# Correlating Groundwater Level Fluctuations of a Fractured Confined Aquifer With Relative Variations in Seismic Velocity: A Way to Estimate the Groundwater Storage

Benoit Vittecoq, Arnaud Burtin, Jerome Fortin

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Benoit Vittecoq, Arnaud Burtin, Jerome Fortin. Correlating Groundwater Level Fluctuations of a Fractured Confined Aquifer With Relative Variations in Seismic Velocity: A Way to Estimate the Groundwater Storage. Geophysical Research Letters, 2025, 52 (7), 10.1029/2024GL110808. hal-05023813

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# Geophysical Research Letters®

## RESEARCH LETTER

10.1029/2024GL110808

**Key Points:**

* Seismic velocity variations are negatively correlated with the seasonal groundwater pressure variations of a confined fractured aquifer

* The relationship occurs above a threshold related to the fractures' properties. Beyond it, fractures open up as groundwater pressure rises

* We propose a method to estimate the storage coefficient's order of magnitude in fractured confined aquifers, validated with pumping test data

**Supporting Information:**

Supporting Information may be found in the online version of this article.

**Correspondence to:**

B. Vittecoq,
b.vittecoq@brgm.fr

**Citation:**

Vittecoq, B., Burtin, A., & Fortin, J. (2025). Correlating groundwater level fluctuations of a fractured confined aquifer with relative variations in seismic velocity: A way to estimate the groundwater storage. *Geophysical Research Letters*, *52*, e2024GL110808. https://doi.org/10.1029/2024GL110808

Received 13 AUG 2024
Accepted 1 MAR 2025

**Author Contributions:**

**Conceptualization:** B. Vittecoq,
A. Burtin, J. Fortin

**Data curation:** B. Vittecoq, A. Burtin,
J. Fortin

**Formal analysis:** B. Vittecoq, A. Burtin,
J. Fortin

**Funding acquisition:** B. Vittecoq

**Investigation:** B. Vittecoq, A. Burtin,
J. Fortin

**Methodology:** B. Vittecoq, A. Burtin,
J. Fortin

**Project administration:** B. Vittecoq

**Resources:** B. Vittecoq, A. Burtin,
J. Fortin

© 2025 The Author(s).
This is an open access article under the
terms of the Creative Commons
Attribution-NonCommercial License,
which permits use, distribution and
reproduction in any medium, provided the
original work is properly cited and is not
used for commercial purposes.

<figure><img src="image_2.png" /></figure>

# Correlating Groundwater Level Fluctuations of a Fractured Confined Aquifer With Relative Variations in Seismic Velocity: A Way to Estimate the Groundwater Storage

B. Vittecoq¹ ID, A. Burtin² ID, and J. Fortin³ ID

¹BRGM, Fort-de-France, Martinique, ²Université de Paris Cité, Institut de Physique du Globe de Paris, CNRS, Paris, France, ³Laboratoire de Géologie, Ecole Normale Supérieure/CNRS, UMR8538, PSL Research University, Paris, France

**Abstract** Analysis of ambient seismic noise is of increasing interest for its potential to monitor aquifers, seismic wave velocity being sensitive to fluctuations of the water table or to pore pressure variations. The correlation with groundwater pressure variations in confined aquifers, which are often strategic, is an open scientific question, as is the stored groundwater volume. Based on an experimental site equipped with a low-cost seismometer located close to a borehole in a confined fractured aquifer, we demonstrate that (a) the auto and inter-components correlation of the time series of the seismometer enables detecting variations in seismic velocities, (b) these changes are negatively correlated with the groundwater pressure variations, and (c) these changes occur above a groundwater pressure threshold related to the fractures' properties. Finally, we propose a method to estimate the storage coefficient's order of magnitude of the confined aquifer using the correlation between $dv/v$ and the groundwater pressure.

**Plain Language Summary** By analyzing the seismic vibrations in the ground, scientists have found a useful way to monitor groundwater movement in aquifers. However, a better understanding of this method is needed for confined aquifers, which are often critical for supplying drinking water. In our study, we set up a simple, inexpensive seismic sensor near a deep well in a fractured confined aquifer. We found that changes in the ground response to seismic vibrations recorded by the sensor matched up with changes in water pressure in the aquifer. This suggests that seismic monitoring could help us understand and manage water resources in confined aquifers. Our study also suggests a new way to estimate how much water these aquifers can hold, which is crucial for water resource management.

