# The extremely shallow Mw 4.9 2019 Le Teil earthquake, France: main ground motion features and comparison with ground motion models

Aurore Laurendeau, Mathieu Causse, Edward Marc Cushing, Céline Gélis, Maria Lancieri, Roxanne Rusch, Paula Fahed, Cécile Cornou, Sébastien Hok

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## To cite this version:

Aurore Laurendeau, Mathieu Causse, Edward Marc Cushing, Céline Gélis, Maria Lancieri, et al. The extremely shallow Mw 4.9 2019 Le Teil earthquake, France: main ground motion features and comparison with ground motion models. Seismica, 2025, 4 (2), 10.26443/seismica.v4i2.1174. hal-05365708

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https://asnr.hal.science/hal-05365708v1

Submitted on 14 Nov 2025

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# The extremely shallow $M_W$ 4.9 2019 Le Teil earthquake, France: Main ground motion features and comparison with ground motion models

A. Laurendeau ID*¹, M. Causse ID², E. M. Cushing ID¹, C. Gélis ID¹, M. Lancieri ID¹, R. Rusch †¹, P. Fahed², C. Cornou ID², S. Hok ID¹

¹Autorité de Radioprotection et de Sureté Nucléaire (ASNR), PSE-ENV/SCAN/BERSSIN, F-92260, Fontenay aux Roses, France, ²University of Grenoble Alpes, University of Savoie Mont Blanc, CNRS, IRD, Univ. Gustave Eiffel, ISTerre, 38000 Grenoble, France

Author contributions: Conceptualization: All. Project Administration: ML, AL, MC, CC. Funding acquisition: ML, CC. Data Curation: AL, MC, EMC, CG, ML, RR, PF.

Formal Analysis: AL, MC, EMC, CG, ML, RR, PF. Validation: AL, MC. Visualization: AL, MC, EMC. Writing – original draft: AL, MC, EMC, ML.

**Abstract** On 11 November 2019, a $M_W$ 4.9 earthquake occurred in Le Teil, southeastern France, at an exceptional depth of 1 to 2 km. We benefit from a comprehensive dataset of high-quality seismic records to investigate ground motion features in terms of source, path, and site effects. Clear regional variations of intensity measures are identified. Additionally, we conduct a residual analysis by comparing observed motions with predictions from ground motion models (GMMs), revealing a systematic underestimation of amplitudes at low frequencies (< 1 Hz), associated with the generation of Rayleigh waves. These waves are generated due to the shallow depth of the rupture and are most prominent in directions orthogonal to the fault. At higher frequencies, additional spatial variations are observed. In particular, ground motions recorded in the southeast show significantly lower amplitudes than those predicted by GMMs. This phenomenon may be attributed to the regional attenuation and geological structure or to local geological conditions combined with the extremely shallow depth of the seismic event, as demonstrated with numerical simulations. Our study emphasises the necessity for further analyses of ground motions generated by such moderate extremely shallow earthquakes.

**Résumé** Le 11 novembre 2019, un séisme de $M_W$ 4.9 s'est produit au Teil, dans le sud-est de la France, à une profondeur exceptionnellement faible de 1 à 2 km. A partir d'un large jeu de données sismologiques de haute qualité, nous analysons les caractéristiques du mouvement du sol en lien avec la source, la propagation des ondes et les effets de site. Des variations régionales des mesures d'intensité ont été observées. Une analyse des résidus, comparant les observations aux prédictions de modèles de mouvement du sol (GMM), révèle une sous-estimation systématique des amplitudes aux basses fréquences (< 1 Hz), en lien avec la génération d'ondes de Rayleigh, favorisée par la faible profondeur de la rupture, principalement dans les directions orthogonales à la faille. A plus haute fréquence, d'autres différences spatiales sont observées. En particulier dans la région sud-est, les mouvements du sol présentent des amplitudes largement inférieures aux prédictions. Ce phénomène pourrait être attribué à l'atténuation régionale et à la structure géologique ou aux conditions géologiques locales combinées à la profondeur extrêmement faible de l'événement sismique, comme démontré par des simulations numériques. Cette étude souligne l'intérêt d'approfondir l'analyse des mouvements du sol générés par des séismes modérés extrêmement superficiels.

**Non-technical summary** On 11 November 2019, a magnitude 4.9 earthquake occurred in Le Teil, Southeastern France, at an unusually shallow depth of 1-2 km, in contrast to most earthquakes that typically originate deeper, beyond 10 km. Recorded by numerous seismic sensors around the epicentre, this event provides a unique opportunity for in-depth analysis of the resulting ground motions, revealing distinct characteristics. Comparison of these observations with statistical models developed from ground motions of other earthquakes, particularly the deeper ones, and used in recent seismic hazard studies, highlights systematic discrepancies. These differences vary depending on the sensor position relative to the earthquake location. We further discuss these variations in light of specific characteristics of this earthquake and the properties of the geological media through which waves propagate. This seismic event challenges conventional expectations and highlights the complexity of shallow earthquakes.

Production Editor:

Gareth Funning

Handling Editor:

Pablo Heresi

Copy & Layout Editor:

Miguel Neves

Signed reviewer(s):

Fabian Bonilla

Received:

23 January 2024

Accepted:

11 September 2025

Published:

22 October 2025

<footnote>*Corresponding author: aurore.laurendeau@asnr.fr</footnote>

<footnote>†Now at Bureau de Recherches Géologiques et Minières (BRGM), DGR/GBS, Orléans, France</footnote>
# 1 Introduction

On 11 November 2019, a moderate moment magnitude (M<sub>w</sub>) 4.9 earthquake struck the town of Le Teil in southeastern France. This event, hereafter referred to as the Le Teil earthquake, caused a maximum macroseismic intensity of VIII on the EMS-98 scale in certain districts of the town (Cornou et al., 2021; Schlupp et al., 2021). Mainland France is characterised by low-to-moderate seismic activity; the strongest known historical earthquake occurred in 1909, 110 km south of Le Teil, reaching a maximum macroseismic intensity (Imax) of IX on the MSK (Medvedev, Sponheuer and Karnik) scale. Some noteworthy recent seismic events took place in the Pyrenees in 1967 (Arette Imax VIII) and 1980 (Arudy Imax VII), as well as in the Alps in 1996 (Epagny Imax VII) and 2014 (Barcelonnette Imax VI) (Jomard et al., 2021; Scotti et al., 2004). In the vicinity of the Le Teil earthquake, testimonies of some individual historical earthquakes (potentially shallow) with M<sub>w</sub> ranging from 3.0 to 4.1 and extremely shallow recent seismic swarms have been documented and observed (Bollinger et al., 2010; Thouvenot et al., 2009; Bollinger et al., 2021; Larroque et al., 2021).

Despite its moderate M<sub>w</sub> of 4.9, this reverse-faulting earthquake is associated with up to 15 cm of uplift along the La Rouvière segment of the Cevennes fault system (Ritz et al., 2020). Its hypocentre is extremely shallow, with an estimated depth between 1 and 2 km (Delouis et al., 2021; Vallage et al., 2021). Such shallow nucleation may have been promoted by rock extraction in a nearby quarry (Ampuero et al., 2019, 2020; De Novellis et al., 2020) or meteoric water recharge (Burnol et al., 2023). While this type of earthquake is relatively uncommon worldwide, some moderate M<sub>w</sub> extremely shallow earthquakes have been reported notably in China (e.g., Qian et al., 2019; Di et al., 2023), Australia (e.g., Allen et al., 2006; Miller et al., 2023) and northeastern South America (e.g., Barros et al., 2015; Assumpção et al., 2025), sometimes causing locally severe damage. The high level of damage (Imax of VIII) from the Le Teil earthquake and the absence of near fault seismic records motivated a study on ground motion modelling. Based on numerical simulations calibrated with in-situ observations of displaced objects, Causse et al. (2021) demonstrated that vertical ground acceleration locally exceeded gravity. At greater distances from the rupture, macroseismic surveys highlighted a rapid decay of the macroseismic field with distance, faster than for deeper earthquakes (Figure 15 of Schlupp et al., 2021). Numerous papers have been published on the Le Teil earthquake, and only the study by Vallage et al. (2021) has analysed the attenuation of peak ground acceleration (PGA) with distance on a regional scale (307 stations, 850 records), comparing the results with predictive ground motion models (GMMs). They found that observations are mostly lower than predictions for distances less than 100 km.

