A Bayesian methodology to update the Probabilistic Seismic Hazard Assessment

In this paper, we present a Bayesian methodology for updating the seismic hazard assessment (the seismic hazard curves) in a point of a geographical domain. The methodology is based on the comparison of predictive exceedance rates of a fixed acceleration level (given by the seismic hazard curves) and the observed exceedance rates in some selected sites. The application of the methodology needs, firstly, the definition of a prior Probabilistic Seismic Hazard Assessment (PSHA) based in a logic tree. In this article, we used the logic tree defined for a preliminary PSHA of SIGMA project. Each main branch corresponds to a probabilistic model of calculus of seismic hazard. The method considers that, initially (or a priori), the weights of all branches of the logic tree are equivalent. Secondly, the method needs to compile the observations in the region. They are introduced in a database (here called REX, Return of Experience) containing the recorded acceleration data (normally during the instrumental period). Nevertheless, the instrumental period in stable zones (as France) shows only very low acceleration levels recorded during a short period of observation. In this study, we present a method to enlarge the REX taking into account the historical data. This article presents an approach to define 'synthetic' accelerations in the sites of observation. The synthetic REX allows to expand the period of observation and to increase the acceleration thresholds used in the Bayesian updating process. The application of the Bayesian approach leads to a new and objective definition of the weights of each branch of the logic tree. The new weights of the branches (or posterior weights) are used to define new seismic hazard curves (mean, median and centile 15% and 85%). The Bayesian approach doesn't change the probabilistic models (seismic hazard curves). It only modifies the weights of each branch of the logic tee. Finally, we present some updates of the seismic hazard using the Bayesian methodology developed, the logic tree of SIGMA project (as prior model) and the REX defined. (authors)