## 1. Introduction

Groundwater is a critical resource for drinking water and agricultural irrigation. Enhancing our understanding of its availability and evolution is crucial for effective resource management. To address society's growing needs for aquifer location, extension and groundwater monitoring, hydrogeologists and geophysicists have developed various methodologies with widely varying costs and relevance, sometimes dependent on the geological context. These methods require validation through boreholes to ensure their effectiveness. However, drilling is generally expensive, and decision-makers aim to minimize drilling failure risks while maximizing the chances of finding water. Additionally, monitoring groundwater in areas where drilling is impractical is also a strategic issue. Thus, improving indirect geophysical methods is a key challenge.

Among the existing methods, the ambient seismic noise method is of interest because it can detect relative seismic velocity perturbations ($dv/v$). This method was developed mainly for volcanic, seismic, and tectonic processes (Brenguier et al., 2016; Campillo, 2006; Gassenmeier et al., 2015; Sens-Schönfelder & Wegler, 2006; Shapiro & Campillo, 2004; Q. Y. Wang et al., 2017; Wegler et al., 2009). Over the past few years, studies (Clements & Denolle, 2018; Gaubert-Bastide et al., 2022; Kim & Lekic, 2019; Kramer et al., 2023; Lecocq et al., 2017; Mao et al., 2022; Voisin et al., 2017; Zhang et al., 2023) focused on tracking correlations between groundwater level variations and changes in $dv/v$. Negative trends between $dv/v$ and groundwater levels as well as synchronous seasonal changes or long-term trends have been observed in Germany (Lecocq et al., 2017), California (Clements & Denolle, 2023; Mao et al., 2022) or Greece (Delouche & Stehly, 2023). Nevertheless, only few studies have confirmed their observations and hypotheses through direct measurements of groundwater level in boreholes (such as Gaubert-Bastide et al., 2022; Voisin et al., 2017). The present scientific issues are to understand how
**Software:** B. Vittecoq, A. Burtin, J. Fortin

**Supervision:** B. Vittecoq, A. Burtin, J. Fortin

**Validation:** B. Vittecoq, A. Burtin, J. Fortin

**Visualization:** B. Vittecoq, A. Burtin, J. Fortin

**Writing – original draft:** B. Vittecoq, A. Burtin, J. Fortin

**Writing – review & editing:** B. Vittecoq, A. Burtin, J. Fortin

groundwater levels and $dv/v$ respectively, evolve; what do the correlations mean; what mechanisms explain these correlations; and how we can better constrain groundwater volume.

Aquifers are permeable geological formations that allow groundwater flow. They are either confined or unconfined. Unconfined aquifers have groundwater levels in equilibrium with atmospheric pressure, fluctuating with seasonal and annual rainfall. In this case, seismic velocity and thus $dv/v$ are sensitive to water saturation (Grêt et al., 2006; Kim & Lekic, 2019). Confined aquifers, fully saturated, and pressurized, cannot exhibit velocity changes due to saturation variations but rather to pore pressure effects (Wyllie et al., 1958). While variations in seismic velocity are often reported in unconfined aquifers, few studies have focused on confined aquifers. Finally, the storage coefficient of aquifers (porosity for unconfined aquifers and storativity for confined aquifers) measures their capacity to release or store water. According to Kuang et al. (2020) and Chowdhury et al. (2022), the specific storage of confined aquifers varies across six orders of magnitude from $3 \times 10^{-9}$ to $6 \times 10^{-3} \text{ m}^{-1}$. For each aquifer type values span about three orders of magnitude. The accuracy of the applied methods is typically within one order of magnitude.

Our study focuses on a confined aquifer (the Galion aquifer) located in Martinique (Figure 1), whose hydrogeological functioning is relatively well defined (Thomas et al., 2024; Vittecoq et al., 2020). We take advantage of having, on the same site, a low-cost seismometer (©Raspberry Shake) and a groundwater level probe in a borehole intersecting the confined aquifer. The analysis of ambient seismic noise by auto- and inter-component correlation of the time series of the seismometer enables the detection of variations in seismic velocities. In this article, we will first demonstrate that $dv/v$ changes are negatively correlated with the groundwater pressure variations of the confined aquifer. Furthermore, we will demonstrate that these changes only occur above a groundwater pressure threshold. Finally, we will propose a method to estimate the storage coefficient's order of magnitude of the confined aquifer.

