Statistical Tests for Scaling in the Inter-Event Times of Earthquakes in California

TL;DR

This paper evaluates the validity of a scaling law for earthquake interevent times in Southern California, confirming the gamma distribution as a good model for most data sets through statistical tests.

Contribution

It applies and compares two statistical tests to validate the scaling law and gamma distribution model for earthquake interevent times in California.

Findings

The scaling law is supported by the Kolmogorov-Smirnov test.

The gamma distribution fits the rescaled inter-event times above 0.01.

Large data sets with magnitude > 2 show deviations from the model.

Abstract

We explore in depth the validity of a recently proposed scaling law for earthquake interevent time distributions in the case of the Southern California, using the waveform cross-correlation catalog of Shearer et al. Two statistical tests are used: on the one hand, the standard two-sample Kolmogorov-Smirnov test is in agreement with the scaling of the distributions. On the other hand, the one-sample Kolmogorov-Smirnov statistic complemented with Monte Carlo simulation of the inter-event times, as done by Clauset et al., supports the validity of the gamma distribution as a simple model of the scaling function appearing on the scaling law, for rescaled inter-event times above 0.01, except for the largest data set (magnitude greater than 2). A discussion of these results is provided.