A note on two alternative probabilistic methods to address parametric uncertainty in magnitude frequency distribution (MFD) logic trees (BEEE-D-22-00704)

The magnitude frequency distributions (MFDs) are one of the most important components of seismic source modeling in probabilistic seismic hazard analysis (PSHA). They describe the annual occurrence rates of ruptures that are expected to occur in the seismic source. Eventually, the occurrence rates (or probabilities) of ruptures affect the exceedance rate (or probability) and the amplitude of the target ground-motion intensity metric, which is the essential product in PSHA. To this connection, proper portrayal of parametric uncertainty in MFDs entails justifiable ground-motion amplitude exceedance distributions. In this paper, we propose two alternative approaches to account for the parametric uncertainties in the modeling of MFDs. Both approaches treat MFD model parameters as random variables and describe their conditional probability distributions conditioned on seismic source activity. Although both approaches are tailored to structure a proper MFD logic-tree, they differ in the way they handle the conditional probabilities to delineate the parametric uncertainty associated with each MFD model parameter. We first explain the theoretical background of the alternative methods, and then discuss their similarities (and differences) from a case study.