## 2. Study Site and Data

### 2.1. Study Area

Martinique is a volcanic island of the Lesser Antilles (Figure 1a). The site is located on the east coast of Martinique (Figure 1b), located 1.5 km from the sea at an elevation of 6 m amsl. Figure 1c shows a geological cross-section of the watershed. The geological formations beneath the site consist of clay and sandy-clay on the first 19 m, constituting a confining unit, below which a fissured and fractured basaltic lava confined aquifer is observed up to a depth of at least 50 m (Figure 1d). Previous studies on this site have focused on hydraulic conductivity evolution induced by earthquakes (Thomas et al., 2024; Vittecoq et al., 2020). The hydraulic conductivity of this aquifer is around $2 \times 10^{-4} \text{ m}^2/\text{s}$ and the storage coefficient is around $3.5 \times 10^{-3}$ (Thomas et al., 2024).

### 2.2. Water Level, Seismic, and Climatic Monitoring

The water level monitoring borehole (PZ-50—national number BSS002NNZL) is equipped with a PARATRONIC SNP pressure sensor with data recording every minute (with $\pm 1 \text{ mm}$ resolution). A Raspberry Shake RS3D (https://raspberryshake.org/), a three-component geophone (station R66E3 and network code AM) with a natural frequency of 4.5 Hz (electronically extended to 0.5 Hz), was installed in 2022 in the technical room near PZ-50 (Figure 1c). Rainfall and air temperature are available close to the site (4 km - meteo.data.gouv.fr).

## 3. Method: Data Processing and Analysis

$dv/v$ are obtained from the interferometry of the seismic noise correlation functions (e.g., Hadzioioannou et al., 2011; Sens-Schönfelder & Wegler, 2006). In our study, we have a single seismic station with three components, oriented vertically (Z), north (N), and east (E). We estimate both autocorrelation and intercomponent correlation functions. This approach aims to approximate the specific case of a collocated source-receiver medium Green's function (Sens-Schönfelder & Wegler, 2006). This method has been validated and applied to coda wave interferometry for estimating $dv/v$ (De Plaen et al., 2016; Sens-Schönfelder & Wegler, 2006). Sens-Schönfelder and Wegler (2006) also compared auto-correlation and common ambient noise correlation functions and found equivalent results (see Figure S1 in Supporting Information S1).
<figure><img src="image_3.png" /><figcaption>**Figure 1.** (a) Location of the Lesser Antilles. (b) Location of the Galion site on Martinique Island. (c) Cross section along the topographic watershed; and (d) Site geological log.</figcaption></figure>

The correlation functions (auto and inter-components) are computed from hourly segments. We use the raw seismic signal in count without applying an instrument correction, as we use a single 3-component geophone and focus on frequencies above 1 Hz. Seismic data are processed following the standard techniques detailed by Bensen et al. (2007). We remove the signal mean and apply a bandpass filter between 0.1 and 10 Hz. The estimated correlation function will contain frequencies within this range, which is broader than the frequencies of interest. However, this allows us to assess waveform similarity. We observe a loss of coherence above 6 Hz, which limits reliable interpretation. To improve computation time, we decimate the signal by a factor of 4, reducing the sampling rate from 100 to 25 Hz. We also apply spectral whitening (in the frequency domain) and a 1-bit normalization (in the time domain) to remove the influence of transient sources like earthquakes and environmental noise (Figure S2 in Supporting Information S1). Finally, we estimate hourly the three auto-correlation functions (ZZ, NN, and EE) and the three inter-components correlation functions (ZN, ZE, and NE) with causal and anticausal parts.

To obtain *dv/v*, we use the stretching technique, where a reference correlation function (averaged over the experiment period) is time-dilated or compressed to obtain the best correlation coefficient or waveform similarity with a daily correlation function (averaged over 24 hourly segments). This procedure is applied at different frequencies by filtering the correlation function with a Gaussian filter centered between 2 and 6 Hz, with a 0.2 Hz step, and a Gaussian width $\sigma_t$ of 0.5 Hz (Figure 2). This allows us to explore *dv/v* time-series from 2 to 6 Hz and identify frequencies that best correlate with hydrological signals. To avoid introducing a priori or a user specific parameter for the selection of the coda time interval, waveform stretching is computed over several delay intervals with a starting window ranging from 2 to 4 s, with a step of 0.125 s (more than 3 times the sampling rate of
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Relative time perturbation analysis. (a) Daily relative velocity variations in time and in frequency from 2 to 6 Hz. The common time delay window is fixed from 2 to 5 s. Positive and negative velocity changes are shown in red and blue, respectively. Monitored groundwater levels variations (vertical right axis) are shown in black (PZ-50 in the confined aquifer, Figure 1d). (b) Coherence of the stretching analysis for the same time period and frequencies. High (low) level of coherence are shown in red (blue). The velocity signal is best retrieved for frequencies below 3.5 Hz.</figcaption></figure>

