On Uncertainties in Probabilistic Seismic Hazard Analysis

Abstract

Probabilistic seismic hazard analysis (PSHA) is, in essence, a method to deal with uncertainty, the importance of which justifies the use of a formal and rigorous background for its study. Therefore, the purpose of this paper is to contribute to the reflections on how to correctly handle uncertainty in PSHA. We start by studying the simplest case, a Poisson process in which only “aleatory” uncertainty exists; then, we remove the Poisson hypothesis and find expressions for the occurrence probabilities of earthquakes in given time frames for general non-Poisson processes. Later, we include a simple variety of epistemic uncertainty and show that the resulting process is not Poissonian anymore, so computation of probabilities has to be made taking into account this fact. Next, we give a rigorous rule to combine uncertainties of aleatory and epistemic origin, which gives reasonable criteria to decide whether the epistemic uncertainty is large or not. Also, we propose unambiguous guidelines to decide whether a particular class of uncertainty has to be included in the hazard calculations as epistemic or as aleatory. Finally, we discuss the problem of how our estimates could differ if we wrongly considered that our epistemic uncertainty is of aleatory nature, or vice versa.