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Authors: Mosca, I.* 
Console, R.* 
D'Addezio, G.* 
Title: Renewal models of seismic recurrence applied to paleoseismological data
Issue Date: 2007
Keywords: earthquake forecast
paleoseismological data
statistical tests
inter-event time
Subject Classification04. Solid Earth::04.06. Seismology::04.06.02. Earthquake interactions and probability 
Abstract: Because paleoseismology can extend the record of earthquakes back in time up to several millennia, it represents a great opportunity to study how earthquakes recur through time and thus provide innovative contributions to seismic hazard assessment. A worldwide compilation of a database of recurrence from paleoseismology was developed in the frame of the ILP project “Earthquake Recurrence Through Time”, from which we were able to extract five sequences with 6 and up to 9 dated events on a single fault. By using the age of the paleoearthquakes with their associated uncertainty we have tested the null hypothesis that the observed inter-event times come from a uniform random distribution (Poisson model). We have made use of the concept of likelihood for a specific sequence of observed events under a given occurrence model. The difference dlnL of the likelihoods estimated under two hypotheses gives an indication of which between the two hypotheses fits better the observations. To take into account the uncertainties associated to paleoseismological data, we used a Monte Carlo procedure, computing the average and the standard deviation of dlnL for 1000 inter-event sets randomly obtained by choosing the occurrence time of each event within the limits of uncertainty provided by the observations. Still applying a Monte Carlo procedure, we have estimated the probability that a value equal to or larger than each of the observed dlnLs comes by chance from a Poisson distribution of inter-event times. These tests have been carried out for a set of the most popular statistical models applied in seismic hazard assessment, i.e. the Log-normal, Gamma, Weibull and Brownian Passage Time (BPT) distributions. In the particular case of the BPT distribution, we have also shown that the limited number of dated events creates a trend to reducing both the observed mean recurrence time and the coefficient of variation for the studied sequence which can possibly bias the results. Our results show that a renewal model, associated with a time dependent hazard, and some kind of predictability of the next large earthquake on a fault, only for the Fucino site, out of the five sites examined in this study, is significantly better than a plain time independent Poisson model. The lack of regularity in the earthquake occurrence for three of the examined faults can be explained either by the large uncertainties in the estimate of paleoseismological occurrence times or by physical interaction between neighbouring faults.
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