GUTENBERG-RICHTER AND CHARACTERISTIC EARTHQUAKE BEHAVIOR IN SIMPLE MEAN-FIELD MODELS OF HETEROGENEOUS FAULTS

The statistics of earthquakes in a heterogeneous fault zone is studied analytically and numerically in a mean-field version of a model for a segmented fault system in a three-dimensional elastic solid. The stud ies focus on the interplay between the roles of disorder, dynamical ef fects, and driving mechanisms. A two-parameter phase diagram is found, spanned by the amplitude of dynamical weakening (or ''overshoot'') ef fects epsilon and the normal distance L of the driving forces from the fault. In general, small epsilon and small L are found to produce Gut enberg-Richter type power law statistics with an exponential cutoff, w hile large epsilon and large L lead to a distribution of small events combined with characteristic system-size events. In a certain paramete r regime the behavior is bistable, with transitions back and forth fro m one phase to the other on time scales determined by the fault size a nd other model parameters. The implications for realistic earthquake s tatistics are discussed.