robust. The simulated results recorded 10 earthquake events with an average earthquake recurrence interval of 117 years. Not only did the results present each rupture nucleation location, but also exhibited the complete details of each earthquake scenario. In addition, we modified the slip-weakening friction law (SWL) by introducing fault healing constraints, making it suitable for earthquake cycle simulations. Comparative analysis of the simulation results between the models with RSF and SWL shows that the cumulative slip histories of fault during earthquake cycle exhibit notable similarities. This consistency demonstrates that the modified SWL captures the earthquake cycle within the model framework. Furthermore, we investigated the effects of varying fault dip angles and initial stress fields on earthquake recurrence intervals in geometrically complex normal faults. Multi-model comparisons revealed that an increase in dip angle anywhere along the normal fault reduces the earthquake recurrence intervals and the increased horizontal stresses shorten the earthquake recurrence intervals. This study provides a novel numerical framework for simulating earthquake cycle in complex normal fault systems.