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.

Scale-free distributions of waiting times for earthquakes

“…The prominent scale-free nature of the distributions in figures 5-11 reinforce the idea that seismic zones can be seen as critical systems (see [9][10][11][12]) using two observables which have not been previously studied, namely the aforementioned waiting times for magnitudes and depths.…”

“…The aforementioned definition waiting times is significantly different from similar ones used in the literature, see, e.g. [9][10][11][12], as we do not look at the time intervals elapsed between subsequent earthquakes, but focus on the time distance between a given trigger earthquake of magnitude M and the first subsequent earthquakes of magnitude larger than M+δ. Naturally, for δ=0 our results are similar to those previously reported in the literature, and exhibit very prominent scale-free distributions, but from the viewpoint of seismic risk assessment the interesting results are those for d ¹ 0.…”

Temporal distribution characteristics of earthquakes in Taiwan, China

“…They found that this method can obtain correct scale parameters regardless of whether it is a Gaussian process or when the variance is infinitely great. Since then, this method has been widely used to analyze temporal distribution of earthquakes in different regions (Jiménez et al, 2006;Zhou et al, 2016). Mega et al (2003) applied DEA to explaining the temporal distribution of different earthquake clusters in California from 1976 to 2002, and identified a correlation between earthquake clusters and subsequent clusters in California on a large temporal scale.…”