Comparing alternative models for multisite probabilistic seismic risk analysis

The risk assessment for a building portfolio or a spatially distributed infrastructure requires multi-site probabilistic seismic hazard analysis (MSPSHA). In fact, MSPSHA accounts for the stochastic dependency between the ground motion intensity measures (IMs) at the sites. Multi-site hazard needs to define the correlation structure for the same IM at different sites (spatial correlation), that of different IMs at the same site (cross-correlation) and that of different IMs at different sites (spatial-cross-correlation). Literature shows that such models usually require a significant amount of regional data to be semi-empirically calibrated. An approximated yet simpler-to-model alternative option is the conditional-hazard approach. The latter, originally developed for single-site analyses as an alternative to vector-valued PSHA, allows computing the distribution of a secondary IM given the occurrence or exceedance of a value of a primary IM. Conditional hazard considers the spatial correlation of the primary IM and the cross-correlation at each site for the two IMs, thus, if it is adopted for MSPSHA, the spatial correlation of the secondary IM as well as the spatial-cross-correlation between the two IMs descends from these two models. In the study, the conditional hazard procedure for MSPSHA is discussed and implemented in an illustrative application. Results in terms of distribution of the total number of exceedances of selected thresholds at the sites in a given time interval are compared with the case of complete formulation of MSPSHA and the differences are quantified. It appears that conditional hazard is a solid, yet simpler alternative for MSPSHA, at least in the considered cases.