Renewal models for earthquake predictability

The new Database of Italy’s Seismogenic Sources (Basili et al. 2008) identifies areas with a degree of homogeneity in earthquake generation mechanism judged sufficiently high. Nevertheless, their seismic sequences show rather long and regular interoccurrence times mixed with irregularly distributed short interoccurrence times. Accordingly, the following question could naturally arise: do sequences consist of nearly periodic events perturbed by a kind of noise; are they Poissonian; or short interoccurrence times predominate like in a cluster model? The relative reliability of these hypotheses is at present a matter of discussion (Faenza et al., Geophys J Int 155:521–531, 2003; Corral, Proc Geoph 12:89–100, 2005, Tectonophysics 424:177–193, 2006). In our regions, a statistical validation is not feasible because of the paucity of data. Moreover, the classical tests do not clearly suggest which one among different proposed models must be favoured. In this paper, we adopt a model of interoccurrence times able to interpret the three different hypotheses, ranging from exponential to Weibull distributions, in a scenario of increasing degree of predictability. In order to judge which one of these hypotheses is favoured, we adopt, instead of the classical tests, a more selective indicator measuring the error in respect to the chosen panorama of possible truths. The earthquake prediction is here simply defined and calculated through the conditional probability of occurrence depending on the elapsed time t₀ since the last earthquake. Short-term and medium-term predictions are performed for all the Italian seismic zones on the basis of datasets built in the context of the National Projects INGV-DPC 2004–2006, in the frame of which this research was developed. The mathematical model of interoccurrence times (mixture of exponential and Weibull distributions) is justified in its analytical structure. A dimensionless procedure is used in order to reduce the number of parameters and to make comparisons easier. Three different procedures are taken into consideration for the estimation of the parameter values; in most of the cases, they give comparable results. The degree of credibility of the proposed methods is evaluated. Their robustness as well as their sensitivity are discussed. The comparison of the probability of occurrence of a Maw >5.3 event in the next 5 and 30 years from January 1, 2003, conditional to the time elapsed since the last event, shows that the relative ranking of impending rupture in 5 years is roughly maintained in a 30-year perspective with higher probabilities and large fluctuations between sources belonging to the same macro region.