Probabilistic exposure model for earthquakes in Metropolitan France
(1) Corentin Gouache - Modelling, R&D Department, CCR
(2) Jean-Philippe Naulin - Modelling, R&D Department, CCR
(3) Pierre Tinard - Quotations Department and Cat Unit, CCR Re
(4) François Bonneau - RING, ENSG, GeoRessources, Université de Lorraine, CNRS, ASGA
(5) Julien Rey - Risks and Prevention Department, Seismic and Volcanic Risks Unit, BRGM
INTRODUCTION
In 2009, CCR began using the RiskLink software developed by RMS (Risk Management Solutions) to estimate probabilistic seismic losses on French territory, both in the Antilles and in mainland France. Since 2015, CCR has closely collaborated with BRGM, under a multiyear framework agreement, to develop its own deterministic seismic loss estimation model. Finally, from 2017 to 2021, the successive completion of an engineering internship and a doctoral thesis made it possible to work on a probabilistic seismic hazard model in Metropolitan France, leading to the creation in 2022 of a model to estimate earthquakeinduced insurance losses specific to CCR in mainland France.
METHODOLOGY
As with other hazards, the earthquake model is composed of three modules: (i) the hazard module, which characterises the intensity of the event, (ii) the vulnerability module, which determines the exposed assets and their ability to withstand a seismic load, and (iii) the damage module, which models the insurance losses resulting from an event.
The hazard module
The quantitative metric of seismic hazard used by CCR is represented by the Peak Ground Acceleration (PGA), which reflects seismically induced movements responsible for damage to structures. The hazard module consists in associating a probability of occurrence to a seismic hazard at each point in the territory.
To do so, CCR uses a stochastic generator of potential earthquakes simulating tens of thousands of years. This approach makes it possible to produce plausible realizations of French seismicity, not by reproducing past seismicity but by basing it on its characteristics. The first step is therefore to study past seismicity through seismotectonic zones within which seismicity and tectonics are considered uniform. On these regionalized data, the statistical relationships between the annual number and magnitude of earthquakes are analysed using the Gutenberg-Richter law [1]. This spatial footprint/ duration analysis only concerns earthquakes that are independent from each other. Aftershocks and precursor earthquakes are therefore identified and disassociated from the study catalogue using the Grünthal declustering algorithm [2]. Once the independent earthquakes have been generated using a non-uniform Poisson distribution, the aftershocks are (i) generated using the distribution of aftershock proportions as a function of magnitude obtained by the declustering algorithm and (ii) associated with their main earthquake using Bath’s law [3]. Finally, for a catalogue of 50,000 hypothetical years, for example, about 80,000 earthquakes of magnitude 4 and above are generated, i.e. 1.6 earthquakes per year, consisting of 62.5% in independent earthquakes and 37.5% in aftershocks. In a final step, the PGA produced by each hypothetical earthquake is calculated in terms of surface area. This is calculated using the following ground motion prediction equation [4]:
which takes as inputs, as a minimum, the magnitude (M) of the earthquake and the distance (D) between the earthquake surface rupture and the site on the surface. The PGA values are then transformed into macroseismic intensities (I). The relationship used between PGA and (I) is the following [5]:
In this study, each site is spaced at 250m intervals, which allows the production of a macroseismic intensity map at a resolution of 250m over the territory impacted by the earthquake.
The vulnerability module
The vulnerability module is based on insurance policies, including the physical characteristics of the associated buildings. For each policy, the macroseismic intensity values produced by the hypothetical earthquakes are recovered.
For earthquake risk, specific information such as building materials, height or age of buildings is obtained from the IGN’s BD Topo ® data. These physical characteristics make it possible to assign a vulnerability index (VI) to each building. This index describes the capacity of a building to resist a seismic shock: from 0 for an ‘invulnerable’ building to 1 for a building with no defence against seismic stress. A multi-year joint work programme with BRGM has made it possible to estimate specific vulnerability indices for the main types of French residential, commercial and industrial buildings [6]. These studies have been regionalised for residential buildings due to the variability of past construction practices in France. Then, a link between buildings and policies is made according to the geolocation quality of the policies and according to the type of risk, nature and use, to associate a VI index with each policy.
