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 studies focus on the interplay between the roles of disorder, dynamical effects, and driving mechanisms. A two-parameter phase diagram is found, spanned by the amplitude of dynamical weakening (or “overshoot”) effects ε and the normal distance $L$ of the driving forces from the fault. In general, small ε and small $L$ are found to produce Gutenberg-Richter type power law statistics with an exponential cutoff, while large ε and large $L$ lead to a distribution of small events combined with characteristic system-size events. In a certain parameter regime the behavior is bistable, with transitions back and forth from one phase to the other on time scales determined by the fault size and other model parameters. The implications for realistic earthquake statistics are discussed.