On occurrence disaggregation of probabilistic seismic hazard

Disaggregation of probabilistic seismic hazard allows to quantify how much one or more earthquake scenarios contribute to the occurrence [exceedance] of a ground motion intensity measure threshold of interest (x) at the construction site. The scenario is usually defined in terms of magnitude (M), source-to-site distance (R), and possibly includes the standardized residual (ε) of the ground motion model considered in the hazard analysis. Analytically, in case occurrence is of interest, disaggregation provides the joint probability density function of or conditional on the event, that is, or . Occurrence disaggregation is important for a number of earthquake engineering applications, and it is typically addressed in the literature in an approximated manner, considering as the conditioning event , with being an arbitrary finite width of the interval. This short communication undertakes a deeper examination of occurrence disaggregation clarifying that: (i) no approximation is needed in the case of disaggregation in terms of magnitude and distance (i.e., when is sought); (ii) is theoretically degenerate, and as such, its approximation via finite can lead to misleading results; (iii) if is chosen coherently with the discretization of the domain used in the hazard integral, it leads to approximated , enabling the conclusion that occurrence disaggregation does not add information with respect to disaggregation.