Recurrence Models based on Extreme Value Theory : Impacts on Probabilistic Seismic Hazard Assessments and Comparison with the Standard Approach

Probabilistic Seismic Hazard Analyses (PSHA) require that at least the mean activity rate be known, as well as the distribution of magnitudes. Within the Gutenberg-Richter assumption, the magnitudes follow an exponential distribution which is upperly truncated to a maximum possible magnitude denoted mmax. This parameter is often fixed from expert judgement under tectonics considerations, due to a lack of universal method.In this paper, we present two alternatives to the exponential distribution of the magnitudes, based on the extreme value theory and that don't require to fix a priori the value of mmax: the first model is based on a generalized Pareto distribution (GPD) to model the tail distribution of the magnitudes; the second model, the Randomized Gutenberg-Richter model, is a variation on the usual exponential distribution where mmax is randomized and follows a distribution defined from an extreme value analysis.We use the maximum likelihood estimates taking into account the time varying level of completeness of the catalog and the uncertainty in the magnitude value itself. We apply both modelizations to the Alps region. Then, we integrate the resulting magnitude-frequency relations into a probabilistic seismic hazard calculation to evaluate their impacts on the seismic hazard levels. These extreme-value-based recurrence models introduce a reduction of the seismic hazard level compared to the common Gutenberg-Richter model conventionally used for PSHA calculations. This decrease is significant mainly for long periods.