correlation functions). We also use a constant coda time width criterion equivalent to 10 wave periods (Figure S3 in Supporting Information S1). Practically, this means a coda time width of 5 s at 2 Hz and 1.6 s at 6 Hz, covering a total time delay window of [2–9]s at 2 Hz and [2–5.6]s at 6 Hz.

The daily *dv/v*, shown in Figure 2a, is the average of 153 estimates. These estimates are derived from 17 different coda time intervals across nine correlation function windows (3 for auto-correlation of ZZ, NN, EE, and six for inter-components correlation, ZN, ZE, and NE, including both causal and anti-causal parts). The analysis of auto-correlation and inter-components correlations yields similar results (see Figure S1 in Supporting Information S1), validating the approach of averaging all the components together.

Groundwater level data, recorded every minute, are averaged daily for comparison with seismic data (Figure 2). The hydraulic head in the aquifer is computed in meter above mean sea level (m amsl) and in water pressure in Pa at the depth of the main fractured zone (42 m depth, i.e. an elevation of –36 m amsl).

# 4. Results

## 4.1. Correlation of dv/v With Confined Aquifer Groundwater Level Variations

Figure 2 shows the time evolution of *dv/v* from 2 to 6 Hz. Two main frequency bands are observed, with a cutoff around 4 Hz. Below 4 Hz, *dv/v* is consistent and shows an inverse relationship with groundwater level (Figure 2a).
<figure><img src="image_5.png" /><figcaption>**Figure 3.** (a) Temporal evolution of *dv/v*: raw daily data, 7-day-long and 30-day-long using Gaussian filters. (b) Temporal evolution of weekly rainfall rate and (c) 7-day-long Gaussian filter temporal evolution of water level (m) and pressure (Pa) (right axis) and *dv/v* (left axis).</figcaption></figure>

Above 4 Hz, *dv/v* does not correlate well with the borehole data. We observe two periods of negative *dv/v* in October–November 2022 and March–April 2023, corresponding to the highest and lowest groundwater levels, respectively (Figure 2a). Analysis of waveform similarity using the stretching method (Figure 2b) indicates that frequencies below 3.5 Hz are most reliable. Therefore, we confidently associate the *dv/v* signal in the [2–3]Hz frequency band with groundwater observations.

The analysis of *dv/v* at [2–3]Hz over time shows a clear seasonal trend (Figure 3a). In order to remove daily variations and following the methodology used by Zhang et al. (2023), the raw *dv/v* data is filtered by 7-day-long and 30-day-long Gaussian filters, and the groundwater levels are also filtered by a 7-day-long Gaussian filter.

Figure 3c shows the temporal evolution of *dv/v* and the groundwater levels, with *dv/v* plotted in reverse direction for easier comparison with groundwater fluctuations. Groundwater elevation varies between 4.4 and 5.8 m amsl and *dv/v* between -1% and +0.5%. This figure clearly highlights a negative correlation between groundwater levels and *dv/v*. The correlation is well established, especially during the rainy seasons (September–December 2022, September–December 2023, July 2024–February 2025) when groundwater levels are high. The *dv/v* signal is therefore not directly sensitive to rainfall (Figure 3b) but to rainfall-induced water pressure variations in the aquifer, considering the transfer time in the recharge zone of the aquifer. During the dry seasons, when the water levels are lower (April–July 2022 and January–July 2023), the correlation is less accurate.

## 4.2. Threshold Effect

Binary diagram (Figure 4a) and box-plot (Figure 4b and Figure S4 in Supporting Information S1) reveal a clear linear trend: when groundwater elevations exceed 4.9 ± 0.1 m amsl *dv/v* decreases as water pressure in the confined aquifer increases and:
<figure><img src="image_6.png" /><figcaption>Figure 4. (a) Binary diagram and (b) Boxplot representation of $dv/v$ 7-day-long Gaussian filters (in %) versus 7-day-long Gaussian filter groundwater level (m amsl), with the linear regression line in red and the 4.9 m threshold in dotted black.</figcaption></figure>

$$ \frac{dv}{v} = -\frac{1}{72}\delta h = -1.39 \ 10^{-2} \delta h = -1.42 \ 10^{-6} \delta P $$

with $\delta h$ being the change in water level and $\delta P$ the water pressure change in the confined aquifer. Furthermore, Figure 4b highlights a threshold: when groundwater elevations are below 4.9 m amsl, there is no correlation, and $dv/v$ is constant.

