FMHex20: An earthquake focal mechanism database for seismotectonic 1 analyses in metropolitan France and bordering regions

1 Abstract 19 We present a compilation of over 1700 focal mechanisms for nearly 1300 earthquakes in 20 metropolitan France and bordering regions of Western Europe. It is based on both 21 published and unpublished sources (articles, reports, observatory websites) for which the 22 focal mechanism solutions have been verified for internal consistency, corrected in cases of 23 minor errors and rejected in cases of major inconsistencies between the parameters. The 24 database, labeled FMHex20, is a first version and should be regularly updated in the future 25 as part of an ongoing effort within the Seismicity Transverse Action of the French Résif 26 research infrastructure. We also present first-order seismotectonic analyses for the whole 27 metropolitan France and for two regions (Western France and Northern Alps-Jura-Vosges)


Introduction 7
The characterization of earthquake sources using focal mechanisms -also called fault 8 plane solutions -is concomitant with the development of modern seismology in the 1950s 9 and the installation in the 1960s of the World-Wide Standardized Seismograph Network that 10 allowed computations of focal mechanisms for large earthquakes everywhere on the globe 11 (e.g., Byerly and Stauder, 1958;Stauder, 1962). These proved an important dataset in the 12 development of the Plate Tectonics framework (Sykes, 1967). Since then, earthquake focal 13 mechanisms are used in most studies of active tectonics, from individual fault mechanics to 14 regional dynamics (e.g., Hardebeck and Michael, 2004;Stich et al., 2006), including in the 15 construction of seismotectonic models for seismic hazard assessments (e.g., Cushing et al., 16 2007;Vanneste et al., 2013). We first present in Section 2 a short review of previous studies that illustrate the 25 current knowledge on focal mechanisms and state of stress in France, with a description of 26 the main limitations on focal mechanism estimations. The FMHex20 database is described in 27 Section 3, including the presentation of the sources, database format and processing. In 28 particular, we present the procedures used for identification and correction of erroneous 29 data, and for estimating the variability between multiple mechanism solutions for the same 30 In parallel, since the 1980s -1990s several global and regional projects, such as the 23 European-Mediterranean Regional Centroid Moment Tensor Catalog (Pondrelli et al., 2002), 24 determine focal mechanisms and Mw magnitudes for moderate to large earthquakes (Mw ≥ 25 4.0-5.0) using time-domain moment tensor inversion of teleseismic and regional 26 waveforms. Owing to the deployment of national broadband networks in the early 2000s, 27 this methodology can be applied for smaller magnitudes (Mw ≥ 3.0-3.5). For earthquakes in 28 France and neighboring regions, computations of moment tensors are performed 29 automatically by regional and national observatories (Delouis, 2014;Rueda and Mezcua, 30 mix of strike-slip and shortening deformation in the French and Swiss foreland. The 23 minimum (resp. maximum) horizontal stress rotates with the Alps curvature in the 24 extension (resp. shortening) domains (Delacou et al., 2004;Kastrup et al., 2004;Sue 25 et al., 1999). 26 • Southwestern Alps and Ligurian Sea: Complex deformation pattern with short spatial 27 variations including extension in the inner (highest topography) region and 28 shortening in the Provence and Italian forelands and the Liguria and Corsica-Sardinia 29 margins (Baroux et al., 2001;Eva et al., 1997;Larroque et al., 2009;Larroque et al., 30 2016). 31 • Pyrenees: Overall orogen-normal extension with lateral variations from transtensive 1 deformation in the East to a mix of extension and local shortening in the West. The 2 minimum principal stress (s3) is horizontal and oriented in the NE-SW quadrant 3 (Chevrot et al., 2011;Rigo et al., 2015;Sylvander et al., 2008). 4 Several limitations are associated with regional focal mechanism studies. The most 5 significant source of uncertainty for these small-to moderate-magnitude earthquakes is the 6 spatial distribution of local and regional seismometers. For earthquakes of magnitude M ≈ 7 2-4, first-motion polarities can only be derived for epicentral distances up to ca. 100-300 8 km, which strongly limits the number and spatial distribution of useable seismic stations. 