# Stochastic Generator of Earthquakes for Mainland France
## 3 Application to Mainland France
### Data Used in This Study
#### 3.1.2 Seismic Catalogues  
The historical French catalogue FCAT-17 [33] is composed of 4250 earthquakes felt and reported by the French population from 463 to 1964. Despite being associated with large uncertainties, such a long catalogue is useful to define the maximal magnitude of the study (\(M_{max}\)) and per region (\(M_{max\,region}\)). In this study, we decide to select these maximal magnitudes as the maximum recorded magnitudes in the FCAT-17 catalogue, plus its uncertainty. The strongest earthquake of this catalogue occurred in Liguria in 1887, with a moment magnitude of 6.7 \(\pm\) 0.6. Thus, the maximal magnitude \(M_{max}\) is set to \(6.7+0.6=7.3\). Since this earthquake is localized in region 4 (compressional Alps, Figure 4), this region is characterized by a \(M_{max\,region}\) equal to 7.3. Table 1 summarizes the maximal magnitudes observed in each SHARE region.  
Consistent with the recent study [34], we consider that a seismic event with a magnitude of up to 5.5 can occur everywhere in France. As a result, the \(M_{max\,region}\) is raised to 5.5 if the estimation using the catalogue leads to a smaller value, which is the case for the OC region (n\({}^{>}\)2, Table 1). Maximal magnitudes are constant and, thus, their uncertainties are not explored in this paper.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Region** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline \(M_{max\,region}\) & 6.5 & 5.5 & 7 & 7.3 & 7 & 6.6 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Maximal magnitude \(M_{max\,region}\) of each region. Region numbers refer to Figure 4.  
Figure 4: SHARE tectonic regionalization [32] used in this paper. Regions 1 correspond to Stable Continental Regions (SCR). Region 2 represents the Oceanic Crust (OC). Regions 3 (Pyrenees) and 4 (Alps) represent compressional active shallow regions, whereas regions 5 (Rhine Basin) and 6 (Alps) correspond to extensional ones.  
This study uses both the instrumental French catalogue SIHex [35] and the ReNaSS catalogues, [[https://api.franceseismre.fr/fr/search](https://api.franceseismre.fr/fr/search)]([https://api.franceseismre.fr/fr/search](https://api.franceseismre.fr/fr/search)) (accessed on 20 December 2021). The former is composed of 37,408 earthquakes recorded between 1965 and 2009, whereas the latter regroups 25,042 seismic events indexed from 2010 to 2020. In total, the merged catalogue brings together 62,450 earthquakes that occurred during the 1965-2020 period.  
Such a catalogue isn't complete since the seismometers' number and resolution have improved over time. Also, the catalogue needs to be processed in order to reveal representative and meaningful information. The classical approach to make this catalogue exhaustive is to consider cut-off magnitudes (\(M_{c}\)) and years (\(Y_{c}\)). The catalogue can be considered exhaustive on a particular territory for earthquakes with a magnitude greater than or equal to \(M_{c}\) only during the period \(Y_{c}\)-2020. For the French territory, we determine \(M_{c}\) and \(Y_{c}\) thanks to the cumulative visual method [36; 37]. The couples of \(M_{c}\) and \(Y_{c}\) that we found are visible in Table 2.  
Figure 5 presents the spatial distribution of the 15,567 earthquakes \(M_{w}\geq 2\) contained in the instrumental catalogue. The strongest earthquake of this catalogue occurred near Arette in 1967, with a moment magnitude of 5.2 \(\pm\) 0.3.  
\begin{table}
\begin{tabular}{c c c} \hline \(M_{c}\) & **2–2.9** & \(\geq\)**3** \\ \hline Period & 1970–2020 & 1965–2020 \\ \hline \end{tabular}
\end{table}
Table 2: Periods of completeness in function of magnitude for the instrumental catalogue.  
Figure 5: SIHex and ReNaSS catalogues (1965–2020) used in this study to calculate the FMD of main shocks for the whole of mainland France. Only the 15,567 earthquakes with magnitudes greater than or equal to 2 are represented.