The scale-dependent slip pattern for a uniform fault model obeying the rate- and state-dependent friction law

摘要

A uniform antiplane fault model obeying the rate- and state-dependent friction law and surrounded by a steady-slipping region with a constant loading rate is studied through quasi-dynamic numerical method. Findings indicate that the model exhibits scale-dependent slip characteristics. Previous studies have demonstrated that the fault slip pattern changes from aseismic creep or slow earthquakes to seismic instabilities as the fault length W increases from around the nucleation size h_c to well above hc. In the latter, instabilities typically nucleate periodically from the center of the fault and develop into characteristic events after the whole fault reaches a background stress level. For a fault with larger W∕h_c, characteristic events nucleate near the boundary or alternatively from both sides before the entire fault returns to background level. As W∕h_c increases further, additional events with rupture size between h_c and W appear. The number of small events is expected to increase with W∕h_c. The reason these small events do not rupture the whole fault is that the locked region forming on the fault when nucleation occurs acts as a large and low stress barrier. These small events continually create stress concentrations that serve as preparations for the next larger earthquake until the final characteristic event occurs. Meanwhile, the fault in this process gradually evolves into extreme sensitivity that any slight perturbation could change the original slip pattern. Although the current result is far from explaining the observed slip complexity on natural faults, it suggests a trend of increasing slip complexity with W∕h_c. Therefore, our understanding of the fault behavior may differ from previous knowledge that a relatively uniform and isolated fault model obeying the rate- and state-dependent friction law only exhibits periodic or aperiodic system-size events.