Complexity and Earthquakes

Abstract

Earthquakes are clearly a complex phenomena. Yet within this complexity there are several universally valid scaling laws. These include Gutenberg–Richter frequency–magnitude scaling, Omori’s law for the decay of aftershock activity, and Båth’s law relating the magnitude of the largest aftershock to the magnitude of the main shock. Other possibly universal scaling laws include power-law accelerated moment release prior to large earthquakes, a Weibull distribution of recurrence times between characteristic earthquakes, and a nonhomogeneous Poisson distribution of interoccurrence times between aftershocks. The validity of these scaling laws is evidence that earthquakes (seismicity) exhibit self-organized complexity. The relationships of such concepts as fractality, deterministic chaos, and self-organized criticality to earthquakes will be discussed. A variety of models that exhibit self-organized complexity have been related to seismicity. Simple cellular automata models such as the slider-block model reproduce some aspects. Damage mechanics can also reproduce statistical aspects such as Omori’s law. Simulation-based approach to distributed seismicity are also discussed. The objective is to produce synthetic models of earthquakes in a region similar to numerical weather forecasts.