To date, a comprehensive understanding of the ground motion characteristics of the Le Teil earthquake at a regional scale is lacking. Benefiting from the extensive number of far-field records, our work has three

main objectives. Our first objective is to investigate if the ground motions from this moderate extremely shallow event exhibit any potential specific features across different frequencies. Our second objective is to verify if the GMMs used in recent seismic hazard studies are consistent with the ground motions observed during the Le Teil earthquake. Indeed, these GMMs are developed from databases that do not contain earthquakes similar to the Le Teil earthquake (Ancheta et al., 2014; Lanzano et al., 2019b), and may not necessarily reflect the wave propagation characteristics for an extremely shallow moderate event in France. Our third objective is to explore potential explanations for the observed ground motion characteristics in terms of source, path, and site effects.

The paper is organized in four sections. The first section, 2.“Data Selection and Processing”, describes the ground motion dataset, composed of 198 three-component records at distances ranging from 8 to 300 km. In the second section, 3.“Analysis of Main Ground Motion Features”, we present the main features of the Le Teil earthquake ground motions (acceleration and velocity peaks, as well as duration), in particular the presence of strong low-frequency waves interpreted as Rayleigh waves. In the third section, 4.“Comparison of Observations with GMMs”, we correct the observed ground motions for path effects using several GMMs and carry out a residual analysis. We highlight that recorded ground motions of the Le Teil earthquake are generally larger at low frequencies and lower at high frequencies, with a strong azimuthal variability. This variability is further investigated using a clustering approach, which reveals clear spatial patterns. Finally, in the section 5.“Interpretation and Discussion”, we explore some avenues for the physical interpretation of the observed azimuthal and frequency-dependent variations. It focuses on two main aspects: (1) the systematic underestimation of low-frequency ground motions, which is linked to the generation of Rayleigh waves, and (2) the spatial variations of high-frequency ground motions, attributed to propagation effects, as supported by regional geology and simple 1D numerical simulations. Our study suggests that a better understanding of the ground motions generated by such moderate extremely shallow earthquakes is important to improve seismic hazard assessment.

# 2 Data Selection and Processing

In recent years, substantial efforts have been dedicated to deploying seismological networks across mainland France. Thanks to these efforts, numerous records of the Le Teil earthquake are available within a 300 km radius around the epicentre (Figure 1). The three-component records are collected from broadband and accelerometric stations distributed through the International Federation of Digital Seismograph Networks (FDSN) Web Services by the European Integrated Data Archive (EIDA) portal (http://www.orfeus-eu.org/data/eida/). Among these, we use 90 stations from the permanent broadband network (Epos-France-RLBP - FR) and 50 from the permanent accelerometric network (Epos-
<figure><img src="image_3.png" /></figure>

**Figure 1** Spatial distribution of the 269 recording stations around the Le Teil earthquake epicentre, part of different networks differentiated by their FDSN codes (see Data and Code Availability - Table 2). The top inset shows a larger view of the study area, with the black rectangle corresponding to the area in the main figure. The earthquake epicentre is represented by a black star in the top inset and is in the main figure at the centre of the circles indicating the epicentral distances between the earthquake and stations. The marker colours distinguish the stations selected in this study from the others in black, with stations from permanent networks available on EIDA in blue and temporary stations from different projects with restricted data or permanent stations with data not normally shared in yellow. A simplified view of the major geological domains around the earthquake is also superimposed on the map using coloured polygons, with the Rhône-Saône River valley in blue, the sedimentary basins in yellow, the crystalline mountains in brown and the deformed northern external domain of the Alps in green.

France-RAP - RA). The closest FR and RA stations to the rupture are OGDF (30 km) and OGLP (22 km), respectively (Figure 1. stations with codes FR and RA in blue).

Within the epicentral area, we also include data from restricted-access or dedicated networks not typically available through public archives (Figure 1. stations in yellow):

* Three temporary broadband stations were installed in the Tricastin nuclear power plant area as part of a scientific project led by the "Institut de Ra-dioprotection et Sûreté Nucléaire" [IRSN], focusing on seismic site effect estimation (Froment et al., 2022; Gélis et al., 2022), and one accelerometric station

operated by the French nuclear operator "Electricité De France" [EDF] is located near the Cruas nuclear power plant (~12 km from the rupture), totalling 4 stations (code 3C).

* The "Société Nationale des Chemins de fer Français" [SNCF] provides records from 18 triggered accelerometric stations deployed along the Mediterranean high-speed railway line [LGV], as part of an earthquake emergency stopping system operated by the French Alternative Energies and Atomic Energy Commission [CEA] (Vallage et al., 2021, code SNCF). Nine of the SNCF stations are within 50 km of the epicentre, with the closest one located 8 km
from the rupture.

To enrich the far-field dataset, we incorporate temporary broadband stations from two major scientific projects (Figure 1. stations in yellow):

* The CIFALPS-2 project (Zhao et al., 2018) provides data from 51 stations spaced 5–10 km apart across the northwestern Alps and Ligurian Alps, located at least 200 km from the La Rouvière fault (code XT).

* The AlpArray project (Hetényi et al., 2018) contributes 29 stations spaced ~52 km across the Alpine regions, enhancing data coverage west and north of the epicentre. The nearest usable record from this network is located about 40 km from the rupture (code Z3).

The overall characteristics of the networks are summarized in the “Data and Code Availability” section (Table 2). As a result, we compile an initial dataset of 269 three-component records from accelerometric and broadband stations (Figure 1).

All records undergo visual inspection to remove defective waveforms (e.g., clipped waveforms, train waves in SNCF data, ...). Then, the frequency band for which seismic energy is available for analysis is defined following the PEER procedure (Ancheta et al., 2013) by ensuring that the Fourier spectra of the signal are at least three times greater than those of the noise, and checking that no linear trends remain in the displacement signal. An acausal Butterworth filter is then applied to the acceleration signal within this range. Details on signal processing are provided in the Supplementary Text S1. Finally, only waveforms with a usable frequency band extending beyond 0.5–5 Hz are selected. The usable frequency band is defined as the bandpass filter frequencies scaled inward by a factor of 1.25, as is classically done in GMM flatfiles (e.g., Ancheta et al., 2014; Traversa et al., 2020). In cases where records are available for two co-located sensors (an accelerometer and a broadband sensors), the accelerogram records (HN channels) are preferred. This is because French accelerometers are typically installed at the surface, whereas broadband sensors can be placed at depth in boreholes to enhance the signal-to-noise ratio. However, this configuration can result in a deamplification of the seismic signal at high frequencies (Holender et al., 2020). The final dataset is composed of 198 three-component stations well-distributed around the Le Teil earthquake epicentre and covering different major geological domains (Figure 1).

# 3 Analysis of Main Ground Motion Features

In this part, our goal is to identify potential specific features of the Le Teil earthquake ground motions. To achieve this aim, we examine the spatial distribution of some ground motion intensity measures, such as acceleration and velocity peaks, as well as duration. Additionally, we conduct a time-frequency analysis of ground motion at three representative stations.

## 3.1 Intensity Measure Maps

We estimate the intensity measures using a Seismic-Intensity-Measure code developed in Python, and the values are provided in an Excel table as supplementary material and available on Zenodo (See Data and Code Availability section, Laurendeau et al., 2024). Figure 2 displays the spatial distribution of the geometrical mean of the two horizontal components for three intensity measures: Peak Ground Acceleration (PGA), Peak Ground Velocity (PGV) and significant relative duration ($D_{SR-5-95\%}$, see Bommer et al., 2009). The highest recorded PGA is 76 cm/s², observed at CAI55 by the SNCF network located 10 km from the rupture fault. As expected, PGA values decrease with increasing distance, although spatial variations are evident based on major geological domains (Figure 1 and Figure 2). At distances of 100–150 km from the La Rouvière fault in the Massif Central, PGAs are around 1 cm/s², five times higher than those recorded in the Alps around 0.2 cm/s². At distances of 250–300 km, PGAs recorded in the Pyrenees are around 0.1 cm/s² and in the Alps around 0.04 cm/s². Thus, a faster decay of PGA with distance is observed southeast of the rupture compared to the northwest region. The highest PGV, equal to 3 cm/s, is recorded at P55 by the SNCF network located 8 km from the rupture fault. The spatial distribution of PGV values appears fairly similar to that of PGA values, except for the area to the south-southeast of the rupture, where there are no longer significant differences in PGV values at the same distances compared to the northwest. $D_{SR-5-95\%}$ increases with distance, and shorter seismic signals are observed in the northwest compared to the southeast. For example, at distances of 100–150 km from the La Rouvière fault, durations are longer in the southeast by at least 20 seconds. The analysis of the spatial distribution of these intensity measures reveals distinct behaviours between the regions around the epicentre, with a clear separation between the northwest and southeast. The observed differences between PGA and PGV values also suggest variations in the ground motion frequency content.

