# Characterization of a heterogeneous limestone vadose zone based on a multimethod and multiscale geophysical approach

Clémence Ryckebusch, Jean-Michel Baltassat, Anatoly Legchenko, Pauline

Kessouri, Jacques Deparis, Nadia Amraoui, Mohamed Azaroual

► To cite this version:

Clémence Ryckebusch, Jean-Michel Baltassat, Anatoly Legchenko, Pauline Kessouri, Jacques Deparis, et al.. Characterization of a heterogeneous limestone vadose zone based on a multimethod and multiscale geophysical approach. Near Surface Geophysics, 2025, 23 (6), pp.555-571. 10.1002/nsg.70026 hal-05334679

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ORIGINAL ARTICLE

Near Surface Geophysics

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# Characterization of a heterogeneous limestone vadose zone based on a multimethod and multiscale geophysical approach

Clémence Ryckebusch<fnref n="1" />,<fnref n="2" /> ID

Jean-Michel Baltassat<fnref n="1" />

Anatoly Legchenko<fnref n="3" />

Pauline Kessouri<fnref n="1" /> ID

Jacques Deparis<fnref n="1" />

Nadia Amraoui<fnref n="1" />

Mohamed Azaroual<fnref n="1" />,<fnref n="2" />

### Correspondence

Clémence Ryckebusch, Division of
Engineering Geology, Lund University, 22363
Lund, Sweden.

Email: clemence.ryckebusch@tg.lth.se

### Funding information

Région Centre Val de Loire, Grant/Award
Numbers: HYMAGE-OZNS project
2020-2024, PhD thesis 2021-2024; Bureau
de Recherches Géologiques et Minières;
Ministère de l'Éducation Nationale, de
l'Enseignement Superieur et de la Recherche,
Grant/Award Numbers: HYMAGE-OZNS
project, PhD thesis, BRGM public service

### Abstract

Water resources are a critical societal issue. As they are more and more limited, their distribution, usage and contamination are of vital importance. In the Beauce region, there are concerns on both the water quality and quantity because of farming and the related groundwater contamination. Since water is a vector of contamination, these questions require a precise vadose zone water content characterization considering the site lithology and water content heterogeneities. We apply a multiscale and multimethod geophysical approach to integrate the limestone heterogeneity at various scales into the characterization. In the first step, at a multi-decametric scale, the joint interpretation of a 3D surface nuclear magnetic resonance water content, electrical resistivity and chargeability models allows to distinguish zones with limestone heterogeneities (clay content, fractures) related to geophysical anomalies. At a decimetric scale, the joint interpretation of borehole nuclear magnetic resonance water content, borehole electrical resistivity and density logs in each zone allows us to precise the spatial fractures and karstification levels in the lower saturated and unsaturated limestone. The second step is to analyse the water content variations to build a water content model of the Beauce limestone. This model goes further into the site porosity description by illustrating how the different limestone water-filled porosities are sensed by geophysical investigations. It is compatible with the known regional specific yield range, with laboratory data and with a previous dynamic evaluation of water column variation during a recharge seasonal episode at field scale. This shows that our preliminary model may be exportable to other calcareous settings and can be used as a basis to study and simulate the vadose zone dynamic.

### KEYWORDS

electrical resistivity tomography, heterogeneity, hydrogeophysics, nuclear-magnetic-resonance, site characterization

## INTRODUCTION

Water resources are more and more limited. Their distribution, usage and contamination are of vital importance. In the Beauce region, one of the most cultivated

and dry areas in France (de Frutos Cachorro et al., 2017), the aquifer is under a high water stress with 80% of groundwater pumped for the intensive agriculture, and the remaining water is pumped as potable water (provided only from the groundwater table) for the

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

© 2025 The Author(s). Near Surface Geophysics published by John Wiley & Sons Ltd on behalf of European Association of Geoscientists and Engineers.

<footnote n="1">¹BRGM, Orléans, France</footnote>

<footnote n="2">²ISTO, UMR 7327, Université Orléans, CNRS, BRGM, OSUC, Orléans, France</footnote>

<footnote n="3">³Université Grenoble Alpes, IRD, IGE, Grenoble, France</footnote>
<figure><img src="image_3.png" /></figure>

population. Moreover, because of the agriculture activi-
ties, the region is one of the highest nitrate-contaminated
areas in France (Commisariat général au développe-
ment durable, 2013; SAGE, 2013a, 2013b). The Beauce
aquifer is a heterogeneous limestone aquifer not pro-
tected by an impervious layer. Therefore, the water and
the contaminants infiltrate the soil and the aquifer, where
the water is pumped. To quantify this contamination and
its infiltration into the vadose zone, it is necessary to
improve the knowledge of the unsaturated groundwater
flow, the vector of this contamination.

