Poisson Behavior Leads to Bias When Testing for Periodicity in the Paleoseismic Record of Large Earthquakes

Abstract

Abstract A Poisson process giving rise to earthquakes that occur randomly in time has become a de facto null hypothesis when assessing the periodicity of large (Mw>∼6–7) earthquakes in the paleoseismic record. This implies an exponential distribution of inter-event times (IETs) and therefore an abundance of IETs that are very short relative to the mean value. As such, the Poisson model posits that large ruptures occurring in rapid succession should be relatively common. Below some threshold IET defined by site specific conditions, however, these short IET earthquakes are unlikely to be recorded as distinct events in the paleoseismic record. This article presents the results of simple Monte Carlo simulations that quantify the potential effects of truncation of short IETs on the apparent periodicity of large earthquakes generated by a Poisson process. Results indicate that this truncation effect results in chronologies that appear systematically more periodic than the original sequence of events. The magnitude of this discrepancy depends primarily on the ratio of the minimum preserved and mean IETs in addition to the number of events in the chronology. As such, previous statistical analyses that have assessed for periodicity in the paleoseismic record of large earthquakes likely incorporated a bias in favor of apparent periodicity by employing Poisson behavior as a null hypothesis. This bias can be corrected if the minimum preserved IET can be determined or reasonably assumed for a particular paleoseismic record or site.