GNGTS 2016 - Atti del 35° Convegno Nazionale

GNGTS 2016 S essione 2.1 295 be larger than a given value. Unfortunately up to now no satisfactory analytical representation has ever been found to match real data distribution within its own error bars. For this reason the scientific community normally uses a poissonian distribution that gives constant probability and requires only one input parameter, the occurrence rate. We can however dispense with an analytical representation altogether and use an empirical distribution, based on a very large number of events, as long as it is representative of the one we are interested in. The big advantage is that a distribution based on a large number of events will be smooth enough to compute numerically stable derivatives, will need also in this case only a normalization factor based on the occurrence rate, and will allow for time-varying probabilities. The theoretical basis of our approach can be found in Corral (2005). This author noted that as time elapses from the previous event, the occurrence probability decreases. This finding is supported by the ISC-GEM catalog. This observation is the formalization of a well known fact, that is, that events clusterize and that the best way of predicting what will be the system behavior in the nearest future is just to look at what is presently occurring, that means the behavior is persistent. A notable example is the 1456 sequence or even more interesting the 1783 sequence in Calabria, or, always in Calabria, the occurrence of the 1905 Vibo and 1908 Messina earthquakes. Since that period, seismicity in that area has been absent. We used all the events reported in the CPTI catalog with the notable exception of the 1456 event where we preferred the solution proposed by Fracassi and Valensise (2007). These authors separate the event in three major episodes. Since there are only 80 events in this time window, including the August 24, 2016 one, we obtain a survival function that is very rough: it cannot be therefore used. Conversely the global data yields a smooth surviving function. Since the survival functions derived from the historical events entirely contains the modern global one, it is simply possible to substitute the latter to the former. In Fig. 1 we show the two survival functions compared to the Poissonian one. In all cases they have been normalized to the occurrence rate. This approach requires the occurrence rate only, exactly as the classical poissonian one. It however yields extremely different occurrence probabilities that can be even 10 times lower than those given by a Poissonian approach. The construction of the survival function requires the knowledge of the occurrence rate only. Its use however requires the knowledge of the timing of the last event. If this knowledge does not exist, we must assume that it is at least as big as the time window of completeness for that given magnitude. The rest of the seismic risk analysis can then be performed with the usual tools. Fig. 1 – Normalized survival functions for the historical data compared to that derived from the events reported in the ISC-GEM catalogue since 1960 for M>6 and for the Poissonian one.