# Stochastic Generator of Earthquakes for Mainland France
## 3 Application to Mainland France
### Data Used in This Study
#### 3.1.3. Faults  
For a first approximation, we propose building a spatial probability map (Figure 2) by using the CHARM database, [[https://infoterre.brgm.fr/page/telechargement-cartes-geologiques](https://infoterre.brgm.fr/page/telechargement-cartes-geologiques)]([https://infoterre.brgm.fr/page/telechargement-cartes-geologiques](https://infoterre.brgm.fr/page/telechargement-cartes-geologiques)) (accessed on 20 December 2021), produced by BRGM (Figure 6a). This database contains fault traces, i.e., intersection lines between faults and the Earth surface mapped on geological maps. The CHARM database is composed of 10,576 terrestrial fault lines covering the whole of mainland France and its vicinity (Figure 6a). As already stated in Section 2.1.2, we decide to consider all faults, regardless of their presumed importance and activity. This map of fault traces is converted into a density map by computing the average length of fault lines per unit area on a Cartesian grid of 5 km. The density map is illustrated in Figure 6b.  
Spatial distributions of past earthquakes (Figure 5) and fault traces (Figure 6) show the same trend. However, one can remark some differences between these two maps. For example, some moderate earthquakes have been observed in the north of Bordeaux, whereas no fault trace is visible nearby. These differences are explained by:  
* Unknown, e.g., [20], and/or new faults;
* The fact that the CHARM database only contains terrestrial fault traces, which means that covered, deep and/or bathymetric faults are missing;
* Very old faults that have probably been inactive for a long period of time (for example, Armorican Massif).  
In order to allow for the possibility of localizing main shocks anywhere [14; 15], thus avoiding specific cases, such as the one observed near Bordeaux, regions where no fault lines have been documented are associated with a minimal density value instead of 0. In this study, in the first instance, this minimal value is arbitrarily set to 1% of the maximal density value. In that sense, we consider that the least represented regions have a density that is 100 times lower than in most represented regions. Concretely, according to Figure 6b, every 5 \(\times\) 5 km cell characterized by a density value lower than \(\frac{0.34}{100}=0.0034\) is associated with this minimal value (0.0034). The cells concerned by this density modification represent around 15% of mainland France. It mainly concerns Parisian and Aquitaine basins (SCR), as well as the Mediterranean Sea (oceanic crust). This map is then transformed to a probability  
Figure 6: (**a**) Fault traces map of the French territory (CHARM database of BRGM). (**b**) Spatial density map of fault traces.  
map due to normalization. The final regionalized fault probability map is used as an input of the generator of earthquakes for mainland France (\"_Regionalized density map of faults depending on magnitude_\", Figure 1).  
Faults (Figure 6a) can also be employed to define the probability density functions (pdf) of azimuth in each region. Please refer to Appendix A for an application to mainland France.