# 5. Discussion

## 5.1. Depth of Investigation of 2–3 Hz Frequency Range

The sensitivity depth of coda wave interferometry is not a straight-forward parameter. First, the wave content must be distinguished between surface and body waves. Obermann et al. (2013) suggest that working at frequencies above 0.5 Hz with large coda time delays makes $dv/v$ sensitive to scattered body waves. The sensitivity kernel for these waves depends on the diffusion constant, which scales with the mean free path or average distance between scatterers (Aki & Richards, 1980; Hillers et al., 2014). Although this parameter is unknown, lower frequencies are expected to sample scatterers at greater depths compared to higher frequencies.

Another consideration is whether the velocity changes are related to P-waves ($V_p$) or S-waves ($V_s$). Sneider (2002) demonstrated that coda wave interferometry consists of 9% of $V_p$ and 91% of $V_s$, indicating that $dv/v$ is generally more sensitive to $V_s$. However, studies by Kim and Lekic (2019) and Sánchez-Pastor et al. (2023) suggest that $dv/v$ variations may be more closely related to $V_p$, in responses to groundwater fluctuations. They also emphasize the importance of distinguishing between auto-correlation, inter-component, and cross-correlation functions. Sánchez-Pastor et al. (2023) suggest that the bulk modulus and thus $V_p$ is highly responsive to fluid-phase variations, while $V_s$ is influenced by density changes and better suited for studying pressure variations. Kim and Lekic (2019) observed an increase in $dv/v$, estimated from auto-correlation functions, that coincided with rising groundwater levels in an unconfined aquifer. This behavior may be explained by the sensitivity of auto-correlation analysis to P-waves, which are more prominent in vertical components. However, since our study focuses on a confined aquifer, a direct comparison with Kim and Lekic (2019) is not possible.

In confined aquifer, both $V_p$ and $V_s$ should respond similarly to fracture opening induced by increasing pore pressure. In Figure S1 in Supporting Information S1, $dv/v$ variations appear consistent across vertical and horizontal components, with larger fluctuations observed in the NE component compared to ZN and ZE. The lack of pronounced changes in vertical components relative to horizontal components suggests our analysis is not predominantly sensitive to P-waves. This difference could arise from the lower frequency content and greater depth
of the aquifer studied by Kim and Lekic (2019). Wave extinction, combining scattering and absorption losses, may amplify P-wave attenuation in the subsurface more than at depth, especially with high-frequency content.

Although we cannot definitively conclude whether $dv/v$ variations are more sensitive to $V_s$ or $V_p$, our observations suggest a likely dominance of S-waves. To improve discrimination between the two, cross-correlation analysis could complement auto-correlation analysis, but this requires additional seismic instruments not available in our study site. Future research may explore this method to refine the interpretation of the $dv/v$ signal.

Consequently, we use the S-wave velocity log from a MASW profile (see Table S1 in Supporting Information S1) to estimate seismic wavelengths ($\lambda$). With an average $V_s$ of 425 m·s$^{-1}$, the wavelengths are 213 m at 2 Hz and 71 m at 6 Hz. Applying the rule of thumb (Darvasi, 2021; Kumagai et al., 2020) which suggests a maximum investigation depth of $\lambda/2$ to $\lambda/3$, we estimate depths of 23–35 m at 6 Hz and 71–107 m at 2 Hz. For the [2–3] Hz frequency range, these depths correspond to a few tens of meters up to about a hundred meters, corresponding to the position of the confined aquifer. This explains why $dv/v$ estimates in the [2–3]Hz frequency band better correlate with water pore pressure observations.

