A model of return intervals between earthquake events

Abstract

Application of the diffusion entropy analysis and the standard deviation analysis to the time sequence of the southern California earthquake events from 1976 to 2002 uncovered scaling behavior typical for anomalous diffusion. However, the origin of such behavior is still under debate. Some studies attribute the scaling behavior to the correlations in the return intervals, or waiting times, between aftershocks or mainshocks. To elucidate a nature of the scaling, we applied specific reshulffling techniques to eliminate correlations between different types of events and then examined how it affects the scaling behavior. We demonstrate that the origin of the scaling behavior observed is the interplay between mainshock waiting time distribution and the structure of clusters of aftershocks, but not correlations in waiting times between the mainshocks and aftershocks themselves. Our findings are corroborated by numerical simulations of a simple model showing a very similar behavior. The mainshocks are modeled by a renewal process with a power-law waiting time distribution between events, and aftershocks follow a nonhomogeneous Poisson process with the rate governed by Omori's law.