On occurrence disaggregation of probabilistic seismic hazard

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