## 5.2. Relationship Between $dv/v$ and Change in Fracture Density

The $dv/v$ range we observed, with a variation of 1.5%, is consistent and within the same order of magnitude as Gassenmeier et al. (2015); Clements and Denolle. (2018); Oakley et al. (2021); Gaubert-Bastide et al. (2022); Zhang et al. (2023) and exhibits a similar trend: $dv/v$ decreases as groundwater level increases. Nevertheless, these studies focused on unconfined aquifers were water level variations modifies the saturated thickness of the aquifer through which seismic waves propagate. This assumption does not apply to our study, as our site features a confined aquifer, fully saturated beneath an impermeable layer.

Wave velocities changes with pressure have been reported in the laboratory. For example, Wyllie et al. (1958) measured ultrasonic $V_p$ as a function of effective pressure in a water-saturated sandstone. They showed that at a constant confining pressure, $V_p$ increases with decreasing pore pressure. Similar observations of changes in ultrasonic wave velocities with effective pressure were reported in cracked granite (Nur & Simmons, 1969; X. Wang et al., 2012) or basalt (Fortin et al., 2011; Stanchits et al., 2006). The interpretation is that pressure deforms the most compliant pores, such as cracks, which affect the stiffness of the rock.

In this study, the aquifer is confined in cracked basalt (Figure 1d). The overall porosity is small (few %), but it is known theoretically (Budiansky & O'Connell, 1976; Guéguen & Kachanov, 2011; Mallet et al., 2013; Zimmerman et al., 1986) and from laboratory experiments (Nur & Simmons, 1969; Wyllie et al., 1958) that cracks and fractures have a strong effect on the elastic moduli. The elastic opening/closure of the cracks/fractures is governed by the effective pressure, defined as $P_c - P$ where $P_c$ is the confining pressure and $P$ the pore pressure. In our case, $P_c$ is constant, and the change in the effective elastic properties and thus $dv/v$ is only controlled by the change in pore pressure, as shown by Figure 4b.

The key parameter that controls the effective elastic moduli is the crack density parameter $\rho$ defined first by Bristow (1960), generalized by Budiansky and O'Connell (1976):

$$ \rho = \frac{1}{V} \sum_{i=1}^{N} c_i^3 \qquad (1) $$

where $c_i$ is the radius of the ith crack and $N$ is the total number of cracks embedded in the representative elementary volume $V$. Equation 1 can be extended to a fractured medium by increasing the volume $V$. In the case of randomly oriented cracks/fractures, the change in the shear modulus can be expressed as (Kachanov, 1993):

$$ \frac{\delta G}{G} = -\psi \delta \rho \qquad (2) $$

where $\psi = \frac{16(1-\nu_0)(1-\nu_0)}{9(1-\nu_0^2)} \approx 1.5$ with $\nu_0 = 0.2$, the Poisson's ratio of the cracked/fractured-free altered basalt.

Note that Equation 2 is valid if $\psi \delta \rho \ll 1$. In addition, Equation 2 applies in a dry or saturated medium as long as the fluid is in a relaxed state (Adelinet et al., 2011; Dvorkin et al., 1995; Fortin & Guéguen, 2021) which is the
case given the frequency range of the ambient seismic noise analysis of 2–6 Hz (Section 3). Considering that $v = \sqrt{G/d}$, where d is the density, assuming to be constant (the aquifer is a confined one and thus always saturated), one gets:

$$ \frac{dv}{v} = \frac{1}{2} \frac{\delta G}{G} \approx -\frac{3}{4} \delta \rho \quad (3) $$

Then, in a confined, fractured aquifer, $dv/v$ changes can indicate changes in fracture density. When water pressure decreases, fractures close up, which leads to a decrease in the crack density and thus an increase in the shear modulus or an increase in $dv/v$. For a water level decrease of 50 cm, the observed change in $dv/v$ of $9 \times 10^{-3}$ is interpreted as a change in fracture density of $\approx +1\%$. The sensitivity of fracture density to pressure is in the same range as those reported by Suzuki et al. (2021) but is much higher (of one-two orders of magnitude) than those reported in the laboratory (Ougier-Simonin et al., 2011).

Finally, Thomas et al. (2024) recently used earth-tide analysis to estimate the aquifer's permeability, finding a linear correlation with groundwater level: permeability increases with rising water levels, and the process is reversible. This dependency on water pressure is attributed to the elastic opening or closure of fractures, aligning with our $dv/v$ observations.

