Power of earthquake cluster detection tests

TL;DR

This paper examines the effectiveness of statistical tests in detecting non-Poissonian clustering in earthquake data, highlighting their limited power due to low event frequency and short catalogues.

Contribution

It introduces the analysis of test power for earthquake clustering detection, revealing limitations and providing a counterexample of a clustered process.

Findings

Current tests have low power to detect clustering in earthquake data.

Short catalogues and rare large events reduce test effectiveness.

A counterexample demonstrates the possibility of undetected clustering.

Abstract

Testing the global earthquake catalogue for indications of non-Poissonian attributes has been an area of intense research, especially since the 2011 Tohoku earthquake. The usual approach is to test statistically for the hypothesis that the global earthquake catalogue is well explained by a Poissonian process. In this paper we analyse one aspect of this problem which has been disregarded by the literature: the power of such tests to detect non-Poissonian features if they existed; that is, the probability of type II statistical errors. We argue that the low frequency of large events and the brevity of our earthquake catalogues reduces the power of the statistical tests so that an unequivocal answer for this question is not granted. We do this by providing a counter example of a stochastic process that is clustered by construction and by analysing the resulting distribution of p-values given by the current tests.