9 This issue is especially important for earthquakes near network borders, such as along the 10 Atlantic or Mediterranean margins. It can result in focal mechanisms computed with a small 11 number of polarities (less than 10-15 readings) and azimuthal gaps leading to an incomplete 12 sampling of the focal sphere (Amorèse et al., 2000). The second major source of uncertainty 13 is the seismic velocity model, which impacts both the hypocenter locations and the seismic 14 ray takeoff angles. The impact of the velocity-model uncertainty and spatial variability on 15 focal mechanism computation can be tested to estimate the resulting variability in the 16 mechanism parameters (Amorèse et al., 2000;Mazabraud et al., 2005;Scognamiglio et al., 17 2016) but, in practice, this source of uncertainty is commonly underestimated (Hardebeck 18 and Shearer, 2002). 19 In our database, as in other compilations, the heterogeneity of the models and 20 parameters used to compute the focal mechanisms represent an important limitation. 21 Solutions from different studies are based on different velocity models and seismometer 22 networks, leading to different biases on the focal mechanisms that cannot be fully 23 evaluated without recomputing all mechanisms with the same models and parameters. In 24 some cases, the compatibility between different analyses can be estimated, to a first order, 25 by comparing the velocity models and seismometer networks used in each study, but this 26 information is not always reported with the adequate level of detail. This issue is particularly 27 true for the FMHex20 database, which compiles tens of different sources, published and 28 unpublished, over a 30-year period during which the seismic networks and knowledge of 29 the crust and mantle velocity structure have strongly evolved. We partly discuss this 30 limitation in Section 3.2 where we compare multiple solutions from different studies of the 31 below). 23 A validation procedure is applied to ensure the internal consistency of the focal 24 mechanism parameters and add missing values when needed. The procedure uses the RFOC 25 package (Lees, 2018) of the R software (R Core Team, 2019) for computation of the 26 parameters. For each solution, the azimuth, dip and rake of the second nodal plane and the 27 azimuths and dips of the P and T axes are computed using the first nodal plane parameters. 28 The computed values are compared to the original ones and the latter are corrected for 29 discrepancies (differences larger than 1 degree) that can be associated with rounding or 30 typographical errors on one or two parameters. The original parameter values are reported 31 in the "Comments" column of the table. Several original solutions involving numerous 1 parameter inconsistencies were noted and excluded from the database as no simple 2 correction could be applied. 3 In a second phase, all solutions are associated to a unique earthquake number (N) 4 and matched to events in the SI-Hex instrumental catalogue (Cara and al, 2015) when 5 possible. This stage involves identifying multiple solutions for the same earthquake, with a 6 level of uncertainty related to small differences in the original earthquake location 7 parameters. The number of different focal mechanism solutions per earthquake is shown in 8 Figure 2. Out of the 1290 individual earthquakes, over three quarters (1006) are associated 9 with a single solution. Double and triple solutions are the next most frequent (resp. 186 and 10 65 earthquakes). Earthquakes with 4-9 different solutions only account for a few tens of 11 events. 12 13

Multiple mechanism solutions 14
Measuring the compatibility between different focal mechanisms is not a 15 straightforward process. Several approaches exist ranging from graphical comparison by 16 superposition of the focal mechanism representations (Amorèse et al., 2000) to geometric 17 comparison of the full moment tensors (Tape and Tape, 2012). In FMHex20, comparisons 18 based on full moment tensors would not be effective because the vast majority of solutions 19 are double-couple mechanisms. In order to estimate the compatibility between multiple 20 mechanisms for a given earthquake, we use an approach based on the angular differences 21 between the P (and T) axes of the compared mechanisms. The angular difference between 22 two axes can vary between 0° (identical vectors) and 90° (orthogonal vectors, maximum 23 incompatibility). 