A Note on Two Alternative Novel Probabilistic Approaches to Address Epistemic Uncertainty in Magnitude Frequency Distribution (MFD) Logic Trees

Abstract 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 magnitudes that are expected to occur on the seismic source. Eventually, the occurrence rates (or probabilities) of these magnitudes affect the exceedance rate (or probability) and the amplitude of the target ground-motion intensity metric (im), which is the essential product in PSHA. To this connection, proper portrayal of epistemic uncertainty in MFDs entails justifiable ground-motion amplitude exceedance distributions. In this paper, we propose two alternative novel approaches to account for the epistemic uncertainties in the modeling parameters of MFDs. Both approaches treat MFD model parameters as random variables (rvs) and describe their conditional probability distributions conditioned on seismic source activity to address their epistemic uncertainty. Although both approaches are tailored to structure a proper MFD logic-tree, they differ in the way they handle the conditional probabilities while delineating the epistemic uncertainty associated with each MFD model parameter. We first explain the theoretical background of these alternative methods, and then discuss their similarities (and differences) from a case study.