Self-organized criticality in a crack-propagation model of earthquakes

Abstract

The distribution of seismic moment or energy of earthquakes is well described by the universal Gutenberg-Richter power law, N(s)\ensuremath{\approxeq}${\mathit{s}}^{\mathrm{\ensuremath{-}}1\mathrm{\ensuremath{-}}\mathit{b}}$, where b\ensuremath{\approxeq}0.5--0.6. We have constructed a simple dynamical model of crack propagation; when driven by slowly increasing shear stress, the model evolves into a self-organized critical state. A power-law distribution for earthquakes with b\ensuremath{\approxeq}0.4 in two dimensions and b\ensuremath{\approxeq}0.6 in three dimensions is found. The critical state is ``at the edge of chaos,'' with algebraic growth in time of a small initial perturbation.