Toward an empirical ground motion prediction equation for France: accounting for regional differences in the source stress parameter

In low-to-moderate seismicity regions such as metropolitan France, characterized by limited strong-motion records in the magnitude-distance range of interest for seismic hazard assessment, the derivation of empirical ground motion prediction equations (GMPEs) is a major challenge. In this study, we take advantage of the RESORCE-2013 database (http://resorce-portal.eu/) that contains uniformly processed records for the Pan-European region including relevant number of French records. After discussing the metadata for French events and stations, we first derive a base-case GMPE that is used to investigate the within-event and between-event residuals. The short-period between-event residuals for French (and Swiss) events show larger variability with respect to larger magnitude events in other regions. We show that the between-event residuals are clearly correlated with the stress parameter and that such larger variability can be explained by accounting for stress-parameter scaling. We derive an empirical scaling of ground motion with stress parameter that is consistent across regions and with the scaling predicted by stochastic GMPEs. This suggests that the scaling of ground motion with stress parameter for a given magnitude is largely region independent whereas the absolute stress parameter values may vary regionally. Based on these results we propose to adopt the scaling model as a function of stress parameter and magnitude by Yenier and Atkinson (Bull Seismol Soc Am 105(4):1989-2009, 2015) by adapting the reference stress parameter to our target regions. By accounting for stress parameter scaling in the GMPE we reduce the between-event variability for French and Swiss small-magnitude events. Finally, we investigate the aleatory variability (sigma) of the GMPE and its components (tau, phi, phi(ss)). We propose a heteroscedastic sigma model to be used when the stress-parameter scaling is not considered in the GMPEs due to lack of information. If enough information on the stress-parameter is available the adjusted GMPE can be applied using a homoscedastic sigma. Despite using small events, the phi(ss) for French stations is found to be consistent with other studies and confirms the stability of phi(ss) across different regions and datasets.