Earthquakes and Faulting: Self-Organized Critical Phenomena with a Characteristic Dimension

Abstract

Earthquakes are among the most frequently cited natural phenomena that exhibit the behavior called self-organized criticality that is found in models of spacially extended dissipative systems. In this article the relevant phenomenological aspects of earthquakes, and of faults, the objects upon which earthquakes occur, are reviewed in terms of this concept. Both earthquakes and faults have fractal (power law) size distributions, a prime characteristic of SOC systems. Earthquake statistics do not vary in space except for a factor that defines the overall rate of activity, and observations of artificially induced seismicity suggests that the continental crust is virtually everywhere in a state close to seismic failure. These observations lead to the conclusion that the continental crust is in a self-organized critical state everywhere, but with geographically varying rates of loading. However, the earthquake system contains a characteristic dimension, the width of the brittle zone, or schizosphere, within which earthquakes can occur, and this has a profound effect on the behavior. Earthquakes of size on either side of this crossover dimension have very different characteristics. The seismic moments of small earthquakes, which are unconstrained to propagate in two dimensions, scale with dimension cubed. For large earthquakes, that may only propagate in one dimension, moment scales with rupture dimension squared. On a given fault, the large earthquakes do not belong to the same fractal set as the small earthquakes. Globally, both small and large earthquakes have power law size distributions but with different exponents, being somewhat less than 2/3 for small earthquakes and 1 for large earthquakes. The morphology of faults also exhibits profound changes at the crossover dimension.