Gutenberg Richter and Characteristic Earthquake Behavior in Simple Mean-Field Models of Heterogeneous Faults

TL;DR

This paper models earthquake statistics in heterogeneous faults using mean-field approaches, revealing how disorder and dynamics influence Gutenberg-Richter and characteristic earthquake behaviors.

Contribution

It introduces a two-parameter phase diagram capturing the transition between power-law and characteristic earthquake regimes in a mean-field fault model.

Findings

Small dynamical weakening and driving force distance produce Gutenberg-Richter statistics.

Large effects lead to characteristic system-size events.

Bistability occurs in certain parameter regimes, causing phase transitions.

Abstract

The statistics of earthquakes in a heterogeneous fault zone is studied analytically and numerically in the 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 (epsilon) and the normal distance (L) of the driving forces from the fault. In general, small epsilon and small L are found to produce Gutenberg-Richter type power law statistics with an exponential cutoff, while large epsilon 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.