Complexity and Earthquakes

Abstract

Earthquakes are clearly a complex phenomenon. Yet within this complexity, there are several universally valid scaling laws. These include the Gutenberg–Richter frequency–magnitude scaling, the Omori law for the decay of aftershock activity, and Bath's law relating the magnitude of the largest aftershock to the magnitude of the mainshock. Other possible 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 can be used to illustrate and quantify the complex behavior of earthquakes. A variety of models that exhibit self-organized complexity have been used to describe the observed patterns of seismicity. Simple cellular automaton models such as the slider-block model reproduce some important statistical aspects of seismicity and capture their basic physics. Damage mechanics models can also capture important features of seismicity. Simulation-based approaches to distributed seismicity are a promising path toward the formulation of physically plausible numerical models, which can reproduce realistic spatially and temporarily distributed synthetic earthquake catalogs. The objective of this chapter is to summarize the most important aspects of the occurrence of earthquakes and discuss them from the complexity theory point of view.