The damage module
The damage module consists in producing damage curves and then estimating the costs associated with a given event. This is done by defining the damage class (D). This class describes the damage suffered by a building, ranging from 0 for ‘no damage’ to 5 for ‘total destruction’. Once each policy has been characterised by a macroseismic intensity (I) specific to each earthquake of the probabilistic category and a vulnerability index (VI), the damage class of a policy (p) impacted by an earthquake (e) is defined as such [7]:
Damage curves are relationships between the damage class (D), the loss frequency (LF) and the destruction rate (DR). These relationships are established by type of risk, nature and use. For each policy (p), LF and DR are multiplied by the insured value (IV) of the policy, to estimate the costs incurred by an earthquake (e) on that policy such as:
RESULTS
To measure the relevance of the hazard, vulnerability and damage modules used in the CCR earthquake model, the costs caused by the three main earthquakes that have impacted Metropolitan France (since the Nat Cat compensation scheme was set up in 1982) are compared with those calculated by the model (Table 1).
Table 1 - Comparison of actual and simulated costs for three French earthquakes. Costs are shown in millions of euros 2021.
# earthquakes
# hazard
# vulnerability
# damage
# probabilistic
# metropolis
In this section, the term “costs” includes the costs of Nat Cat compensation for contents and containers of residential and professional (commercial, industrial, agricultural) buildings.
The results of the CCR earthquake model are close to the actual costs of the three earthquakes analysed. This observation is all the more encouraging as the Le Teil earthquake is difficult to simulate given its specific nature (very shallow depth). The costs of so-called historical earthquakes (pre-1982) were also estimated. This is the case, for example, of the Arette (1967) and Lambesc (1909) earthquakes, which were estimated at €178m and €1.5bn respectively.
As the model generates probable years of claims, it is possible to calculate the average annual cost as well as the costs associated with different return periods. The map shown in Figure 1 illustrates the departmental distribution of the average annual cost in Metropolitan France according to CCR’s earthquake model and based on CCR’s market portfolio. The most exposed regions are unsurprisingly the mountain ranges, especially the Western Pyrenees and the Northern Alps. More unexpectedly, the Rhône Valley and the central-western part of France are also quite exposed. This latter region corresponds to the SouthArmorican shear, linking the south of Brittany to the north-western border of the Massif Central. Conversely, a large part of the Aquitaine and Paris basins, which are known to be seismically inactive, are confirmed as being among the regions least exposed to seismic risk.
Figure 2 shows the earthquakes in volved in the costliest hypothetical year out of the 50,000 years generated. This year consists of a main earthquake in the Pyrenean foothills, followed by 26 aftershocks. The simulated costs at commune level for all these events are also illustrated. All these costs amount to more than €47bn. Although about 1,000 communes, spread over 5 departments, are affected by these earthquakes, the most affected region is located between Pau and Lourdes. The presence of many hypothetical earthquakes of varying strengths (magnitudes 4 to 6.2) near Pau, the agglomeration of which includes more than 200,000 inhabitants, explains the high costs simulated. The three most affected communes (> €1bn) are also part of the Pau agglomeration: Pau itself with more than €6bn of costs as well as Billère and Lons with just over €1bn each.
Figure 1 - Map of average annual costs obtained per department from the CCR earthquake model and based on CCR’s market view.
Figure 2 - Costs per commune generated by the twenty or so earthquakes that took place in the same hypothetical year according to CCR’s earthquake generator. This ensemble includes a main earthquake of magnitude 6.2 and its aftershocks, located along the fault (oriented NW-SE) associated with the main earthquake. The size and colour of the earthquakes represent the magnitude and costs of each event respectively.
THE PARTNERS
ASGA is French not-for-profit organisation. Created on 24 May 1955, its purpose is to promote teaching and research in the fields of Earth Science. ASGA has supported and managed the RING (Research for Integrative Numerical Geology) project since 1989. This project is supported by an international consortium of 10 industrial sponsors including CCR since 2018 and more than 140 academics. The consortium largely funds the RING research team of the Ecole Nationale Supérieure de Géologie (ENSG) in Nancy and the GeoRessources laboratory, the main supervisors of which are the University of Lorraine and the CNRS.
