Local to moment earthquake magnitude conversion in mainland France and implications for seismic hazard assessment

Modern ground motion prediction equations used in probabilistic seismic hazard assessment studies are now almost exclusively expressed as a function of moment magnitude M_W. Yet, earthquake catalogues produced by seismic observatories often provide local magnitude M_L only. It is for instance the case for the Laboratoire de Détection Géophysique (LDG) catalogue recently published by Duverger et al. (2021) for mainland France. A conversion relationship was proposed by Cara et al. (2015) from M_L (LDG) to M_W. It appears however that this relationship does not result in a good fit when compared to recently compiled M_W values for France and neighboring areas (Laurendeau et al., 2020). In this work, we propose a new conversion relationship based on the inversion of M_L-M_W couples for events present in both the LDG catalogue and the compilation of Laurendeau et al. (2021). In order to avoid the choice of an arbitrary number of segments to model the M_W=f(M_L) relationship, the inverse problem is solved in a Bayesian framework by means of the reversible jump Markov chain Monte Carlo (rj-McMC) algorithm (Green, 1995; Bodin et al., 2012). The number of segments, as well as their respective slopes and intercepts, are jointly invert for. As moment magnitude uncertainty is not known, it is also considered as an unknown, while the M_L uncertainties provided in the LDG catalogue are fully accounted for by random sampling during the McMC process. We observe a geographical dependence of the differences between the available M_W values and those obtained from calculation so a location-dependent term is also modeled. This allows to account for the regional attenuation variations that can affect M_L estimates. The new conversion law is then applied to the full LDG catalogue and its impact on seismic hazard assessment is explored.