## 3.2 Focus on Three Representative Stations

To further investigate the spatial variations highlighted above, we conduct an in-depth analysis of signals from three representative stations: OCOL, OGCH, and IRVG (locations in Figure 2). These stations are selected based on their positions at three different azimuths from the Le Teil rupture (OCOL to the northwest, OGCH to the northeast, and IRVG to the southeast), at similar distances (~120–150 km), and especially because they are on rock sites ($V_{S30} \ge 1400$ m/s), minimizing the impact of soil conditions on the signals. It is noteworthy that all three stations are accelerometers from the RA network, facilitating data comparisons.

Figure 3 illustrates the three-component velocity time series at these stations, as well as their time-frequency representations (Stockwell et al., 1996). For this analysis, the north and east horizontal components are rotated into radial and transverse components. The figure in acceleration is provided in the supplementary material.
<figure><img src="image_4.png" /><figcaption>**Figure 2** Spatial distribution of three intensity measures (IMs) around the Le Teil earthquake epicentre recorded by the 198 stations: top-left panel, PGA values (m/s²), top-right panel, PGV values (m/s) and bottom-left panel, D<sub>SR-5-95%</sub> (s). The three IMs are computed as the geometrical mean of the two horizontal component values. The waveforms of the three stations (OCOL, OGCH, IRVG) indicated in the maps are analysed in Figure 3.</figcaption></figure>

rial (see Figure S.2). Firstly, differences are observed in the acceleration waveforms, with more impulsive signals for OCOL and OGCH, characterised by a large-band increase in energy for body-waves, particularly rich in high frequencies. In contrast, the signal at IRVG is more elongated in time and has a poorer high-frequency content. Additionally, the Stockwell transform at IRVG exhibits less high frequency after 40 seconds, and the high-frequency decay of the Fourier spectrum is faster than for the other two selected stations. This is consistent with previous observations that northwest and northeast stations have stronger PGA and shorter durations compared to southeast stations (see Figure 2 and S.2). Secondly, examining the low-frequency part of the signal, the time-frequency analysis reveals an energy increase at the OCOL and IRVG stations on the radial and vertical components between around 30 and 50 seconds and for frequencies below 1 Hz. These waves are spread out over time, with the lowest frequencies arriving first and then the highest frequencies with energy between 0.4 and 1 Hz. Given this dispersive feature

and the presence of these waves in the radial and vertical components, they are interpreted as Rayleigh waves. These waves are less visible on the Stockwell transform at IRVG than at OCOL due to a more complex signal. They are well visible on the waveforms (Figure 3 - grey rectangles), supporting the PGV at IRVG station for the radial and vertical components and at OCOL station for the radial component. At OCOL, the amplitudes of the Fourier spectra of the radial and vertical components are notably greater than the transverse component between 0.1 and 0.5 Hz. This can also be observed at IRVG but not across the entire frequency range of 0.1–0.5 Hz. Conversely, at station OGCH, it is not possible to identify these Rayleigh waves. This observation is also consistent with PGV observations (Figure 2), where no significant difference was noted between the northwest and south-southeast, while lower PGV<sub>S</sub> were observed in the northeast.

Thus, the spatial distribution of intensity measures and the waveform analysis at three representative stations highlight (1) a faster decay of high-frequency
<figure><img src="image_5.png" /><figcaption>**Figure 3** Waveforms in velocity, corresponding Stockwell transform and Fourier spectra in acceleration for the OCOL (north-west), IRVG (southeast) and OGCH (northeast) stations for the transverse (red), radial (blue) and vertical (green) components. The location of the three stations is given in Figure 2. The presence of Rayleigh waves at OCOL and IRVG is indicated by grey rectangles on the waveforms and dotted lines on the Stockwell transforms. On the waveforms, the purple cross indicates the PGV, and grey vertical dotted lines indicate the significant relative duration, i.e., the time interval between 5% and 95% of the cumulative Arias Intensity over time ($D_{SR-5-95\%}$). The same figure in acceleration is provided in the supplementary material (see Figure S.2).</figcaption></figure>

ground motion with distance in the southeast direction and (2) the prevalence of Rayleigh waves for frequencies lower than 1 Hz in the northwest-southeast directions. We will propose several physical interpretations to these observed differences in section 5.“Interpretation and Discussion”, but first, we further investigate the specific features of the Le Teil earthquake through a comparison with GMMs.

## 4 Comparison of Observations with GMMs

This part aims to achieve two main objectives: (i) to highlight any specific ground motion features by analysing the ground motion residuals (i.e., the difference between observations and GMM predictions), obtained by correcting for path effects using various GMMs, and (ii) to verify the ability of GMMs employed in recent seismic hazard studies to predict the Le Teil earthquake ground motions, knowing that the databases used for their development lack data with identical scenario characteristics. To perform this comparative analysis, five GMMs are selected, comprising three GMMs developed from global databases (Boore et al., 2014; Chiou and Youngs, 2014; Cauzzi et al., 2015) and two from European-Mediterranean databases (Bindi et al., 2014; Kotha et al., 2020, 2022). These models are selected based on their recent use

in seismic hazard studies predicting ground motions of shallow crustal earthquakes in active tectonic regions (e.g., Weatherill and Danciu, 2018; Beauval et al., 2020; Weatherill et al., 2020; Türker et al., 2022). Main characteristics of these GMMs are summarized in Table S.1.

For each station, the geometric mean (GM) and the orientation-independent, non-geometric mean (RotD50) (Boore, 2010) are computed from the two horizontal components to maintain consistency with the definitions used in the selected GMMs. This RotD50 value is used only if it is included within the usable frequency band (defined in the part 2.“Data Selection and Processing”). The input parameters required for these GMMs, or to compute them, are presented in Table 1. Site-to-fault distances ($R_{JB}$, $R_{RUP}$, and $R_X$) are computed by approximating the fault as a rectangular plane. The location, strike and length of the fault plane on the surface are determined based on the trace of the fault observed from InSAR analysis (Ritz et al., 2020) (approximately 5 km on the InSAR image). The fault width is estimated from the slip inversion results (Vallage et al., 2021; Cornou et al., 2021). Finally, these GMMs employ the $V_{S30}$ parameter, which represents the time-averaged shear wave velocity in the top 30 m of soil and provides a first-order estimate of subsoil stiffness at the surface, particularly in the presence of soft shallow layers, although it does not fully capture site response (e.g., Castellaro et al., 2008; Cadet et al., 2010). In this study,
$V_{S30}$ is available for only 32 of the 198 stations used (see Figure S.3). Most of these values were obtained from characterisation campaigns conducted within the framework of the Epos-France-RAP projects (Regnier et al., 2010; Hollender et al., 2018) and are published in the Epos-France-RAP and -RLBP dataset (Traversa et al., 2020). For the IRSN station named ADHE, as well as for the SNCF station named P71, located in similar geological conditions, the $V_{S30}$ value is provided by Gélis et al. (2022). For stations without measured $V_{S30}$ values, a common approach in GMM development is to estimate $V_{S30}$ from topographic slope (e.g., Wald and Allen, 2007), and such proxies have been widely used in recent studies (e.g., Lanzano et al., 2019a). However, a preliminary comparison with French data shows a poor correlation between slope-based estimates and measured $V_{S30}$ values, particularly for hard-rock sites on low-slope limestone plateaus in southeastern France (see Figure S.4). This observation is consistent with the findings of Lemoine et al. (2012), who advise against the use of slope-based proxies for local studies in such geological contexts. To minimize the bias introduced by unreliable proxy values, we choose to assign a uniform $V_{S30}$ value of 800 m/s to all stations in the main analysis presented in this paper. The impact of this assumption is illustrated in Figure S.5, which shows how ground motion predictions change when using $V_{S30}$ values of 300 m/s or 2000 m/s instead of 800 m/s. Additionally, we provide in the Supplementary Material alternative analyses using other plausible $V_{S30}$ values to assess the robustness of our conclusions. These tests indicate that the various assumptions for the $V_{S30}$ values have no impact on the main conclusions of our study, as explained subsequently.

