The role of disorder and stress concentration in nonconservative fault systems

The aim of this paper is to understand the origin of the deviations from the Gutenberg–Richter law observed for individual earthquake faults. The Gutenberg–Richter law can be reproduced by slider-block fault models showing in its quasi-static limit self-organized criticality. However, in this model limit the earthquake ruptures are described by propagating narrow slip pulses leading to unrealistic low stress concentrations at the rupture front. To overcome such unrealistic rupture behavior, we introduce a new state-dependent stress distribution rule accounting for broader slip pulses up to crack-like behavior. Our systematic analysis of the generalized model shows that the earthquake characteristics can be described in terms of critical point behavior, resulting in subcritical, critical, and supercritical system states. We can explain the realized state of self-organized systems by the effect of individual ruptures on the stress field. This effect depends strongly on the fault roughness. For spatially smooth systems, more realistic rupture characteristics lead to supercritical behavior, equivalent to characteristic earthquake distributions empirically observed for several individual faults. For rough faults, earthquakes cannot rupture the whole system and seismic energy is released by small events only. The transition between both regimes occurs at an intermediate degree of heterogeneity, where the earthquake activity is reminiscent of self-organized criticality. Thus, our results predict that for individual faults one should in general observe systematic deviations from the Gutenberg–Richter law for large earthquake sizes.