Numerical Simulation Of Fault Slip Behaviors With The Rate-and State-dependent Friction Law

The laboratory-derived rate-and state-dependent friction law is introduced. We study how the friction law affects and controls the scaling of source parameters, seis-mic slip complexity, as well as rupture dynamics for a fault model obeying the law. The friction on the fault surface has strong influences on the natural fault behavior and earthquakes. Our understanding in the fault slip and earthquakes depends on how much we known about friction. Therefore, we first detailed review how the rate and state fric-tion law is proposed and developed, and then, give the stability analysis under a simple single-degree-of-freedom spring-slider model, and also summarize the latest friction facts from high-speed rock friction experiments over the past decade, as well as related thermal weakening theories. A comprehensive and systematic knowledge of the rock friction serve to understanding of the nature of faults and earthquakes.The field observation of source parameters varying with the seismic moment is one way by which seismologists explore the self-similarity of earthquakes. In this study, a single-degree-of-freedom spring-slider model is used to numerical simulate the implied scaling relation of source parameters under the rate-and state-dependent friction law. In this case, earthquake size is controlled by the fault size W (being inversely propor-tional to the stiffness k) and source parameters are affected by the ratio of W and the nucleation size hc. The simulation result shows source parameters are scale-dependent for small events, but are almost self-similar for large events. The transition is attribut-ed to the relatively large proportion of both aseismic slip and fracture energy in small events. However, the model shows evident increase in stress drop and apparent stress if a thermal pressurization is included.A numerical method that could simulate both the fault slip behavior in very long time-scale and co-seismic process in extremely short time-scale, based on the traction boundary integral equation method in time domain, is developed and compared with widely used quasi-dynamic method. The two methods produce generally similar slip patterns and rupture styles in an uniform or slightly nonuniform fault model, although the latter cannot represent the seismic wave effects correctly in the co-seismic process. The effect of the relative fault size W/hc on the rupture style and the slip complexity is studied by both the quasi-dynamic and new developed dynamic methods. It is observed that the fault with a small W/hc produces regular, periodic crack-like characteristic event and the fault with a large W/hc produces the similar event, as well as more self-stopping and pulse-like events. It implies an uniform fault would spontaneously evolve into complex slip patterns with increasing W/hc.This study indicates the rate-and state-friction law is scale-dependent. The rel-ative fault size W/hc affects all aspects of faults and earthquakes. The micro-scale rupture characteristics and the macroscopic seismic complexity hence have an unified interpretation under the friction law.