<table><caption>**Table 1** Parameters used in the selected GMMs and for computing various distance definitions between the fault and each recording station.</caption><tr><td>M<sub>w</sub></td><td>4.9</td></tr><tr><td>Focal Depth (km)</td><td>1</td></tr><tr><td>Hypocentre Latitude (°)</td><td>44.5178</td></tr><tr><td>Hypocentre Longitude (°)</td><td>4.6709</td></tr><tr><td>Z<sub>TOR</sub> (km)</td><td>0</td></tr><tr><td>Strike (°)</td><td>45.16</td></tr><tr><td>Rake (°)</td><td>82</td></tr><tr><td>Dip (°)</td><td>45</td></tr><tr><td>Reference Latitude (°)</td><td>44.509</td></tr><tr><td>Reference Longitude (°)</td><td>6.638</td></tr><tr><td>Fault width (km)</td><td>2</td></tr><tr><td>Fault length (km)</td><td>5.09</td></tr><tr><td>V<sub>S30</sub> (m/s)</td><td>800</td></tr></table>

## 4.1 Spectral Accelerations vs Distance

Figure 4 compares the spectral accelerations observed and predicted by five GMMs (median values) as a function of distance for four frequencies. Firstly, the comparison of the GMMs reveals differences depending on frequency and distance. At low frequencies, all five GMMs predict relatively similar spectral accelerations, except for near-fault distances (< 20 km). This variation

can be attributed to the use of different sites-to-fault distance definitions: CY14 and Ca15 use $R_{RUP}$ and predict the highest spectral accelerations, whereas the other GMMs use $R_{JB}$, and thus are calibrated on the median of ground motions generated by earthquakes of various depths. Among the GMMs using the $R_{JB}$ distance, which does not account for the earthquake's depth, Ko20 predicts the highest spectral acceleration at short distances. This model is unique in that it is defined for three different classes of hypocentral depth, and the class used here corresponds to hypocentral depths lower than 10 km. As the frequency increases, discrepancies between GMMs become more apparent at large distances, reflecting differences in the term describing the attenuation of seismic waves. Ko20 and CY14 exhibit the highest ground motion attenuation at large distances, while Bi14 has the lowest attenuation.

Secondly, when comparing the observed data to the GMM predictions, several trends are observed. At low frequencies (0.5 Hz and 1 Hz), the observations tend to be higher than the median GMM predictions, with some observations being up to five times higher than the median predicted values at distances up to 150 km. At 2 Hz, observations closely align with the predictions, while at higher frequencies, observations are mostly below predictions, except for the three closest stations. Notably, at large distances (> 100 km), there is a large dispersion in the observations, with the Ko20 and CY14 models appearing to be median for these observations.

## 4.2 Residual Analysis

To highlight the main features of the Le Teil earthquake and assess the ability of GMMs to predict observations, a residual analysis is conducted. The GMM can be expressed in a general form as follows:

$$ \ln (SA_{obs}(f))_{es} = f(PV, \theta(f)) + \epsilon(f)_{es} \quad (1) $$

where $SA_{obs}(f)$ represents the observed response spectrum for an earthquake *e* at a station *s*, $f(PV, \theta)$ is the median ground motion model with *PV* as the vector of predictor variables (e.g. earthquake magnitude, distance to ruptured area, etc.) and *θ* the vector of model coefficients, and $\epsilon(f)_{es}$ is the total residuals, called hereafter epsilon. $\epsilon(f)_{es}$ represents the log-difference between observed spectral acceleration ($SA_{obs}$) and median predictions ($SA_{pred}$). This term can be decomposed into repeatable and aleatory components using mixed-effects regression methods (Abrahamson and Youngs, 1992; Al Atik et al., 2010):

$$ \epsilon(f)_{es} = \delta B_e(f) + \delta W_{es}(f) \quad (2) $$

where $\delta B_e$ and $\delta W_{es}$ are the between-event and within-event components of residuals, respectively. $\delta B_e$ represents the average shift of all ground motions recorded for an earthquake from the median ground motion calculated using a GMM. It is generally interpreted as a term quantifying remaining source effects averaged over all azimuths. It reflects the influence of factors such as stress drop (e.g., Bindi et al., 2017; Oth et al., 2017) and slip variation in space and time that are
<figure><img src="image_6.png" /><figcaption>**Figure 4** Spectral acceleration (SA) in m/s² for five ground motion models compared to observations of the Le Teil earthquake defined in RotD50 for four different frequencies in terms of R<sub>JB</sub> distance definition. To facilitate model comparison across various distance definitions, we adopt the assumptions R<sub>JB</sub> = R<sub>RUP</sub> and R<sub>X</sub>=- R<sub>JB</sub>. The V<sub>S30</sub> parameter is set to 800 m/s in the GMMs.</figcaption></figure>

not modelled by the source predictor variables of the model, such as the magnitude and the source depth. δB<sub>e</sub> can be computed using the formulation of Abrahamson and Youngs (1992):

$$ \delta B_e(f) = \frac{\tau(f)^2 \sum_{s=1}^{n_e} SA_{obs_{es}}(f) - SA_{pred_{es}}(f)}{n_e(f)\tau(f)^2 + \varphi(f)^2} \quad (3) $$

where n<sub>e</sub> is the number of observations for the considered earthquake, τ and ϕ are the standard deviations of the between-event and within-event components, respectively, defined for the selected GMM. δW<sub>es</sub> represents the remaining differences in source, path, and site effects not captured by distance and site variables, once δB<sub>e</sub> has been considered.

### 4.2.1 Between-Event Residuals

Figure 5 displays δB<sub>e</sub> computed from the five selected GMMs and for the Le Teil earthquake ground motions. Figure 6 illustrates these residuals for the three representative stations already presented in section 3. “Analysis of Main Ground Motion Features”. As a reminder, the main analysis presented here assumes a fixed V<sub>S30</sub> value of 800 m/s for all stations, as justified before. δB<sub>e</sub> values for all GMMs are positive at low frequencies (< 1 Hz),

reaching values up to unity, suggesting that, on average, all GMMs underestimate the low-frequency ground motions of the Le Teil earthquake (Figure 5). Figure 6 (left panels) highlights a bump in the observed acceleration response spectra for stations OCOL and IRVG, not predicted by the Ko20 GMM, resulting in positive epsilon values (in blue). The δB<sub>e</sub>-corrected prediction (in green) better matches the observed spectra at low frequencies for stations OCOL and IRVG. The positive δB<sub>e</sub> in Figure 5 probably reflects the presence of a dominant number of stations with this special feature. At high frequencies (> 1 Hz), δB<sub>e</sub> values computed with different GMMs exhibit wide variability (Figure 5), with slightly positive values for CY14 and negative values around -1.5 for Ca15, indicating a substantial overestimation of predictions compared to observations.

### 4.2.2 Within-Event Residuals

In the following, the Ko20 GMM, on which the 2020 update of the European Seismic Hazard Model (ESHM20 Danciu et al., 2021), is retained for presenting the within-event residuals, δW<sub>es</sub>. Ko20 has the advantage of being less dependent on the V<sub>S30</sub> parameter than other GMMs, minimizing the impact of assuming V<sub>S30</sub> = 800 m/s (see Figure S.5). Furthermore, we verified that δB<sub>e</sub> values computed with Ko20 are poorly sensi-
<figure><img src="image_7.png" /><figcaption>**Figure 5** Between-event residuals ($\delta B_e$) computed from the five GMMs with respect to the frequency. Note that for each frequency, the number of stations used to compute $\delta B_e$ varies according to the usable frequencies for each record, and for Ca15, $\delta B_e$ is computed using a reduced number of stations compared to other GMMs, as this model is defined for $R_{RUP}$ up to 150 km (Table S.1).</figcaption></figure>

tive to the selected $V_{S30}$ values (either the default 800 m/s or measured values or inferred from the topographic slope) and to the considered distance range (see Figure S.6). Once $\delta B_e$ is defined from Ko20 under the assumption of $V_{S30} = 800$ m/s, $\delta W_{es}$ is calculated from (1) and (2).

Firstly, it is insightful to examine these within-event residuals for the three representative stations OCOL, IRVG, and OGCH (Figure 6, right panel, green lines). Three distinct behaviours are observed:

1. For the OCOL station (northwest), $\delta W_{es}$ is close to zero up to 3 Hz and positive for higher frequencies.

2. For the IRVG station (southeast), $\delta W_{es}$ displays slightly positive values up to 0.7 Hz, followed by a clear downward trend in the high-frequency range, forming an 'S-shape' residual pattern.

3. For the OGCH station (northeast), $\delta W_{es}$ is negative at low frequency and slightly positive at high frequency.

For these three stations, we also compare results using measured $V_{S30}$ values (> 1400 m/s) instead of the default 800 m/s. While this leads to some differences, mainly at high frequencies, the main spectral features, including the 'S-shape' at IRVG and the low high-frequency content, remain consistent. Thus, OCOL and IRVG behave similarly at low frequencies, while OCOL and OGCH exhibit similar behaviour at high frequencies.

