Strain-, moment- and energy-based self-correcting models for probabilistic seismic hazard analysis in Italy.

This study presents a series of self-correcting models that were obtained by integrating information about seismicity and fault sources in Italy. Four versions of the stress release model are analyzed, in which the evolution of the system over time is represented by the level of strain, moment, seismic energy, or energy scaled by the moment. We carried out the analysis on a regional basis by subdividing the study area into eight tectonically coherent regions. In each region, we reconstructed the seismic history and statistically evaluated the completeness of the resulting seismic catalog. The conditional intensity function that characterizes each self-correcting model was estimated following the Bayesian paradigm and by applying Markov chain Monte Carlo methods. In this way, we obtain not only the parameter estimates given by their posterior mean, but also a measure of their uncertainty expressed by the simulated posterior distribution. The comparison of the four models through the Bayes factor indicates overall significant, albeit to different degrees, evidence in favor of the stress release model based on the scaled energy. Therefore, among the quantities considered, this turns out to be the most appropriate measure of the size of an earthquake for use in stress release models. At any instant, the 'time to the next event' is the realization of a Gompertz distributed random variable with a shape parameter that depends on time through the value of the conditional intensity at that instant. In light of this result, the issue of the forecasting problem is tackled through both retrospective and prospective approaches. Retrospectively, the forecasting procedure is carried out on the occurrence times of the events recorded in each region, to determine whether the stress release model reproduces the observations used in the estimation procedure. Prospectively, the estimates of the time to the next event are compared with the date of the earthquakes that occurred after the end of the learning catalog. Four earthquakes of Mw at least 5.3 occurred in the 2003-2012 decade, excluding their aftershocks, and all of these fall within the 75% highest probability density intervals of the forecast.