Stress release model and proxy measures of earthquake size. Application to Italian seismogenic sources

• We examine a point process based on strain, moment, energy or scaled energy.
• Application to seismogenic sources of eight tectonically coherent Italian regions
• Time-dependent Gompertz distribution of the interevent times for retrospective test
• Prospective forecasting is shown for out-of-sample earthquakes from 2003 to 2012.
• Bayes factor and Ando & Tsay information criterion are used for model comparison.

This study presents a series of self-correcting models that are 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 carry out the analysis on a regional basis by subdividing the study area into eight tectonically coherent regions. In each region, we reconstruct the seismic history and statistically evaluate the completeness of the resulting seismic catalog. Following the Bayesian paradigm, we apply Markov chain Monte Carlo methods to obtain parameter estimates and a measure of their uncertainty expressed by the simulated posterior distribution. The comparison of the four models through the Bayes factor and an information criterion provides evidence (to different degrees depending on the region) in favor of the stress release model based on the energy and the scaled energy. Therefore, among the quantities considered, this turns out to be the measure of the size of an earthquake to use in stress release models. At any instant, the time to the next event turns out to follow a Gompertz distribution, 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 forecasting 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 dates of the earthquakes that occurred after the end of the learning catalog, in the 2003–2012 decade.