# Stochastic Generator of Earthquakes for Mainland France
## 1 Introduction  
Mainland France seismicity is considered as low to moderate due to its high return periods and weak maximal magnitudes. Only a few earthquakes have produced damages in this territory since the introduction of the French insurance compensation system in 1982. The six major earthquakes occurring after 1982 resulted in less than EUR 600 M of insured losses, representing approximately 1.5% of the total amount compensated with this compensation scheme, [[https://catastrophes-naturelles.ccr.fr/](https://catastrophes-naturelles.ccr.fr/)]([https://catastrophes-naturelles.ccr.fr/](https://catastrophes-naturelles.ccr.fr/)) (accessed on 20 December 2021). Nevertheless, major earthquakes could strike this territory (e.g., Liguria in 1887, Basel in 1356) and create financial losses and casualties. For example, CCR (_Caisse Centrale de Reassurance_, French insurance company) and BRGM (_Bureau de Recherches Geologiques et Minites_, French geological survey) have quantified the probable insurance losses associated with historical earthquakes if they occurred in the present day:  
* Arette (1967): EUR 120-140 M [1];
* Lambesc (1909, last earthquake-related deaths): EUR 1.8-2.5 Bn [2];
* Marais vendeen (1799): EUR 1.5-2.3 Bn [3];
* Liguria (1887) localized in front of Nice [4]: EUR 9-13 Bn, [[https://catastrophes-naturelles.ccr.fr/documents/148935/368920/Bilan+Cat+Nat+1982-2020.pdf/22925938](https://catastrophes-naturelles.ccr.fr/documents/148935/368920/Bilan+Cat+Nat+1982-2020.pdf/22925938)]([https://catastrophes-naturelles.ccr.fr/documents/148935/368920/Bilan+Cat+Nat+1982-2020.pdf/22925938](https://catastrophes-naturelles.ccr.fr/documents/148935/368920/Bilan+Cat+Nat+1982-2020.pdf/22925938)) -97e6-4 ad4-dft6a-f47 aed6b31357=1623850155584 (accessed on 20 December 2021). It shows that estimating the seismic hazard and risk is necessary even in low-to-moderate seismic areas, since losses can be significant. The Probabilistic Seismic Hazard Assessment (PSHA) [5] is a group of methodologies that estimates seismic hazard in a probabilistic way using seismic, tectonic and geologic data, as well as their uncertainties. It leads to a measure of probabilities of exceedancefor different hazard levels (e.g., Peak Ground Acceleration) in a given site. The spatio-temporal analysis of past seismicity recorded in an area leads to distributions of the earthquake's occurrence and location that are the cornerstone of the PSHA. Traditionally, these distributions can be used in an integrative way [5] or as an input to constrain a stochastic generator of earthquakes [6]. The main advantage of the latter is to explicitly consider some synthetic seismic events that allow for the computation of the contributions of these earthquakes to the hazard evaluated at a given site. This aspect is useful in an insurance context and also makes it possible to link earthquakes to others hazards (e.g., [7] for tsunamis, [8] for liquefaction, [9] for landslides and so on). Regardless, this study only focuses on earthquakes. The PSHA process takes into account the spatio-temporal behavior of seismicity. To carry this out, three principal methods can be involved:  
* Homogeneous seismotectonic zones, hereafter called the zoning method [5]. Seismicity and tectonics are considered homogeneous within each zone. Seismic temporality is defined by computing a specific Frequency-Magnitude Distribution (FMD) in each zone. These zones are produced from various and complex data, such as seismic, geodesic and geologic ones, e.g., [10] (for France application);
* The smoothing method [11; 12]. FMD is computed smoothly in space based on the past seismicity;
* The active faults method, e.g., [13] (for recent California application). Each known active fault is analyzed in order to associate it with its own FMD. Each of these methods have drawbacks and advantages. These methods are classically used in parallel in order to take into account the advantages of each. Their application depends on the user's wishes and mainly on the studied region.