Capturing the Uncertainty of Seismic Activity Rates in Probabilistic Seismic Hazard Assessments

A new two-step approach is proposed to quantify the uncertainties of the seismicity rate ν(M) estimated by Gutenberg-Richter relations of seismic area source zones in logic tree-driven probabilistic seismic hazard analysis. The first step makes use of the possibility that the uncertainties of the Gutenberg-Richter parameters α and β (or a and b), expressed by their covariance matrix C(α, β) (or C(a, b)), can completely be propagated to ν(M). In the second step, the resulting one-dimensional probability distribution of ν(M) for any fixed magnitude M is approximated by a finite set of values and weights in a statistically optimal manner (Miller and Rice, 1983). The procedure yields a set of alternative recurrence models which exhaustively approximates the epistemic uncertainties of the seismicity rate. Introduction The estimation of the seismicity rates based on cataloged earthquake data is an essential prerequisite for any probabilistic seismic hazard analysis (PSHA). This step also requires the estimation of the uncertainties associated with these input data to quantify the resulting uncertainties in the hazard (Abrahamson and Bommer, 2005; Bommer et al., 2005). The subject of this paper is an improved statistical description of the uncertainties connected with the Gutenberg-Richter (GR) magnitude-frequency relation as the standard rate model of an area source zone in which it is assumed that the seismicity is uniformly distributed within the source area. The empirical relation of the total number of earthquakes equal and above magnitude M of a specific region observed in a fixed time period may be quantitatively described by (Gutenberg and Richter, 1944) ν(M) = ∫ M eα−βm dm (1) with activity and rate parameters α and β. With respect to hazard calculations, it is usually expressed by the equation