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

Abstract A new two‐step approach is proposed to quantify the uncertainties of the seismicity rate ν ( M ) estimated by Gutenberg–Richter (GR) 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 GR parameters α and β (or a and b ), expressed by their covariance matrix C ( α , β ) (or C ( a , b )), can be completely propagated to ν ( M ). In the second step, the resulting 1D 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 that exhaustively approximates the epistemic uncertainties of the seismicity rate.