Bayesian Analysis of a Probability Distribution for the Regional Intensity Attenuation

The regional intensity attenuation and its variation as a function of the distance and earthquake size is still a critical problem in the seismic hazard evaluations. We present a method that allows us to incorporate additional information of the historical earthquake felt reports in the probability estimation of the regional intensity attenuation. The approach is based on two ideas: a) standard intensity versus epicentral distance relationships constituite an unnecessary filter between observations and estimates; b) the intensity decay process is affected by many, not well known elements (physical parameters of the source, propagation path effects, building conditions, semi-qualitative character of macroseismic scales, etc.) and hence it should be treated as a random variable like the macroseismic intensity. We assume that the decay, defined on the set {0, 1,...,Io}, follows a binomial distribution with parameters (Io , p); p depends on the distance from the epicenter and is related to the probability of having null decay at that distance. According to the Bayesian approach this p parameter is, in its turn, a Beta random variable. The observations related to earthquakes with epicenter outside the area in exam, but belonging to homogeneous zones, are used as prior knowledge on the phenomenon, while the data points of the events inside the area are used to update the estimates through the posterior means of the quantities in interest. A detailed description of this methodology is given by applying it to the Umbria-Marche area, Central Italy. The data sets examined are the macroseismic intensity database DOM4.1 and the zonation ZS.4, both compiled by the Italian Group for the Defence against Earthquakes (GNDT). Moreover the method is validated comparing the observated and the estimated intensity data points of the Camerino (28/07/1799) and of the Colfiorito (26/09/1997) earthquake