ALBERT

Description: The societal importance and implications of seismic-hazard assessment forces the scientific community to pay increasing attention to the evaluation of uncertainty in order to provide accurate assessments. Probabilistic seismic hazard assessment (PSHA) formally accounts for the natural variability of the involved phenomena, from seismic sources to wave propagation. Recently, increased attention has been paid to the consequences of alternative modeling procedures on hazard results. This uncertainty, essentially of epistemic nature, has been shown to have major impacts on PSHA results, leading to extensive applications of techniques like the logic tree. Here, we develop a formal Bayesian inference scheme for PSHA that allows us, on the one hand, to explicitly account for all uncertainties and, on the other hand, to consider a larger set of sources of information, from heterogeneous models to past data. This process decreases the chance of undesirable biases and leads to a controlled increase of the precision of the probabilistic assessment. In addition, the proposed Bayesian scheme allows (1) the assignment of a subjective reliability to single models, without requirement of completeness or homogeneity, and (2) a transparent and uniform evaluation of the strength of each piece of information used on the final results. The applicability of the method is demonstrated through the assessment of seismic hazard in the Emilia–Romagna region of northern Italy. In this application the results of a traditional Cornell–McGuire hazard model based on a logic tree are updated with the historical macroseismic records to provide a unified assessment that accounts for both sources of information.

Description: 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 article, we explore in detail the reasons for this controversy regarding 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 call 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 within the scientific domain. Second, it provides a proper and clear description of the aleatory variability and epistemic uncertainty that can help stakeholders 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 too many branches.