Scaling of small repeating earthquakes explained by interaction of seismic and aseismic slip in a rate and state fault model

Because of short recurrence times and known locations, small repeating earthquakes present a rare predictable opportunity for detailed field observations. They are used to study fault creeping velocities, earthquake nucleation, stress drops, and other aspects of tectonophysics, earthquake mechanics, and seismology. An intriguing observation about repeating earthquakes is their scaling of recurrence time with seismic moment, which is significantly different from the scaling based on a simple conceptual model of circular ruptures with stress drop independent of seismic moment and no aseismic slip. Here we show that a model of repeating earthquakes based on laboratory-derived rate and state friction laws reproduces the observed scaling. In the model, a small fault patch governed by steady state velocity-weakening friction is surrounded by a much larger velocity-strengthening region. Long-term slip behavior of the fault is simulated using a methodology that fully accounts for both aseismic slip and inertial effects of occasional seismic events. The model results in repeating earthquakes with typical stress drops and sizes comparable with observations. For a fixed set of friction parameters, the observed scaling is reproduced by varying the size of the velocity-weakening patch. In simulations, a significant part of slip on the velocity-weakening patches is accumulated aseismically, even though the patches also produce seismic events. The proposed model supplies a laboratory-based framework for interpreting the wealth of observations about repeating earthquakes, provides indirect evidence that rate and state friction acts on natural faults, and has important implications for possible scenarios of slip partition into seismic and aseismic parts.