In hydrodynamic modelling, the vadose zone is often
presented as a 1D transit of surface water to the aquifer
assuming homogeneous sources (rainfall, runoff) and
sinks (evapotranspiration). This approach allows for esti-
mating the mean flow value. However, the Beauce
aquifer is an inertial groundwater table with at least two
water flow dynamics: an annual recharge with transit
time of 3 months and a pluriannual recharge with a tran-
sit time of 17 years (Seguin, 2016). These different transit
times are consistent with the structure of a limestone
rock, characterized by a complex and heterogeneous
porosity system (Covington et al., 2023), with variable
velocity flow (Hermans et al., 2023). Following Coving-
ton et al. (2023), a limestone rock has three types of
porosities: (1) the matrix porosity, related to the rock for-
mation, with a function of storage because of a long
transit time of about a decade; (2) the fracture porosity,
related to the fractures, with a function of both water stor-
age and transport and a transit time of about a month;;
and (3) the karst conduit, as an extent of the fracture
network, with a function of water transport and a tran-
sit time of about a day. Consequently, it is necessary to
identify the different types of porosity and their propor-
tion in the limestone to better estimate how much water
flows with a short or a long transit time and thus better
estimate the recharge. In the Beauce aquifer, because
there are two different recharge transit times (Seguin,
2016), we expect at least two types of porosity: the
matrix and fractures porosities. Jointly processing water
flow calculated from 1D HYDRUS modelling and time-
lapse surface nuclear magnetic resonance (SNMR) data
measured each month during 1 year, Legchenko et al.
(2020) showed that the SNMR water column is coherent
with the cumulated effective rainfall in the vadose zone
with a 3-month delay before the water level response.
Monteil (2011) and Flipo et al. (2012) found a value of 25
days with a water balance model of the Beauce aquifer
at a regional scale. Both of these transit time values cor-
respond to the seasonal transit time that Schnebelen
(2000) estimated between 15 and 45 days for normal
years and between 2 and 3 months for dry years. It can
be attributed to the fracture porosity. With water content
values and hydraulic conductivity curves measured in
lab, Aldana (2019) estimated a transit time of 30 years
in the vadose zone of the study site. This transit time cor-
responds to the matrix infiltration with a plurennial transit
time. These transit time characterizations provide infor-

mation about the water flow dynamic but not about the
water repartition in the different porosities.

Because these geological heterogeneities have an
effect on the water flow velocities in the vadose zone,
they should be taken into account in hydrodynamic mod-
elling, and it requires a more precise characterization of
the vadose zone (Hermans et al., 2023). For that pur-
pose, different authors applied geophysical methods to
characterize the heterogeneities.

For example, Comte et al. (2019) combined lab
data, field observations, electrical resistivity tomography
(ERT) and SNMR measurements with petro-physical
relationships to characterize the lithology and the
hydraulic properties of a micashist aquifer at catchment
scale and build a conceptual model to help parametrize
their hydrogeological model. This approach focuses on
the aquifer. Flinchum et al. (2019) combined surface and
borehole nuclear magnetic resonance (NMR) with seis-
mic refraction data to characterize the weathering profile
of a granite aquifer critical zone. They distinguished the
unsaturated, saturated saprolite and fractured rock with
multiscale NMR water content and relaxation time vari-
ations and observed the lateral variability by combining
the NMR and seismic refraction data.

In this paper, we investigate the efficiency of different
geophysical methods applied to the vadose zone char-
acterization, and we applied the following methods: (1)
ERT and induced polarization (IP); (2) the NMR meth-
ods applied at the different scales (surface NMR) and
(borehole NMR) (Behroozmand et al., 2015; Legtchenko,
2013). We combined field (3D SNMR, ERT and IP)
and borehole (borehole nuclear magnetic resonance
[BNMR], electrical resistivity and density) geophysi-
cal data measured during the same period from late
August-beginning of September 2020 into a multiscale
joint interpretation. Borehole electrics measured in May
2020, only are not synchronous. The goals are (1) to
identify the lithology variations of the heterogeneous
limestone (clay, fractures) by a joint interpretation of
the whole data. (2) To estimate the water content vari-
ations associated with these lithology variations and
propose a multiscale water content model of the study
site by interpreting the SNMR water content, BNMR
water content and the Archie porosities calculated in
the saturated zone with the borehole electrical resistiv-
ity (BER) data. Geophysical results are compared with a
laboratory study reported by Aldana (2019) and Aldana
et al. (2021).