### 5.3. Threshold and Relationship Between $dv/v$ and Storage Coefficient

Figure 4a, highlights a threshold in pressure, interpreted as the pressure for which fractures are partially closed, that is, fractures are no more sensitive to effective pressure. Following Walsh (1965), the effective closure pressure is:

$$ (P_c - P)_{\text{closure}} = \frac{\pi E_o \xi}{4(1 - \nu_0^2)} \quad (4) $$

where $\xi$ is the mean fracture aspect ratio, $E_o$ is the Young modulus of the fractured/cracked-free altered basalt. $(P_c - P)_{\text{close}} \approx (1.1-0.4) = 0.7$ MPa at a depth of 42 m, $P_c = 1.1$ being the average weight of soil and aquifer above the fractured zone, assuming a density of 2.7. Using $\nu_0 = 0.2$ and $E_o = 10$ GPa, this leads to a mean fracture aspect ratio $\xi = 8.6 \times 10^{-5}$, in the range of $10^{-4}$, meaning that for fractures of $\sim 10$ m in length, the mean aperture is $\sim 1$ mm.

The specific storage coefficient under fixed stress condition is defined as:

$$ S_{\sigma} = (\delta\xi/\delta P)_{P_c} \quad (5) $$

with $\xi$ being the variation of fluid mass (H. Wang, 2001). If we assume that the fluid is stored in the fractures, which are much more compliant than the fluid and the matrix, a rough estimation of the specific storage coefficient is:

$$ S_{\sigma} \approx (\delta\phi/\delta P)_{P_c} \quad (6) $$

where $\phi$ is the porosity. Recalling that the porosity of a fractured rock is given by $\phi = 2\pi\rho\xi$, and assuming that the variation of the aspect ratio with pore pressure is small compared to the variation of crack density with pore pressure, we get:

$$ S_{\sigma} \approx 2\pi\xi(\delta\rho/\delta P)_{P_c} \quad (7) $$

The storage coefficient, which is the quantity of practical interest, under fixed stress conditions is $S = \rho_w g H S_{\sigma}$, H being the aquifer thickness, which leads using Equations 3 and 7:

$$ S = \frac{-8}{3} \pi \rho_w g H \xi \frac{dv/v}{\delta P} \quad (8) $$
The aquifer thickness is not precisely known, but is at least 30 m thick (as intersected by the borehole) and does not exceed 200 m (based on geological observations and similar aquifer thicknesses on the island). Considering these constraints, an average thickness of 100 m is a reasonable estimate. Thus, using *H* = 30, 100, and 200 m, $\frac{dv/v}{\delta P} = -1.42 \times 10^{-6}$ Pa$^{-1}$ and considering the uncertainty of the threshold (±0.1 m) and the uncertainty of the slope of the linear regression of Figure 4, this leads to: $3 \times 10^{-4} < S < 3 \times 10^{-3}$ (with $S_H=100m = 1 \times 10^{-3}$).

This approach is only valid for a fractured aquifer and involves several assumptions. In addition, *dv/v* integrates the medium properties collectively along the pathways of coda waves. Nevertheless, the calculated storage coefficient range is of the same order of magnitude as the value of $3.5 \times 10^{-3}$ obtained through a classical pumping test (Thomas et al., 2024).

## 6. Conclusion

Our study highlights the potential of seismic ambient noise analysis for monitoring confined aquifers using a low-cost seismic monitoring. We demonstrate that *dv/v*, derived from auto and inter-components correlations of the seismometer time series, are negatively correlated with seasonal groundwater pressure variations in a confined fractured aquifer. Additionally, we show that above a threshold related to the fractures' properties, when groundwater pressure increases, fractures progressively open up, leading to a decrease in *dv/v*. Finally, we propose a method to estimate the storage coefficient's order of magnitude of a fractured confined aquifer based on the correlation between *dv/v* and groundwater pressure.

## Data Availability Statement

Seismic recordings for station R66E3 and network AM (Raspberry Shake, 2016) are collected from the Raspberry Shake data center (https://data.raspberryshake.org/fdsnws/). The raw continuous seismic recordings and relative velocity variations are processed by using MATLAB (https://mathworks.com). 2–3 Hz frequency range daily *dv/v* data, daily groundwater level data, daily rainfall and daily air temperature data are available in Vittecoq et al. (2025).

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The authors thank the funding organizations for their support. The equipment at the Galion experimental site was co-funded by BRGM, ENS, and CNRS, with partial support from the "Ecosphere Continentale et Côteière" (EC2CO) initiative of the Institut National des Sciences de l'Univers (INSU/CNRS). Part of this work was carried out within the framework of the "Sism'Eau Project," a research program led by BRGM.
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