24 For each earthquake associated with multiple solutions, we compute the average P 25 (and T) axis angle between a given solution i and the others: where N is the number of solutions for the selected earthquake, and Pi and Pj are the P axis 1 vectors (in Cartesian coordinates) for the i th and j th solutions (a similar equation is used for 2 the T axis angle). For earthquakes associated with only two solutions, the average angular 3 differences are the same for each solution (diffP1 = diffP2, diffT1 = diffT2) and simply 4 correspond to the difference between the two mechanisms. For earthquakes with more 5 than two solutions, the angular differences of each solution are the average differences with 6 all the others. 7 For all earthquakes associated with multiple solutions, 50% of the P and T angular 8 differences are smaller than 22°, 25% are smaller than 11° and 25% are larger than ca. 40°. 9 for all four solutions, indicating a reasonable agreement in the P axis azimuths and dips. In 12 contrast, the T axis angular differences are significantly larger (diffT ≈ 25-50°) due to the 13 strong disagreement of solution #4 with the other three (Figure 3a). In comparison,14 earthquake N = 272 (1985/01/04) has large angular differences (30-70°) for both P and T 15 axes, reflecting the poor agreement between all solutions except the first two and the fact 16 that solutions #3 and #4 are almost diametrically opposite to each other (Figure 3b). 17 These angular differences do not provide information on the "right" or "preferred" 18 solution for earthquakes with multiple mechanisms. Only a reanalysis of the signal polarities 19 and the focal mechanism solutions with their specific locations and velocity models would 20 allow discussing their respective quality. However, the angular differences can serve as 21 guidelines when using the database for seismotectonic studies, considering that an 22 earthquake associated with multiple solutions that strongly disagree (differences over 40-23 50°) should be probably viewed as poorly constrained (unless discussed in the original 24 source). It is worth noting that the opposite may not be true: multiple solutions that 25 strongly agree are not necessarily an indication of robust mechanisms but may simply be 26 due to mechanism inversions performed with the same data and parameters. 27 28 4. Regional seismotectonics 29 In this section, we present short analyses of the FMHex20 database at national and 1 regional scales in order to illustrate how it can help constrain seismotectonic models and 2 seismotectonic zonations for seismic hazard studies. These first-order analyses are based on 3 statistical and spatial distributions of the focal mechanism parameters and comparisons 4 with additional data. 5 In particular, we compute spatial averages of the faulting styles, orientations of the 6 near-horizontal P axes and orientations of the near-horizontal T axes on a regular grid of 7 spacing d (in km): At each grid point, the averages and standard deviations of these three 8 indicators are computed using all mechanisms within a distance d of the grid point, 9 providing there are at least Nmin mechanisms available (grid points with less than Nmin 10 mechanisms within ± d km are left empty). For the P and T axes orientations, the means and 11 standard deviations are computed for a circular distribution modulo 180° using only near-12 horizontal axes (dip ≤ 25°). For the faulting style, each focal mechanism is associated with a 13 scalar value S (-1 ≤ S ≤ 1) based on its rake r: styles vary over short distances (e.g., Delacou et al., 2004). 25 A weighting scheme is used in the computation of the grid averages in order to 1 ensure that (1) all earthquakes have the same weight, including those with multiple 2 mechanism solutions, and (2) multiple mechanisms for the same earthquake are weighted 3 based on their compatibility with the others: 4 • for earthquakes with only one solution, the mechanism has a weight w = 1; 5 • for earthquakes with two solutions, both mechanisms have a weight w = 0.5; 6 • for earthquakes with more than two solutions, each mechanism has a weight w 7 ∝ 1 / DiffP + 1 / DiffT (normalized so that the sum of all weights equals 1). 8 As an example, earthquake N150, 1980/07/16 (Figure 3a) is associated with four 9 mechanism solutions of faulting styles S = (0. 75, 0.74, 0.71, 0.14) and weights w = (0.31, 10 0. 31, 0.20, 0.18), representing the strong similarity of the first two mechanisms versus the 11 dissimilarity of the third and fourth relative to the others. As a result, the first and second 12 mechanisms contribute nearly 2/3 of the weight for this earthquake and the average style is 13 S = 0.62. 14 15

Metropolitan France 16
