Estimation of main shock frequency–magnitude distributions by adapting the inter-event time method for low-to-moderate seismicity areas: application to French mainland

Assessing seismic risk in low-to-moderate seismic activity areas like French mainland is a challenge. In these areas, the estimation of large earthquake hazard calls for models driven by sparse observation data and interpretative seismic knowledge. This leads models used in probabilistic seismic hazard assessment (PSHA) and declustering algorithms to large epistemic uncertainties that are overrepresented due to the large amount of parameters used in it. To concentrate epistemic uncertainties into one single method, we intend to limit the number of parameters under consideration by using the non-parametric inter-event time method. This method is empirical and needs a lot of data to be accurate. In the context of sparse large earthquake data, this paper proposes an implementation of the inter-event time method that ensures the stability of main shock proportions for sparse seismic data. We call this implementation magnitude of inferred main shock proportion (MIMP). This method is applied to the historical French seismic catalogue. We use a Monte Carlo Markov Chain to sample the whole space of magnitude uncertainties contained in this catalogue. We produce a set of equiprobable main shock proportion–magnitude and frequency–magnitude distributions. Results are discussed in the light of reference works published in the literature.