The use of the possibility theory to investigate the epistemic uncertainties within scenario-based earthquake risk assessments

This paper presents a methodology to represent and propagate epistemic uncertainties within a scenario-based earthquake risk model. Unlike randomness, epistemic uncertainty stems from incomplete, vague or imprecise information. This source of uncertainties still requires the development of adequate tools in seismic risk analysis. We propose to use the possibility theory to represent three types of epistemic uncertainties, namely imprecision, model uncertainty and vagueness due to qualitative information. For illustration, an earthquake risk assessment for the city of Lourdes (Southern France) using this approach is presented. Once adequately represented, uncertainties are propagated and they result in a family of probabilistic damage curves. The latter is synthesized, using the concept of fuzzy random variables, by means of indicators bounding the true probability to exceed a given damage grade. The gap between the pair of probabilistic indicators reflects the imprecise character of uncertainty related to the model, thus picturing the extent of what is ignored and can be used in risk management.