Fault self-organization as optimal random paths selected by critical spatiotemporal dynamics of earthquakes

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Abstract
We study a simple 2D dynamical model of a tectonic plate with long range elastic forces and quenched disorder. The interplay between long-range elasticity, threshold dynamics, and the quenched featureless small-scale heterogeneity allows us to capture both the spontaneous formation of fractal fault structures by repeated earthquakes and a short-time spatiotemporal chaotic dynamics of earthquakes, well-described by a Gutenberg-Richter power law. Faults are mapped onto a minimal interface problem, which in 2D correponds to the random directed polymer problem and are thus self-affine with a roughness exponent 2/3.