Secondly, the spatial distribution of $\delta W_{es}$ across all stations defined from Ko20 is analysed at different frequencies (see Figure 7). Results from other GMMs are provided as supplementary material (see Figures S.7 to S.10). Darker shades of red indicate higher observations than $\delta B_e$-corrected predictions and darker shades of blue indicate lower observations than $\delta B_e$-corrected predictions. White indicates cases where $\delta B_e$-corrected predictions match observations. At 0.5 Hz, most stations in the western (e.g., OCOL) and southeastern (e.g., IRVG) regions show $\delta W_{es}$ close to zero (light colours),

while stations in the northeastern part (e.g., OGCH) at long distances (> 100 km) in the Alpine topographies (and also some stations in the eastern Pyrenees) predominantly have negative $\delta W_{es}$ values (in blue). This negative region extends south-eastward with increasing frequency, resulting in two distinct zones at 5 Hz: predominantly positive $\delta W_{es}$ values appear northwest of the rupture (e.g., OCOL), and negative values are southeast of the rupture (e.g., IRVG). In the latter case, some stations exhibit particularly negative $\delta W_{es}$ values (in dark blue), as seen in the case of IRVG.

To assess the robustness of the results, two additional sensitivity analyses are performed. First, we tested the influence of the $V_{S30}$ values on the spatial distribution of $\delta W_{es}$ by (1) using only the 32 stations with measured $V_{S30}$, and (2) including all stations, assigning slope-based $V_{S30}$ estimates to those without measurements (see Figures S.11 and S.12). In both cases, the observed patterns remain consistent with those in Figure 7. Second, we test the regional GMM of Kotha et al. (2020), in which the random part $\epsilon(f)_{es}$ is decomposed into several components, in particular by looking in a specific region at the repetitive effects of (1) earthquakes, representative of earthquake locality-to-locality variability $\delta_{L2L}$, and (2) path, representative of the region-specific anelastic attenuation $\delta_{c3}$. By correcting the median spectrum for these two variables, a region-specific prediction is obtained. The model indicates higher attenuation ($\delta_{c3}$) in the southeast at 10 Hz. Nevertheless, the overall within-event residual patterns remain consistent with those obtained using the median Ko20 model, with very low $\delta W_{es}$ values in the southeast (see Figure S.13).

Finally, to explore if the three $\delta W_{es}$ patterns identified at the representative stations (OCOL, IRVG, and OGCH, Figure 6) can be extended spatially on a broader scale, we employ the k-means clustering algorithm (Arthur and Vassilvitskii, 2007) to classify all stations into distinct groups with similar $\delta W_{es}$ characteristics. K-means clustering is a data-driven method that assigns each station to the nearest cluster centroid in a feature space, where proximity is measured using the L2-norm between $\delta W_{es}$ observations. As such, stations located near cluster boundaries may share characteristics with multiple clusters, and their final assignment can be sensitive to small variations in the input data or initialisation (Jain, 2010). This approach thus provides a simplified categorisation that highlights dominant spatial trends, rather than strict, sharply defined groupings.

We select 182 stations for which response spectra, and thus $\delta W_{es}$, are defined between 0.4 and 7 Hz. After several trials and errors, we determine that four clusters effectively capture the main regional features of $\delta W_{es}$ identified in the previous section. Figure 8 displays the $\delta W_{es}$ curves of these four clusters and their spatial distribution on a map. Clusters #1 to #3 each include one of the three representative stations OGCH, OCOL and, IRVG, respectively. Overall, stations in the vicinity of these three representative stations are assigned to the same cluster and exhibit similar variations in $\delta W_{es}$ with frequency. In contrast, cluster #0 (in red) stands out by grouping spatially scattered stations that neverthe-
<figure><img src="image_8.png" /><figcaption>**Figure 6** Left panel, comparison between observed (black dashed lines) and predicted spectral accelerations by Ko20's GMM for three representative stations. Spectral accelerations are in m/s², with predictions using a fixed $V_{S30}$ value of 800 m/s in blue and predictions corrected for the between-event residual, $\delta B_e$, in green. Right panel, display of the corresponding residuals. Blue lines represent the total residual (epsilon), and green lines represent the within-event residual ($\delta W_{es}$). The purple dashed lines indicate, for reference, the prediction obtained when the measured $V_{S30}$ value at each station (true $V_{S30}$) is used in the GMM, along with the corresponding epsilon value. The locations of the three stations are indicated in Figure 2.</figcaption></figure>

less share a common $\delta W_{es}$ pattern, systematically positive across the entire frequency range (around 1). Several of these stations are located in rather deep sedimentary basins like those of Grenoble (e.g., Guéguen et al., 2007), Nice (e.g., Régnier et al., 2020) or Annecy (e.g., Thouvenot et al., 1998). Their spectral amplitudes are up to ten times higher than the predicted values (see Figure S.14), consistent with findings from other studies (e.g., Courboulex et al., 2013). Another part of the stations from cluster #0 is located in the Rhône Valley. The Rhône Canyon, hundreds of metres deep, is

one of the deep canyons formed around the Mediterranean during the Messinian salinity crisis, a major geodynamic event of the Cenozoic (Clauzon, 1982; Do Couto et al., 2024). The strong impedance contrast between the canyon composed of Mesozoic sedimentary series and its thick Plio-Quaternary marly and sandy filling is responsible for site amplification (e.g., Gélis et al., 2022; Froment et al., 2022). The significant amplification at low frequencies is likely due to thick sedimentary fill and strong impedance contrasts, features not accounted for by Ko20 under the assumption of $V_{S30}$ =
800 m/s, and likely not even when using the measured V<sub>S30</sub> values (see Figure S.14). Assigning a uniform V<sub>S30</sub> value of 800 m/s to all sites facilitated the identification of sites with strong low-frequency amplification as a distinct cluster. Cluster #0 therefore contains stations strongly affected by local site conditions. These sites are spatially isolated and will not be further discussed in the section 5. ‘Interpretation and Discussion’. A more detailed understanding of the residuals at these sites would require additional V<sub>S30</sub> measurements, which is beyond the scope of the present study.

In summary, clusters #1 to #3 delineate spatially co-
herent regions, each anchored by a representative sta-
tion, and thus can be interpreted as reflecting regional
trends in ground motion. At low frequencies, under-
estimation of GMM predictions is visible around the
epicentre, except for the northeast (cluster #1). At
higher frequencies, ground motions in the southeast
(clusters #1 and #3) are significantly lower than pre-
dicted. In the following section, we further investigate
the physical explanations for the observed spatial vari-
ations in ground motions for clusters #1 to #3, first ad-
dressing low-frequency ground motions and then high-
frequency ground motions.

**5 Interpretation and Discussion**

## 5.1 Underestimation of Low-Frequency Ground Motions

An important outcome of comparing ground motion
observations from the Le Teil earthquake with GMM
predictions is the systematic underestimation of low-
frequency amplitudes (Figure 5). As previously men-
tioned, the analysis of within-event residuals reveals
however that this underestimation is not uniform
across the network. It is particularly pronounced in
the northwest (OCOL) and southeast (IRVG) directions,
while stations in the northeast (such as OGCH, clus-
ter #1) exhibit amplitudes that are closer to the pre-
dicted values (Figure 7). The waveform analysis high-
lights the presence of Rayleigh waves at the OCOL and
IRVG stations (Figure 3), where the largest amplitudes
generally coincide with their arrival. Additionally, these
Rayleigh waves result in bumps in the acceleration re-
sponse spectra of these two stations, which may be at-
tributed to the presence of Rayleigh waves, which are
not captured by the GMM (Figure 6).

Theory indicates that shallow seismic sources are
particularly efficient in generating low-frequency sur-
face waves (Aki and Richards, 2002; Rösler and van der
Lee, 2020). Large amplitude Rayleigh waves are gener-
ally reported in regional records for very shallow earth-
quakes and explosions (< 3 km) with periods ranging
from 0.4 to 2.5 seconds (Båth, 1975; Saikia, 1992; Kafka,
1990). Numerous studies have documented the pres-
ence of Rayleigh waves in very shallow earthquakes
(deep < 5 km) with M<sub>w</sub> between 4.0 and 5.5, across re-
gions such as China (e.g., Luo et al., 2011; Qian et al.,
2019; Wang et al., 2023), Australia (Allen, 2020; Allen
et al., 2006; Miller et al., 2023; Somerville and Ni, 2010)
and Canada (Kim et al., 2006). The shallower the earth-

quake, the greater the amplitude of Rayleigh waves; if
the source is beyond a depth of 5 km, these waves are
not visible (Tsai and Aki, 1970; Kafka, 1990). In ad-
dition, surface waves such as Rayleigh waves attenu-
ate more slowly with distance than body waves due to
their geometric spreading (amplitude decaying as 1/√r
compared to 1/r for body waves) and lower intrinsic at-
tenuation at low frequencies (Aki and Richards, 2002).
This slower decay explains why they dominate ground
motion at regional distances, particularly for shallow
sources where their generation is more efficient.

While the presence of Rayleigh waves thus serves
as a reliable indicator of an extremely shallow seismic
source, they can be observed only in specific azimuthal
directions. Rösler and van der Lee (2020) analysed the
radiation patterns of Rayleigh waves considering source
depth and frequency. Given the rupture characteristics
of the Le Teil earthquake (strike, dip, and rake values of
50°, 45°, and 90°, respectively, Ritz et al., 2020), Rayleigh
waves are generated in the northwest and southeast di-
rections, and thus are minimal in the northeast and
southwest directions (see Figure S.15). This coincides
with the identification of Rayleigh waves at OCOL and
IRVG and their absence at OGCH (Figure 3), and more
broadly, with distinction of clusters #1, #2, and #3 (Fig-
ure 8). Notably, the selected GMMs consistently under-
estimate low-frequency ground motions at all distances
(see Figure 5 and S.6), except in the northeast direction,
corresponding to a node in the surface wave radiation
pattern (see Figure S.16).

The limitations in current GMMs arise from the
databases used in their development (e.g., Ancheta
et al., 2014; Lanzano et al., 2019b), which contain few or
no earthquakes with extremely shallow depths (< 3 km).
In the Ko20 GMM, earthquakes have been classified into
three depth categories, including a category for earth-
quakes with depths less than 10 km. The Ko20 GMM
predicts higher amplitudes at short distances (< 30 km)
for the 0–10 km depth class than for the 10–20 km depth
class across the entire frequency range, particularly at
high frequencies (see Figure S.17). According to theo-
retical expectations, the amplitude of Rayleigh waves is
stronger at low frequencies as depth decreases, espe-
cially for sources shallower than 5 km (e.g., Saikia, 1992;
Kafka, 1990). Besides, since surface waves attenuate
more slowly than body waves, they significantly affect
ground motions from the source to large distances (see
Figure S.6), a feature not currently captured by GMMs.
GMMs should therefore treat earthquakes with depths <
5 km as a separate category, even though the available
data for this depth range remains limited. To our knowl-
edge, only the Somerville et al. (2009) GMM, developed
from extremely shallow earthquakes occurring in Aus-
tralian cratonic region (a model not tailored to our case
study), considers the presence of Rayleigh waves in the
response spectrum.

To summarise, a large part of the observed spatial
variability at low frequencies is attributed to the radi-
ation pattern of Rayleigh waves generated by this shal-
low earthquake (1–2 km). Their slower attenuation with
distance further amplifies their impact on ground mo-
tions, highlighting a gap in current GMMs for shallow
<figure><img src="image_9.png" /><figcaption>**Figure 7** Spatial distribution of within-event residuals ($\delta W_{es}$) computed using Ko20's GMM under the assumption of $V_{S30}=800$ m/s for four frequencies. The colour scale is limited to ±3 to emphasize differences; some data points fall outside these limits.</figcaption></figure>

seismic sources.

## 5.2 Spatial Variations of High-Frequency Ground Motions

The analysis of within-event residuals revealed clear spatial patterns at high frequencies, in particular faster attenuation of high-frequency ground motions towards the southeast of the rupture (clusters #1 and #3) compared to the northwest (cluster #2) (Figure 8).

It is noteworthy that studies of the Le Teil earthquake source have reported no evidence of rupture directivity (Causse et al., 2021; De Novellis et al., 2020; Delouis et al., 2021), suggesting that the observed azimuthal variations in high-frequency amplitudes should not be attributed to this phenomenon. Additionally, stress drop, a key parameter influencing high-frequency ground motion (e.g., Cotton et al., 2013), was estimated at 1.0 MPa for this earthquake (Causse et al., 2021), which is consistent with the average of worldwide reported stress drops (e.g., Courboulex et al.,

2016) and thus unlikely to explain the overall low level of high-frequency ground motion compared to GMMs (Figure 4). As explained in the following, the variations in high-frequency amplitudes observed across the region are likely to be primarily related to wave propagation effects.

Seismic wave attenuation is generally quantified by the quality factor Q. The amplitude of body waves decays as a function of distance r and frequency f according to $exp(-\pi.f.r/c.Q)$, where c is the wave velocity. Seismic attenuation is primarily controlled by two phenomena, including absorption (i.e., the conversion of seismic energy into other forms, e.g., Aki, 1980) and scattering (i.e., the redistribution of seismic energy in the medium due to heterogeneities, inducing a lengthening of the ground motions, e.g., Sato, 1989). Analyses of the quality factor in mainland France reveal frequency and regional variations (Calvet et al., 2013; Campillo and Plantet, 1991; Drouet et al., 2010; Mayor et al., 2018). In particular, Mayor et al. (2018) provided
<figure><img src="image_10.png" /><figcaption>**Figure 8** Left panel, spatial distribution of the four clusters identified in this study in relation to simplified geology. Right panel, the $\delta W_{es}$ values with respect to frequency are depicted for each cluster. The frequency range considered in the clustering analysis (0.4 - 7 Hz) is highlighted in grey. The dark-coloured lines represent the average behaviour of each cluster, while the black lines depict the $\delta W_{es}$ curves for the three representative stations shown in Figure 6.</figcaption></figure>

an absorption map derived from the coda wave analysis, showing that the southeast region appears to be a strong absorption region across the entire frequency range (~1–30 Hz). Furthermore, a 3-D shear wave velocity model of the Alpine region (Nouibat et al., 2022) indicates significantly lower S-wave velocities in the southeastern basin (~2.7 km/s at 6 km depth) compared to faster velocities west of the Cevennes fault, towards the Massif Central (~3.4 km/s). Indeed, the southeast basin region has undergone two phases of compressive deformation due to the Pyrenean and the Alpine orogenies (folding in both directions, see Figure 8). It is, therefore, highly folded and fractured, which could favour scattering and explain the large observed attenuation.

In this section, we also explore another attenuation mechanism through simple numerical simulations. This mechanism, distinct from absorption, is suggested by the combination of specific 1D-features in the velocity structure southeast of Le Teil and the shallow rupture depth.

### 5.2.1 Local Geological Structure Southeast of Le Teil

We present a simplified cross-section based on geological information obtained from four deep (> 2 km) boreholes located around Le Teil and aligned along a N35° E strike (see Figure 9). The earthquake epicentre

is located approximately 2 km southeast of this cross-section. The latter illustrates the main geological layers around the La Rouvière fault and their lateral variations. Causse et al. (2021) produced shear wave velocity ($V_s$) profiles using a three-component beamforming method (Wathelet et al., 2018), analysing seismic noise recorded at 19 temporary post-seismic stations near the rupture zone (refer to Figure 9 for station locations). This velocity profile indicates an increase in $V_s$ for a layer between approximately 500 and 1000 m depth, followed by a distinct $V_s$ inversion beneath this layer. At greater depths, the velocity profile becomes less constrained. Causse et al. (2021) associated the high $V_s$ value layer with shallow competent limestone units (Berriasian recifal limestone) and marly limestone from the Hauterivian series. The lower $V_s$ layer is linked to softer formations rich in marl from the Late Cretaceous (Valanginian argillaceous limestone). However, it should be noted that the stations used are located between two boreholes, presenting significant lateral variations in the depth of the geological layers. Moreover, the general eastward dip of the geological formations implies that the series identified at the position of the epicentre are probably a little deeper (~200 to 500 m). Finally, the “theoretical” position of the velocity profile is representative of a large volume of the geological series, considering the spatial extension of the seis-
<figure><img src="image_11.png" /></figure>

