A dissipation‐based analysis of an earthquake fault model

Abstract

We analyze the dynamics of a discrete dynamical model of earthquake faulting, derived from the Burridge‐Knopoff model. The system is shown to exhibit a characteristic event size (L* = 2v2f l2) that separates two distinct regimes in the statistical distribution of event sizes and magnitudes. The dynamics of the system exhibits scaling laws that are in agreement with observed seismic laws. Influence of the frictional rate of dissipation, of the elastic stiffness coupling, and of the system size is investigated. The dynamics of the system is rather insensitive to the numerical treatment of the nonsmooth friction. In contrast, the exact form of the velocity weakening friction law is shown to have a major effect on the dynamics. For friction laws allowing local reversal backslipping, the distribution of the magnitudes does not exhibit a Gutenberg and Richter (GR) distribution, while by precluding backslipping a GR distribution is observed. Two populations of events can be characterized based on dissipation: weakly dissipative events that allow the mechanical energy of the system to increase; and strongly dissipative events that release a large fraction of the elastic potential energy of the system and introduce large stress heterogeneities. A coarse grain analysis in terms of the stored elastic energy and the magnitude of the disorder provides new interesting insights on the dynamics of the model. Weakly dissipative events, which reproduce the seismic laws, are shown to follow a deterministic evolution. A statistical criterion for the initiation of big dissipative events is proposed.