Interevent Time Distribution in Seismicity: A Theoretical Approach

Abstract

This paper presents an analysis of the distribution of the time τ between two consecutive events in a stationary point process. The study is motivated by the discovery of unified scaling laws for τ for the case of seismic events. We demonstrate that these laws cannot exist simultaneously in a seismogenic area. Under very natural assumptions we show that if, after rescaling to ensure Eτ =1, the interevent time has a universal distribution F, then F must be exponential. In other words, Corral’s unified scaling law cannot exist in the whole range of time. In the framework of a general cluster model we discuss the parameterization of an empirical unified law and the physical meaning of the parameters involved.