# Stochastic Generator of Earthquakes for Mainland France
## 5 Conclusions  
In this paper, a new generator of earthquakes is proposed and applied to mainland France. Applying a stochastic generator of earthquakes to a French context is not new (see, for example, Ref. [48] for a Pyrenean application). However, the method of generating synthetic seismicity is new. Classically, two methods exist to compute a Frequency-Magnitude Distribution (FMD) of main shocks: (i) smoothly through a kernel approach [11; 12] or (ii) discretely by using a zoning approach [5]. This allows us to analyze spatial and temporal behaviors of seismicity at the same time, but calls for data number reduction. In intraplate domains, i.e., far from tectonic plate boundaries, data are sparse. Thus, contrary to these classical approaches, the proposed generator uses a FMD of main shocks at a national scale in order to generate main shocks in time and magnitude in order to maximize the number of data available. These main shocks are then spatially distributed through the use of a probability map and regionalization. The former is used to guide the location of main shocks, whereas the latter allows us to limit the distribution of large earthquakes in space. Intraplate seismicity seems to be more uniformly positioned than in active regions [14; 15], structural inheritance _\"can play a strong role in deformation localization\"_[16] and stable faults' activity is difficult to define [21; 22; 23]. For these reasons, faults, regardless of whether they are supposed as active or not, are used to produce the probability map. Aftershocks are then produced by using the Bath law [28; 29], the seismic moment ratio [30] and the Proportion-Magnitude Distribution (PMD) of main shocks. This approach defines aftershocks and main shocks differently from the famous ETAS models. Nevertheless, it remains consistent, since the numbers of main shocks and aftershocks are complementary and depend on data. Moreover, unlike ETAS models, this approach has the advantage of being non-parametric. Temporal and energetic behaviors of generated main shocks are in line with inputs (FMD of main shocks and regionalization) and our knowledge of mainland France seismicity. However, some improvements can be achieved, such as completing the fault map; in particular, by bathymetric faults, and better describing maximal magnitudes in each region. Moreover, we have seen that using instrumental seismicity to produce the DPM of  
Figure 13: Number of aftershocks produced over 100,000 years by using the PMD estimated from the exhaustive historical French catalogue (FCAT-17). (**Left**): Number of main shocks and aftershocks as function of magnitude. (**Right**): Number of aftershocks produced by one main shock according to magnitude of the latter. Red line represents the regression of Equation (13) on these results: \(k=0.887\) and \(\alpha=0.331\). main shocks is not representative enough. Using the FCAT-17 historical French catalogue could be a solution, but it needs to be carried out with care due to its large uncertainties and its overestimation of magnitudes. Finally, the method proposed in this paper should be applied to other stable continental regions, such as Northwestern European countries, Australia and so on in order to test its effectiveness. Conceptualization, P.T., C.G. and F.B. ; methodology, C.G., P.T. and F.B. ; data curation, C.G. and P.T. ; writing--original draft preparation, C.G. ; writing--review and editing, C.G., F.B. and P.T. All authors have read and agreed to the published version of the manuscript. This work was performed in the frame of the RING and EXTRA& CO/ICEEL projects at Universite de Lorraine. It has been funded by Caisse Centrale de Reassurance (CCR). Not applicable. The authors declare no conflict of interest. The following abbreviations are used in this manuscript: