METHODOLOGY FOR THE REASSESSMENT OF MAGNITUDES ASSIGNED TO HISTORICAL EARTHQUAKES Cedric GIRY 1 , Yi ZHU 2 , Irmela ZENTNER 3 , Sophie CAPDEVIELLE 4 , Frederic RAGUENEAU 5 , Emmanuelle NAYMAN 6 ABSTRACT Since the end of nineteeth century, France has encountered several large earthquakes, however, the country faces, (1) the small amount of data and (2) uncertainties related to the macro-seismic intensity, as well as those related to the epicenter location. No considerable damage has been reported in historical documents found up to now. This work propose a re- evaluation of the intensity based on probabilistic method and structural analysis. The method is built on an approach initially proposed by Ryu and Baker, who applied Bayesian updating to re-evaluate magnitudes of earthquakes based on the distribution of the damage states of the building stock. Several structures in the area considered for this study, still existing nowadays, have experienced historical earthquakes. Among them, a statue has been selected to develop and illustrate the global method. Despite the lack of precise information regarding this structure, this choice is motivated by the relative simplicity of the structure and the possibility to consider model based on rigid-body motion. More particularly, this model of inverted pendulum proposed by Housner is used to investigate the response of the statue under the seismic loading. The different damage levels are defined in terms of amplitude of the rotation of the rigid-body, sliding or rocking. Despite its simplicity, this type of models gives sufficient information in order to compute fragility curve. Keywords: historical earthquakes; fragility curves; Bayesian actualization; inverted pendulum. 1. INTRODUCTION For about 40 years, having been started in support of the development of the nuclear industry in France, efforts have been jointly made by BRGM (Bureau de Recherche Géologique et Minière), EDF (Electricité de France) and IRSN (Institut de Radioprotection et Sûreté Nucléaire) to collect, compile, and distribute information related to historical events. The SISFRANCE macroseismic database contains 100,000 macroseismic observations (MSK intensity scale—Medvedev et al. (1967)) associated to 6000 earthquakes (AD463-2007). These Intensity Data Points (IDPs) are representative of earthquake effects in terms of damages and population perception at various localities. The descriptions of these effects, used to assess intensity values are collected from historical archives for each event. Epicentral location is determined and provided, together with the epicentral intensity value when possible (see Lambert et al. (2015) for epicentral location and intensity assessment explanations). IDPs are associated to quality factors that reflect confidence related to numerical value 1 Ast. Prof., LMT, ENS Cachan, CNRS, Université Paris-Saclay, 94235 Cachan, France, cedric.giry@ens-paris- saclay.fr 2 MSc, Eng., LMT, ENS Cachan, CNRS, Université Paris-Saclay, 94235 Cachan, France. 3 PhD, Eng., EDF R&D Lab Paris-Saclay. 91120 Palaiseau, France. irmela.zentner@edf.fr 4 PhD, LMT, ENS Cachan, CNRS, Université Paris-Saclay, 94235 Cachan, France. sophie.capdevielle@ens- paris-saclay.fr 5 Prof., LMT, ENS Cachan, CNRS, Université Paris-Saclay, 94235 Cachan, France. raguenea@lmt.ens- cachan.fr 6 Eng., EDF – DIPNN CEIDRE – TEGG, 13097 Aix-en-Provence, France. emmanuelle.nayman@edf.fr