Power-Law Time Distribution of Large Earthquakes

Abstract

We study the statistical properties of time distribution of seimicity in California by means of a new method of analysis, the Diffusion Entropy. We find that the distribution of time intervals between a large earthquake (the main shock of a given seismic sequence) and the next one does not obey Poisson statistics, as assumed by the current models. We prove that this distribution is an inverse power law with an exponent µ = 2.06 ± 0.01. We propose the Long-Range model, reproducing the main properties of the diffusion entropy and describing the seismic triggering mechanisms induced by large earthquakes. The search for correlation in the space-time distribution of earthquakes is a major goal in geophysics. At the short-time and the short-space scale the existence of correlation is well established. Recent geophysical observations indicate that main fracture episodes can trigger long-range as well as short-range seismic effects [1,2,3,4]. However, a clear evidence in support of these geophysical indications has not yet been provided. This is probably the reason why one of the models adopted to describe the time distribution of earthquakes is still the Generalized Poisson (GP) model [5,6,7,8,9]. Basically the GP model assumes that the earthquakes are grouped into temporal clusters of events and these clusters are uncorrelated: in fact the clusters are distributed at random in time and therefore the time intervals between one cluster and the next one follow a Poisson distribution. On the other hand, the intra-cluster earthquakes are correlated in time as it is expressed by the Omori's law [10,11], an empirical law stating that the main shock, i.e. the highest magnitude earthquake of the cluster, occurring at time t 0 is followed by a swarm of correlated earthquakes (after shocks) whose number (or frequency) n(t) decays in time as a power law, n(t) ∝ (t − t 0 ) −p , with the exponent p being very close to 1. The Omori's law implies [12] that the distribution of the time intervals between one earthquake and the next, denoted by τ , is a power law ψ(τ ) ∝ τ −p . This property has been recently studied by the authors of Ref.[12] by means of a unified scaling law for ψ L,M (τ ), the probability of having a time interval τ between two seismic events with a magnitude * Corresponding author: vito.latora@ct.infn.it larger than M and occurring within a spatial distance L. This has the effect of taking into account also space and extending the correlation within a finite time range τ * , beyond which the authors of Ref.[12] recover Poisson statistics.In this letter, we provide evidence of inter-clusters correlation by studing a catalog of seismic events in California with a new technique of analysis called Diffusion Entropy (DE) [13,14]. This technique, scarcely sensitive to predictable events such as the Omori cascade of aftershocks, is instead very sensitive when the deviation from Poisson statistics generates Lévy diffusion [14,15]. This deviation, on the other hand, implies that the geophysical process generating clusters ha...

Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation

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Conditions for the emergence of scaling in the inter-event time of uncorrelated and seasonal systems

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