Accounting for Epistemic Uncertainty in PSHA: Logic Tree and Ensemble Modeling

Abstract

Any trustworthy probabilistic seismic hazard analysis (PSHA) has to account for the intrinsic variability of the system (aleatory variability) and the limited knowledge of the system itself (epistemic uncertainty). The most popular framework for this purpose is the logic tree. Notwithstanding its vast popularity, the logic tree outcomes are still interpreted in two different and irreconcilable ways. In one case, practitioners claim that the mean hazard of the logic tree is the hazard and the distribution of all outcomes does not have any probabilistic meaning. On the other hand, other practitioners describe the seismic hazard using the distribution of all logic tree outcomes. In this paper, we explore in detail the reasons of this controversy about the interpretation of logic tree, showing that the distribution of all outcomes is more appropriate to provide a joined full description of aleatory variability and epistemic uncertainty. Then, we provide a more general framework - that we name ensemble modeling - in which the logic tree outcomes can be embedded. In this framework, the logic tree is not a classical probability tree, but it is just a technical tool that samples epistemic uncertainty. Ensemble modeling consists of inferring the parent distribution of the epistemic uncertainty from which this sample is drawn. Ensemble modeling offers some remarkable additional features. First, it allows a rigorous and meaningful validation of any PSHA; this is essential if we want to keep PSHA into a scientific domain. Second, it provides a proper and clear description of the aleatory variability and epistemic uncertainty that can help stakeholders to appreciate the whole range of uncertainties in PSHA. Third, it may help to reduce the computational time when the logic tree becomes computationally intractable because of the too many branches.