BRGM is a public organisation of an industrial and commercial nature which aims to understand geological phenomena and the associated risks in support of public policy on risk reduction and control. In addition to its fundamental research work, BRGM conducts a great deal of applied research in partnership with socio-economic players, including companies, in response to their needs, and in particular for many years in the field of natural risks with CCR.
CONCLUSION
The main components of the CCR model used to estimate the insurance costs related to earthquakes in Metropolitan France are presented in this article. The model is composed of (i) a hazard module generating tens of thousands of years of hypothetical and plausible seismicity and calculating the maximum ground accelerations associated with the hypothetical earthquakes, (ii) a vulnerability module based on built structures and local studies having allowed to specify its physical characteristics and finally (iii) a damage module producing damage curves by risk, nature and use from a reference and claims data. On average, at least one earthquake of magnitude 4 or greater is generated annually, which corresponds to the observations of instrumental seismicity on French territory over the last 50 years. Nevertheless, most of these earthquakes are of low to moderate magnitude (<4.5). The areas impacted by these weak earthquakes are small and the hazards produced are not high. As a result, very few of them ultimately result in damage.
This is consistent with the situation observed by the population in Metropolitan France, since the majority of earthquakes felt are not associated with any notable damage. The latest example is the earthquake near Mulhouse on 10 September 2022 with a local magnitude of 4.8. However, the model does not exclude the scenario where several strong earthquakes occur in the same year. If these earthquakes occur in densely populated areas, the damage to property over a year can amount to several billion euros. Several areas of improvement can be envisaged, such as considering faults in the location of hypothetical earthquakes [8] or the dynamic modification of vulnerability indices between the occurrence of a main earthquake and its aftershocks. Indeed, after the occurrence of an earthquake, the built structures are damaged, which tends to increase their original vulnerability. Beyond these improvements, a similar model is being developed for the French Caribbean territories. Finally, it is envisaged to develop a tsunami model specific to CCR which would be coupled with the seismic hazard module./
REFERENCES
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2. G. Grünthal, (1985) “The updated earthquake catalogue for the German democratic Republic and adjacent areas-statistical data characteristics and conclusions for hazard assessment”, presented at Proc. 3rd Int. Symp. On the Analysis of Seismicity and Seismic Risk, Liblice Castle, Czechoslovakia.
3. M. Båth, (Dec. 1965) “Lateral inhomogeneities of the upper mantle”, Tectonophysics, vol. 2, no 6, p. 483-514, doi: 10.1016/0040-1951(65)90003-X.
4. S. Drouet and F. Cotton, (2015) “Regional stochastic GMPEs in low-seismicity areas: Scaling and aleatory variability analysis—Application to the French Alps”, Bull. Seismol. Soc. Am., vol. 105, no 4, p. 1883-1902, doi:10.1785/0120140240.
5. C. B. Worden, D. J. Wald, T. I. Allen, K. Lin, D. Garcia, and G. Cua, (Dec. 2010) “A Revised Ground-Motion and Intensity Interpolation Scheme for ShakeMap”, Bull. Seismol. Soc. Am., vol. 100, no 6, p. 3083-3096, doi: 10.1785/0120100101.
6. J. Rey and P. Tinard, (2020) “Study carried out as part of BRGM’s 2019-2020 Public Service projects (CCR - BRGM Specific Implementation Agreement)”, p. 23.
7. Z. V. Milutinovic and G. S. Trendafiloski, (Sept. 2003) “WP4: Vulnerability of current buildings.”, RISK-UE, EVK4-CT-2000-00014. 8. C. Gouache, P. Tinard and F. Bonneau, (2022 ) “Stochastic Generator of Earthquakes for Mainland France”, Appl. Sci., vol. 12, no. 2, p.571, doi: 10.3390/ app12020571.
CITATION
Gouache et al, First probabilistic model of earthquake exposure in Metropolitan France. In CCR 2022 Scientific Report; CCR, Paris, France, 2022, pp. 10-13