Earthquake Simulation by Restricted Random Walks

This article simulates earthquake slip distributions as restricted random walks. Random walks offer several unifying insights into earthquake behaviors that physically based simulations do not. With properly tailored variables, random walks generate observed power law rates of earthquake number versus earthquake magnitude (the Gutenberg–Richter relation). Curiously, b -value, the slope of this distribution, not only fixes the ratio of small to large events but also dictates diverse earthquake scaling laws such as mean slip versus fault length and moment versus mean slip. Moreover, b -value determines the overall shape and roughness of earthquake ruptures. For example, mean random walk quakes with b = −½ have elliptical slip distributions characteristic of a uniform stress drop on a crack. Random walk earthquake simulators, tuned by comparison with field data, provide improved bases for statistical inference of earthquake behavior and hazard.