**Figure 9** Summary of recent geophysical and geological studies carried out in the vicinity of the hypocentre of the Le Teil earthquake (represented by a red star). In the top panel, a geological map on which the faults are represented by black segments, with the La Rouvière fault highlighted in red. Four boreholes, almost aligned along a NE-trending direction, are represented by red squares (letters and numbers are the uniform notation of series on French geological maps - www.infoterre.fr). Additionally, stations (nodes and seismometers) used to compute the V<sub>s</sub> profile by Causse et al. (2021) given below are represented. The pink shape with a solid line corresponds to the part of the profile for which the inversion of the dispersion curves is relatively robust, whereas the shaded part with a dashed line corresponds to a more uncertain result. In the lower panel, a cross-section based on geological information from the four deep boreholes represented by black lines is presented. The colours used in this cross-section correspond to those on the geological map. V<sub>p</sub> profiles in blue from the Valvignères and Marsanne boreholes (seismic coring) are given on each side of the cross-section. The V<sub>s</sub> profile from Causse et al. (2021) and the corresponding station coverage are indicated on the cross-section (grey rectangle). Geological interfaces and the surface (simplified) are represented in altitude (above or below sea level). Geological information for the boreholes comes from BSS database (www.infoterre.fr). Wells are: Vallon Pont d'Arc (BSS002BMNT), Valvignères (BSS002ARWX), Savasse (BSS002ASEZ) and Marsanne (BSS002ASXR).

stations. The one-dimensional hypothesis consid-
ered when calculating the dispersion curves is therefore
not respected and the representativeness of the column

must be considered with caution. Furthermore, seis-
mic coring and sonic measurements conducted at the
boreholes provide Vp values (Thomasset et al., 2024).
Figure 9 presents $V_p$ profiles for the Valvignères and Marsanne boreholes. In these $V_p$ profiles, no velocity variation is observed between the Valanginian and Hauterivian series. Higher velocities are found for the Tithonian Kimmeridgian limestones. Deeper, a layer of lower velocity is observed at the level of the Callovo-Oxfordian black shales, which are less competent layers than the overlying limestones. Based on these $V_p$ profiles, the velocity inversion seems more closely related to this black shale series. Defining a velocity profile in this region and correlating it with the local geology remain an open question. Regardless of the geological units associated with this poorly competent layer, the velocity structure of the Le Teil earthquake area is unambiguously characterised by a velocity inversion. We next analyse the effect of the presence of such a layer near the earthquake source on seismic ground motion.

### 5.2.2 Effect of a Shallow Velocity Inversion on the Ground Motion Decay from Simulations

Here, we conduct numerical simulations to analyse the effect of such a velocity inversion on the decay of ground-motion parameters up to a distance of 50 km. For the sake of simplicity and to better emphasise the involved physical processes, we consider simplified versions of the 1D-velocity profile. This is, of course, a great simplification of the geological complexity of the region. If the low velocity layer is made up of the succession of black shales topped by the Tithonic slab, this simplification has the advantage of considering the continuity of that structure at the scale of the southeast basin which is the reality. However, as the basin deepens rapidly towards its centre, the assumption of a horizontal layer is not very realistic. Furthermore, although the tectonic deformations are not very pronounced to the east of the Cevennes, the same cannot be said for the subalpine ranges, where the layers are highly deformed, bringing to the surface the black shales that are so characteristic of the Baronnies and Diois regions.

We perform ground motion simulations up to a frequency of 5 Hz for two 1D-velocity models (Figure 10). The first model, considered as a reference, consists of a homogeneous half-space overlaid with a 2.5 km-thick layer. In this model, the shallow layer has the lowest $V_s$ value. In contrast, the second model is characterised by a velocity inversion, defined by adding a 1.5 km-thick low-velocity layer buried at 1 km (referred to as LV layer in the following) to the first model. To mimic the source process of the Le Teil event, we use a point source model with (strike, dip, rake) equal to (0°, 45°, 90°). The dip and rake values are consistent with Ritz et al. (2020). The point source is positioned at 0.5 km depth, which roughly corresponds to the depth of the maximum static slip imaged by InSAR data (Cornou et al., 2021). The duration of the source time function is 2 s (Causse et al., 2021) and is represented by a regularised Yoffe function (Tinti et al., 2005). The surface receivers are positioned along a line at epicentral distances from 2 to 50 km, with interstation distance of 2 km up to 20 km and 5 km from 20 to 50 km. Seismograms are obtained by convolving the source time function with Green's functions

computed using the discrete wave number technique of Bouchon (1981) (AXITRA computer package, Cotton and Coutant, 1997), for the various 1D-media. The following results are presented for a source-receiver azimuth of 90°, but we have checked that they remain unchanged for azimuths of 45° or 135°. The values of Sa(f) are finally defined as the geometrical mean of spectral acceleration computed on the longitudinal and vertical components.

<figure><img src="image_12.png" /><figcaption>**Figure 10** Shear-wave velocity profiles used for the ground motion simulations. The reference model is composed of a homogeneous half space overlaid with a 2.5 km-thick layer. In the second model a low-velocity (LV) layer is introduced, resulting in a velocity inversion. The P-wave velocity is equal to 1.7 $V_s$.</figcaption></figure>

Figure 11 shows that the decay of Sa(f) with distance is remarkably faster beyond ~10 km in the presence of a LV layer at 2 Hz and 5 Hz. This is the case considering absorption in the layers (represented by quality factors $Q_p$ and $Q_s$ equal to $V_p/10$ and $V_s/10$, respectively, with $V_p$ and $V_s$ in m/s) or purely elastic medium (infinitesimal quality factors). The mechanisms responsible for such decay are analysed hereafter. In the absence of LV layer, the acceleration time series are dominated by a very weakly dispersive Rayleigh wave propagating at the Rayleigh speed (0.92 $V_s$), which controls the PGA and results in a short-duration signal (Figure S.18). The presence of a LV layer generates strong later wave arrivals resulting in a drastic increase of the signal duration and significantly smaller peak values (Figure S.18). Such arrivals have a dominant frequency of about 2 Hz (Figure S.19). A snapshot of the velocity particle inside the medium clearly reveals that those late arrivals emanate from the leakage of waves trapped and amplified in the LV layer at the interface between the top and the LV layer (Figure 12). An analysis of the normal modes and dispersion curve of the Rayleigh waves shows that the late arrivals result from the excitation of higher modes (Figure S.20). These simulations are consistent with observations, with lower spectral amplitudes (Figure 3) and longer durations (Figure 2) in the southeast than in the northwest.

We then examine the persistence of the fast decay of
<figure><img src="image_13.png" /><figcaption>**Figure 11** Decrease of spectral acceleration Sa(f) with distance at various frequencies for the 1D-velocity media of Figure 10, that is with the presence of a buried low-velocity (LV) layer (in grey), or without (in red). Sa(f) is computed considering a purely elastic medium (crosses) or with quality factors Qs and Qp equal to Vs/10 and VP/10, respectively (Vs and VP in m/s).</figcaption></figure>

Sa(f) at 2 and 5 Hz with distance as the LV layer and source properties are varied. Firstly, we also observe a faster decay with distance when the velocity inversion is weaker ($V_s=2$ km/s in the LV layer instead of $V_s=1$ km/s). The amplification inside the LV layer is then weaker but it is counterbalanced by a stronger leakage at the top, resulting in similar fast decay of Sa(f) (Figure S.21). Secondly, we verify that the decay persists in the case of a thicker LV layer (2.5 km instead of 1.5 km) and is not sensitive to the dip angle (tested values of 30°, 45° and 60°). It is also poorly sensitive to the source depth as long as the source is located within the surface layer (Figure S.22). However, the fast decay is not observed when the LV layer is buried more than approximately 1.5 km below the surface (Figure S.23). In this case, the amplitude of the late arrivals becomes too weak to control the PGA values (Figure S.24), and the decay of Sa(f) with distance becomes similar with and without the LV layer.

These calculations highlight an additional effective mechanism for the attenuation of high-frequency ground-motion, distinct from classical absorption. Such mechanism may occur when there is a shallow LV layer (above~1.5 km considering our hypotheses)

and a shallow source (located above the LV layer). For the shallow Le Teil earthquake, those conditions were likely met southeast of the epicentre. At this moment, it remains however difficult to evaluate the real contribution of this mechanism to the faster high-frequency ground motion amplitude decay observed toward the southeast and up to which distance it may have acted. The assumption of a 1D-velocity model is an oversimplification of the real geological structure at the scale of the southeast basin, which deepens towards the south-east. Further geological and geophysical investigations are necessary to map the geometrical properties of the geological units characterised by low shear-wave velocities. Our simulations indicate that the depth of the top of the low-velocity layers seems to be the most critical property. This can provide insights into the extent of the area on which the approximation of a 1D-velocity model is relevant or help in designing more realistic models (2D).

