FAULT SELF-ORGANIZATION AS OPTIMAL RANDOM-PATHS SELECTED BY CRITICAL SPATIOTEMPORAL DYNAMICS OF EARTHQUAKES

We study a simple 2D dynamical model of a tectonic plate with long-ran ge elastic forces and quenched disorder. The interplay between long-ra nge elasticity, threshold dynamics, and the quenched featureless small -scale heterogeneity allows us to capture both the spontaneous formati on of fractal fault structures by repeated earthquakes and a short-tim e spatiotemporal chaotic dynamics of earthquakes, well described by a Gutenberg-Richter power law. Faults are mapped onto a minimal interfac e problem, which in 2D corresponds to the random directed polymer prob lem and are thus self-affine with a roughness exponent 2/3.