On occurrence disaggregation of probabilistic seismic hazard

Abstract

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 (Formula presented.) 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 (Formula presented.) or (Formula presented.) conditional on the (Formula presented.) event, that is, (Formula presented.) or (Formula presented.). 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 (Formula presented.), with (Formula presented.) 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 (Formula presented.) is sought); (ii) (Formula presented.) is theoretically degenerate, and as such, its approximation via finite (Formula presented.) can lead to misleading results; (iii) if (Formula presented.) is chosen coherently with the discretization of the (Formula presented.) domain used in the hazard integral, it leads to approximated (Formula presented.), enabling the conclusion that (Formula presented.) occurrence disaggregation does not add information with respect to (Formula presented.) disaggregation.