On Multisite Probabilistic Seismic Hazard Analysis

Seismic hazard assessment, in its classical format, models the stochastic process of occurrence of earthquakes causing the exceedance of ground-motion intensity measure (IM) thresholds at a specific site. This is because civil structures typically require probabilistic seismic hazard analysis (PSHA) for one location. On the other hand, there are cases in which it may be required to count the number of exceedances of a vector of IM thresholds at multiple sites over time. In these situations, in general, a form of stochastic dependence arises among the processes counting multiple earthquake exceedances of IM at the sites. The present study analyzes this dependence and shows how it is linked to the correlation among IMs at the sites in one earthquake. Indeed, it provides a formalization and derives closed-form solutions for multisite PSHA, showing that hazards at multiple sites are independent if and only if exceedances at the sites in one earthquake are mutually exclusive. The other key results of the work are: (1) probabilistically rigorous insights into the form of dependence among hazard at multiple sites are derived, and (2) it is shown that site-specific and multisite PSHA are unified, that is, how and why the latter is a special case of the former when only one location is considered. In addition, the applicative value of the formalization provided is illustrated by means of simple examples, including a loss assessment for a portfolio of structures and a hazard validation exercise.