The Weibull - Log Weibull Distribution for Interoccurrence Times of Earthquakes

TL;DR

This study analyzes earthquake interoccurrence times in Japan and finds that their distribution can be modeled as a combination of Weibull and log-Weibull distributions, revealing a transition in dominant statistical behavior.

Contribution

It introduces a combined Weibull-log Weibull model for earthquake interoccurrence times and demonstrates a transition in dominant distribution with increasing earthquake magnitude.

Findings

Large earthquakes follow Weibull distribution with exponent less than 1.

The ratio of Weibull to total distribution increases with magnitude threshold.

Interoccurrence times transition from log-Weibull to Weibull dominance.

Abstract

By analyzing the Japan Meteorological Agency (JMA) seismic catalog for different tectonic settings, we have found that the probability distributions of time intervals between successive earthquakes --interoccurrence times-- can be described by the superposition of the Weibull distribution and the log-Weibull distribution. In particular, the distribution of large earthquakes obeys the Weibull distribution with the exponent $\alpha_1 <1$, indicating the fact that the sequence of large earthquakes is not a Poisson process. It is found that the ratio of the Weibull distribution to the probability distribution of the interoccurrence time gradually increases with increase in the threshold of magnitude. Our results infer that Weibull statistics and log-Weibull statistics coexist in the interoccurrence time statistics, and that the change of the distribution is considered as the change of the dominant distribution. In this case, the dominant distribution changes from the log-Weibull distribution to the Weibull distribution, allowing us to reinforce the view that the interoccurrence time exhibits the transition from the Weibull regime to the log-Weibull regime.