The FMHex20 database is shown for the whole metropolitan diameter, in order to highlight significant regional-scale tectonic variations (e.g., inner Alps 23 vs. Alpine foreland distances ca. 50-150 km), while smoothing out the short-scale variability 24 associated with specific faults and structures (few 10s km). 25 Average faulting styles in France vary mostly between strike-slip and normal ( Figure  26 4b). Over two thirds of the distribution correspond to S ≤ 0, with 28% of S ≤ -0.25 (i.e., 27 transtensive to normal). In contrast, transpressive to reverse styles (S ≥ 0.25) represent only 28 12% of the distribution and are limited to a few areas in western France, the Ardennes, the 29 Alpine forelands and the Ligurian Basin. It is important to note that the grid averaging tends 1 to limit the expression of extreme values (S ≈ -1 or S ≈ 1), especially when very different 2 faulting styles are included in a grid-point computation (this is directly related to the 3 difficulty of defining an average faulting style in cases where normal and reverse 4 mechanisms coexist within a few tens of kilometers). In Figure 4b, the symbol sizes provide 5 a measure of the compatibility of the mechanisms used in the averaging. The smallest 6 symbols correspond to grid points for which the standard deviation of the individual 7 mechanism styles is larger than 0.5, indicating very different mechanisms and an average 8 value that should be analyzed with care before interpretation. 9 The average orientations of the near-horizontal P and T axes show a strong 10 clustering in the NW-SE and NE-SW quadrants, respectively (Figures 4c and 4d). Half of the 11 average P axes are oriented N135° ± 30° (SE) whereas only 10% are N45° ± 30° (NE). The 12 clustering is slightly stronger for the average T axis orientations, with more than half (56%) 13 oriented between N45° ± 30° (NE) and only 4% between N135° ± 30° (SE). These overall 14 orientations are consistent with the general pattern of maximum and minimum horizontal 15 compressive stresses (sH and sh) evidenced by in-situ stress data, which indicate average 16 orientations of sH (resp. sh) about NW-SE (resp. NE-SW) for France and most of Western 17 Europe (Paquin et al., 1978;Heidbach et al., 2018;Müller et al., 1992). can be related to first-order plate tectonic processes, described either in terms of boundary 24 forces such as the mid-Atlantic ridge push and Nubia-Eurasia collision resistance (Gölke and 25 Coblentz, 1996) or in terms of gravitational potential energy from the topography, crust and 26 lithosphere density structures (Camelbeeck et al., 2013;Maury et al., 2014). The 27 reconstitution of local and regional stress from brittle deformation in the European Platform 28 further suggests that this overall NW-SE compression may exist since the Late -Post 29 Miocene period (ca. 4-7 Ma), at least along and near the Alpine Arc (Bergerat, 1987). 30 Regional variations exist within this overall deformation pattern, such as in southern 1 Western Alps -Provence region where the near horizontal P-axis orientation remains 2 roughly N-S over the whole area whereas the faulting style switches from reverse to normal 3 over ca. 100 km (Figures 4b and 4c). Interestingly, this focal mechanism P-axis orientation is 4 consistent with horizontal compression derived from Post Miocene fault data in Provence 5 but not in the southern Western Alps (Bergerat, 1987), suggesting the possibility of a 6 present-day forcing mechanism different from plate tectonics in the latter region. 7 In-depth regional analyses are beyond the scope of this article and would require 8 several specific tasks such as detailed examinations (and potential new computations) of the 9 focal mechanism solutions in order to identify preferred solutions, comparisons with 10 independent data (e.g., local faults, geodetic strain rates), etc. However, we present in the 11 next sections two first-order examples of how focal mechanism analyses can be used to help 12 constrain seismotectonics for seismic hazard zonation in a context of relative data paucity 13 (Western France and Brittany) and for regional tectonics and geodynamics in a case of high 14 data density (example of the Jura-Vosges region). Additional figures and maps are also 15 provided for other regions of metropolitan France (cf. Figure 4a)

Western France 19
