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

The distribution of seismic moment or energy of earthquakes is well described by the universal Gutenberg-Richter power law, N(s)≊${\mathit{s}}^{\mathrm{-}1\mathrm{-}\mathit{b}}$, where b≊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≊0.4 in two dimensions and b≊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.