A New Generation of Earthquake Recurrence Models Based on The Extreme Value Theory and Impact on Probabilistic Seismic Hazard Assessments

Probabilistic Seismic Hazard Analysis (PSHA) procedures require that at least the mean activity rate be known, as well as the distribution of magnitudes. Within the Gutenberg-Richter assumption, that distribution is an Exponential distribution, upperly truncated to a maximum possible magnitude denoted $m_{max}$. This parameter is often fixed from expert judgement under tectonics considerations, due to a lack of universal method. In this paper, we propose two innovative alternatives to the Gutenberg-Richter model, based on the Extreme Value Theory and that don't require to fix a priori the value of $m_{max}$: the first one models the tail distribution magnitudes with a Generalized Pareto Distribution; the second one is a variation on the usual Gutenberg-Richter model where $m_{max}$ is a random variable that follows a distribution defined from an extreme value analysis. We use the maximum likelihood estimators taking into account the unequal observation spans depending on magnitude, the incompleteness threshold of the catalog and the uncertainty in the magnitude value itself. We apply these new recurrence models on the data observed in the Alps region, in the south of France and we integrate them into a probabilistic seismic hazard calculation to evaluate their impact on the seismic hazard levels. The proposed new 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 for all frequencies below 10 Hz, mainly at the lowest frequencies and for very long return periods. To our knowledge, both new models have never been used in a probabilistic seismic hazard calculation and constitute a new promising generation of recurrence models.