As reviewed in Section 2, the general deformation and stress pattern in Western 20 France (Armorican Massif, Normandy, northwestern Massif Central, cf. Figure 4) has been 21 characterized in previous studies as a mix of extension and strike-slip deformation regimes, 22 with a maximum horizontal compressive stress oriented NW-SE to NNW-SSE (Amorèse et 23 al., 2000;Delouis et al., 1993;Mazabraud et al., 2005). This pattern is also evidenced in the 24  ). The P and T axis distributions confirm this concentration of normal to strike-slip 30 mechanisms with over two thirds of the T axes near-horizontal (dip ≤ 25°) and oriented ca. 1 N065°, whereas the P axes vary between horizontal and vertical with a mean orientation ca. 2 N122° (Figures 5b and 5c). 3 For this regional application (and that in Section 4.3), we fix the averaging distance 4 to d = 25 km (Nmin = 2) in order to provide the highest resolution on spatial variability of the 5 deformation styles, while still smoothing out short-scale noise due to individual focal 6 mechanisms. This choice of distance is somewhat arbitrary, but owing to the smoothing 7 effect of the method, results based on distances d = 10 -30 km show similar patterns. The 8 spatial distribution of grid averages indicates significant local variations within the overall 9 regional pattern (Figure 6). In particular, the area on the south side of the southern branch 10 of the South Armorican Shear Zone appears to be dominated by transpressive deformation 11 and stands out in contrast with areas to the south and north, which are consistent with the 12 general transtensive to normal styles (Figures 6a and 6b). A pocket of local reverse faulting 13 exists in southern Cotentin. In both cases, these local faulting styles are constrained by a 14 small number of mechanisms (15 and 3, respectively) and would require more detailed 15 analyses of individual mechanism solutions to establish their robustness. Similarly, the area 16 between Anger and Poitiers is associated with near-horizontal P and T axis orientations that 17 are nearly orthogonal to the general trends (Figures 6c and 6d). This observation is also 18 based on few mechanisms and should be confirmed by further investigation. 19 These simple observations can form the basis of a regional seismotectonic model in 20 which the whole region is dominated by a large-scale stress pattern with a minimum 21 horizontal compressive stress sh oriented about NE-SW and corresponding to the smallest 22 principal stress s3. Under this stress pattern, preexisting faults, including but not limited to 23 those associated with the South Armorican Shear Zone, tend to be reactivated in a mix of 24 strike-slip and normal faulting (with permutations of the two largest principal stresses s1 25 and s2 between horizontal and vertical along a NW-SE orientation). This overall system 26 accommodates a general NE-SW extension or transtension (Figure 6). However, a few 27 complex cases may exist, in which the same preexisting structures and faults are locally 28 reactivated in a mix of strike-slip and reverse faulting under variations of local stresses, 29 including drastic permutations between the maximum and minimum horizontal stresses. 30 These smaller areas could be identified as independent seismotectonic zones for seismic 31 hazard analysis (e.g., the elongated zone south of the South Armorican Shear Zone, Figures  1   6a and 6b). 2 3

Northern Alps-Jura-Vosges 4
In FMHex20, the Northern Alps-Jura-Vosges region (cf. Figure 4) comprises 501 focal 5 mechanism solutions for 364 individual earthquakes (1954 to 2018, magnitudes 1.7 ≤ Mw ≤ 6 5.5). The majority of earthquakes is associated with strike-slip to normal faulting styles, with 7 less than 10% of the solutions indicating reverse faulting (Figure 7a). The P and T axes also 8 show strong concentrations, with T axes mostly horizontal (dip ≤ 25°) with a mean 9 orientation ca. N065° and P axes varying between horizontal and vertical along a mean 10 orientation ca. N133° (Figures 7b and 7c). This general pattern is consistent with previous 11 studies based on subsets of the FMHex20 database (Delouis et al., 1993;Kastrup et al., 12 2004). It is also worth noting these general statistics are almost identical to those observed 13 in Western France: same small proportion of reverse faulting styles (10-20%), same average 14 orientations of P and T axes (N120-130° and N065°, respectively), cf. Figure 5 vs. Figure 7. 15 The regional grid averages (d = 25 km, Nmin = 2) are shown in Figure 8. Over the 16 whole region, the near-horizontal P axis orientations remain remarkably coherent (roughly 17 NW-SE, including across major geological boundaries such as the Jura / Upper Rhine Graben 18 transition), with a 30-50° counter-clockwise rotation from NNE-SSW in the east to ENE-19 WSW in the south (Figures 8a and 8c). This general orientation is consistent with that of the 20 maximum horizontal compressive stress measured in boreholes (Paquin et al., 1978;21 Heidbach et al., 2018). In contrast, the average faulting style shows strong spatial variations: 22 mostly transtensive to normal in the Upper Rhine Graben, Black Forest and western Swiss 23 Alps, versus mostly transpressive to reverse in the central Swiss Alps and south of the Lake 24 Geneva (Figure 8b). The Jura Mountains also show strong spatial variations in the average 25 faulting style, but these average values are associated with large standard deviations (s > 26 0.5) indicating that they are based on very different mechanisms within a small (± 25 km) 27 distance. These would require detailed analyses of the mechanisms in order to study the 28 actual local deformations. 