To summarise, the spatial variability observed at high frequency may be mainly controlled by attenuation mechanisms, including one that could result from the combination between the local velocity properties and the shallow rupture depth.
<figure><img src="image_14.png" /><figcaption>**Figure 12** Snapshot at 7s of the particle ground velocity inside the 1D-velocity profile in case of velocity inversion (Figure 10). The LV layer is between the two dashed lines. The Peak Ground Velocity values (PGV) are indicated. The source depth is 0.5 km. The quality factors $Q_S$ and $Q_P$ equal to $V_S/10$ and $V_P/10$, respectively ($V_S$ and $V_P$ in m/s).</figcaption></figure>

# 6 Conclusions

On 11 November 2019, a moderate $M_W$ 4.9 earthquake occurred at an exceptionally shallow depth (1–2 km) near the town of Le Teil in southeastern France. Numerous good quality ground motion records are available and well distributed around the epicentre (198 stations ranging from 8 to 300 km). Their analysis reveals specific features, including consistent large-scale spatial and frequency-dependent ground motion patterns related to source and path effects. Firstly, at lower frequencies (< 1 Hz), significant Rayleigh waves are generated due to the shallow depth of the rupture, especially in the northwest and southeast directions (orthogonal to the fault direction). In these configurations, various GMMs selected underestimate observations at low frequency across all distances because these waves attenuate less rapidly than body waves. In the northeast direction, which corresponds to a node in the Rayleigh wave radiation pattern, good agreement is observed. Secondly, a clear difference emerges between ground motions in the northwest, characterised by short-duration signals rich in high frequency, and those in the southeast, exhibiting longer durations and high-frequency spectra largely lower than those predicted by GMMs. Several mechanisms may be responsible for this high-frequency attenuation in the southeast. Absorption models, 3-D shear-wave velocity models, and geological evidence of particularly fractured sedimentary formations, support a slower propagation and a faster attenuation of seismic waves in the southeast basin. Furthermore, using simple numerical simulations, we show that the combination of local geological information, including the presence of a low velocity layer beneath the hypocentre, and the extremely shallow depth of the earthquake could be responsible for a faster decay of

high-frequency ground motion with distance, and for longer signal durations. To determine whether this significant high-frequency attenuation is specific to the extremely shallow depth of the Le Teil earthquake, or whether it is a regional feature, it would be necessary to carry out a statistical analysis of the Epos-France-RAP and -RLBP dataset of ground motions in mainland France (Traversa et al., 2020; Buscetti et al., 2024). Studies on this subject are currently in progress (Personal communication from S. R. Kotha). Finally, these results still present some limitations, as site conditions are not well constrained and are represented using non-site-specific $V_{S30}$ values (e.g., 800 m/s) in the GMMs. However, several sensitivity tests were performed to support these findings. The clustering analysis also helps to identify stations exhibiting strong low-frequency amplification, particularly in areas with well-documented site effects, such as the Rhône Valley, and the Grenoble and Nice basins. Continued efforts to characterise seismic stations (e.g., Hollender et al., 2018) therefore remain essential to better constrain residual analyses and improve ground motion models.

The Le Teil earthquake is part of a broader context of repeated extremely shallow seismicity in the region. Our analysis demonstrates that GMMs classically used for SHA in mainland France inadequately capture the main ground motion features of the Le Teil earthquake. Improving GMM predictions for extremely shallow earthquakes is essential for accurate seismic hazard assessment in such contexts. This study should be extended to other shallow earthquakes to see if certain systematisms can be found globally. However, identifying such earthquakes in databases can be challenging, as depth is a parameter that is often poorly constrained. Recently, Di et al. (2023) provided an inventory of mod-
<table><caption>**Table 2** Main characteristics of the station networks used in this study.</caption><thead><tr><th>Institutes Projects</th><th>FDSN codes</th><th>Status</th><th>Access</th><th>Type of station used</th><th>Recording</th><th>References</th></tr></thead><tbody><tr><td rowspan="5">Epos-France</td><td>FR</td><td>Permanent</td><td>Public</td><td>HH, HN</td><td>Continuous</td><td>Epos-France (1995)</td></tr><tr><td>RA</td><td>Permanent</td><td>Public</td><td>HN</td><td>Continuous</td><td>RESIF (1995)</td></tr><tr><td>MT</td><td>Permanent</td><td>Public</td><td>HH</td><td>Continuous</td><td>French Landslide Observatory - Seismological Datacenter / RESIF (2006)</td></tr><tr><td>XT</td><td>Temporary</td><td>Restricted<sup>a</sup></td><td>HH</td><td>Continuous</td><td>Zhao et al. (2018)</td></tr><tr><td>3C</td><td>Temporary</td><td>Public</td><td>HH, HN</td><td>Continuous and triggered</td><td>Bertrand et al. (2019)</td></tr><tr><td>AlpArray</td><td>Z3</td><td>Temporary</td><td>Restricted<sup>a</sup></td><td>HH</td><td>Continuous</td><td>AlpArray Seismic Network (2015)</td></tr><tr><td>SNCF</td><td></td><td>Permanent</td><td>Restricted</td><td>HN</td><td>Triggered</td><td>Vallage et al. (2021)</td></tr><tr><td>GEOSCOPE</td><td>G</td><td>Permanent</td><td>Public</td><td>HH, HN</td><td>Continuous</td><td>Institut de physique du globe de Paris (IPGP) et École et Observatoire des Sciences de la Terre de Strasbourg (EOST) (1982)</td></tr><tr><td rowspan="3">SED</td><td>CH</td><td>Permanent</td><td>Public</td><td>HH</td><td>Continuous</td><td>Swiss Seismological Service (SED) At ETH Zurich (1983)</td></tr><tr><td>8D</td><td>Temporary</td><td>Public</td><td>HH</td><td>Continuous</td><td>Swiss Seismological Service (SED) At ETH Zurich (2005)</td></tr><tr><td>C4</td><td>Permanent</td><td>Public</td><td>HH</td><td>Continuous</td><td>CERN (2016)</td></tr><tr><td>University of Genoa</td><td>GU</td><td>Permanent</td><td>Public</td><td>HH</td><td>Continuous</td><td>University of Genoa (1967)</td></tr></tbody></table>

erate shallow earthquakes associated with surface rupture (earthquakes mainly in China and in Australia) that could have generated significant local damage. Their ground motions could be investigated to improve the seismic hazard of such extremely shallow earthquakes, including Human-induced earthquakes (e.g., Foulger et al., 2018), especially in regions of low-to-moderate seismic activity like mainland France.

## Acknowledgments

We thank Anne Paul for the transmission of Le Teil earthquake data from the AlpArray and CIFLAPS-2 projects. These data were under embargo during the project period and have since become publicly available through Epos-France. We also thank Florence Marcilly from SNCF for giving us to the seismic signals of Le Teil earthquake recorded by these stations, as well as CEA for preparing the data and providing information on metadata, with special thanks to Damien Grenié and colleagues. We thank the team «Retour d'expérience post sismique et expérimental pour actualiser les méthodes d'ingénierie conventionnelles» (Post-seismic and Experimental Feedback to Update Conventional Engineering Methods) action within the « Groupe de Gestion de Programme Mécanique des Structures et Séisme» (GGP MSS), more specifically Paola Traversa, for fruitful discussions. The work was partially funded by GGP MSS and the Institute of Research for Development. The authors are grateful to Fabian Bonilla and an anonymous reviewer for their careful reading and comments.

## Data and Code Availability

Seismological data are provided by the European Integrated Data Archive (EIDA, http://www.orfeus-eu.org/

data/eida/) and the French seismological and geodetic network (Epos-France, https://www.epos-france.fr/). The overall network characteristics and references are described in Table 2. To compute the seismic intensity measures, the Seismic-Intensity-Measure code developed in Python by Maria Lancieri was employed (https://github.com/fiorellalan/Seismic-Intensity-Measure). Data analyses have been performed using both the software python (cartopy, matplotlib, obspy, pandas, scikit-learn, ...) and the software Matlab version R2019A. The basemap is the World Terrain Base map supplied by ArcGIS on this link https://server.arcgisonline.com/arcgis/rest/services/World_Terrain_Base/MapServer. The programs disd3D.exe developed by D. Boore to calculate fault-to-station distances are available online at http://www.daveboore.com/software_online.html (last accessed July 2021). For GMMs, we used the models available in the package gsim of the version 3.13 of openquake. The dataset build during the current study is provided as supplementary material and available on Zenodo (Laurendeau et al., 2024). The Axitra program was used for the numerical simulations.

## Competing Interests

The authors have no competing interests.

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The article *The extremely shallow Mw 4.9 2019 Le Teil earthquake, France: Main ground motion features and comparison with ground motion models* © 2025 by A. Laurendeau is licensed under CC BY 4.0.