Rate- and state-dependent friction law and statistical properties of earthquakes

In order to clarify how the statistical properties of earthquakes depend on the constitutive law characterizing the stick-slip dynamics, we make an extensive numerical simulation of the one-dimensional spring-block model with a rate- and state-dependent friction law. Both the magnitude distribution and the recurrence-time distribution are studied with varying the constitutive parameters characterizing the model. While a continuous spectrum of seismic events from smaller to larger magnitudes is obtained, earthquakes described by this model turn out to possess pronounced "characteristic" features.