29 As an example of a possible seismotectonic study using complementary datasets 1 such as geodetic data (e.g., Rabin et al., 2018;Walpersdorf et al., 2018), a comparison is 2 shown in Figure 8d with horizontal Global Positioning System (GPS) strain rates. This 3 example corresponds to a strain rate model derived from GPS velocities smoothed over 4 characteristic distances of ca. 100-200 km (Masson et al., 2019). Assuming that the average 5 mechanism faulting styles and near-horizontal P axis orientations can be interpreted as first-6 order indicators of crustal deformation and horizontal compression, the comparison with 7 the geodetic strain rates reveals some complex patterns: 8 • In the French Jura-northwestern Alps area, the focal mechanisms and geodetic 9 strain rates agree in styles and orientations. Both indicate NW-SE shortening in 10 the Jura, transitioning a dual pattern of E-W transpression and N-S extension in 11 the northwestern Alps (Figure 8b vs. Figure 8d). 12 • In the central Swiss Alps, Black Forest and Upper Rhine Graben, the agreement is 13 also reasonable between the P axis and geodetic shortening orientations. 14 However, while both datasets indicate shortening in the central Swiss Alps, the 15 geodetic data show strong shortening in the Black Forest and Upper Rhine 16 Graben in contrast with transtension in the focal mechanisms (Figure 8b vs. 17

Figure 8d). 18
This comparison provides a good example of the difficulty in defining a robust 19 seismotectonic model for most of metropolitan France. Due to the very low deformation 20 rates, the datasets are typically limited in size (e.g., number of focal mechanisms) and 21 resolution (e.g., geodetic strain rates). These limitations are added on top of the complexity 22 of the present-day tectonics and dynamic processes at the origin of the deformation and 23 seismicity, such as in the Alpine system where the role of isostatic adjustment to the last 24 glaciation or to ongoing erosion remains debated (Sternai et al., 2019). Such processes may 25 contribute to apparent inconsistencies between geodetic and seismic data (i.e., the former 26 may include large visco-elastic aseismic deformation). 27 28

Conclusion 29
The FMHex20 database is a compilation of over 1700 focal mechanism solutions for 1 nearly 1300 individual earthquakes in metropolitan France and bordering regions of 2 Western Europe. It is based on published and unpublished sources for which the 3 mechanisms have been verified and corrected for minor errors when required. This first 4 version of the database aims to be the starting point of regular updates as part of the 5 Seismicity Transverse Action of the Résif research infrastructure. These updates may be 6 partly automatic by linking the Résif earthquake bulletin and FMHex database, and partly 7 manual through specific online forms to integrate new research products. 8 We present first-order analyses of the database for the whole metropolitan France 9 and for a couple of regions taken as examples (Western France and Northern Alps-Jura-10 Vosges) using statistics and maps of the mechanisms and spatial averages of their 11 parameters (faulting styles, P and T axis orientations). These examples illustrate how the 12 FMHex20 database can be used to construct seismotectonic models and serve as a basis for 13 a variety of projects, from geodynamic studies to zonation for seismic hazard computations. 14 They also highlight the complexity of present-deformation and its driving processes in 15 France. While an overall pattern of NW-SE horizontal compression across the whole 16 territory can be related to classical plate-tectonic processes (e.g., Atlantic ridge push), a 17 variety of other processes, such as isostatic adjustment to erosion or glaciation cycles, are  Baroux, E., Béthoux, N. and Bellier, O., 2001. Analyses of the stress field in southeastern 9 France from earthquake focal mechanisms: Geophysical Journal International, 145, p. 336-10

White dashed ellipses in (a)-(d)
show specific areas discussed in the text. 10 11