MATERIALS AND METHODS

The O-ZNS observatory site in the Beauce aquifer (France)

The study site is located in Villamblain, at 30 km north-
west of Orléans city (France), at the south-west of
the Beauce limestone aquifer and in the Loire basin
<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /><figcaption>**FIGURE 1** Localization of the study site in Villamblain, near Orléans (France), within the Beauce aquifer. Poiseaux and Bricy stations provide, respectively, groundwater level (GWL) and meteorological data. DEM, digital elevation model.</figcaption></figure>

(Figure 1). It is the place of O-ZNS, an observa-
tory of the vadose zone (https://www.isto-orleans.fr/
en/observatories/transfers-unsaturated-zone/) which is
composed of a well with an exceptional size of 4 m diam-
eter and 20 m depth crossing the vadose zone down
to the aquifer and is surrounded by eight instrumented
scientific boreholes (Abbar et al., 2022).

Previous studies made a first geological characteriza-
tion of the site by combining log data, lab measurements
and surface geophysical studies. In laboratory, Aldana
(2019) and Aldana et al. (2021) described the geology
of the site with samples extracted from three boreholes.
They characterized a heterogeneous limestone with clay
and cracks and measured water content, porosities and
densities on core samples. Isch et al. (2022) compared
the water content lab measurements with the water con-
tent simulated in a 1D hydrogeological model based on
core samples measurements. At the field scale, ERT and
IP measurements extended the geology description in
three boreholes and showed lateral variations, including
a conductive anomaly interpreted as clay (Abbas et al.,
2022; Mallet et al., 2022). The geology of the study site
consists of a heterogeneous limestone with three layers:
(1) a soil layer with clay (130–128 m); (2) a highly het-
erogeneous limestone (128–122 m); and (3) a fractured
limestone (122–106 m) with 90% of CaCO3 (Figure 2).

All the elevations are in NGF (French General Levelling).

Poiseaux and Bricy stations provide, respectively, the GWL (groundwater level) and meteorological data (rainfall and potential evapotranspiration—ETP) (Figure 1). From 1966 to 2017, the mean effective rainfall (=rainfall – evapotranspiration) calculated during a hydrologic year (from September of the previous year to August of the year) was 452 mm. The mean GWL was at an elevation of 111 m. The annual recharge is of 110 mm from 1946 to 1994, and there is no run-off (Flipo et al., 2012; Schnebelen et al., 1999).

Geophysical survey

The multimethod and multiscale geophysical survey was done simultaneously in late August–beginning of September 2020 excepting the Borehole Electrical Resistivity (BER) in May 2020, to characterize the site in 3D before the large well construction. At the date of the study, the water table was at an elevation of 112 m (May) and 111 m (late August–beginning of September). The data measured from surface are 3D SNMR/ERT/IP and in borehole are BNMR, BER and density. Figure 3 shows the positions of the geophysical acquisitions on the study site.
<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /><figcaption>**FIGURE 2** Summary of the boreholes (SC1, SC2, SC3) geology (a), granulometry (b) and other characteristics from lab measurements (c) of the experimental site (Aldana et al., 2021).</figcaption></figure>

## Surface nuclear magnetic resonance (SNMR)

The SNMR method measures the water content by using the proton spin magnetic resonance principle. A transmitter loop energizes spin protons by injecting a current pulse with an amplitude $I_0$ during a delay $\tau$ ($q = I_0 \tau$) at the proton resonance (Larmor) frequency, $\omega_0$ in the geomagnetic field $B_0$ ($\omega_0 = \gamma B_0$ with $\gamma$ the gyromagnetic ratio). This electromagnetic pulse causes a spin precession and generates a magnetic resonance field $M_\perp$. The transmitter loop switches to a receiver connected to the same loop (Tx–Rx) or a separated (Rx) loop and measures a signal proportional to the sum of the precessing magnetic moments with an exponential decay. The two measured parameters are as follows: (1) the initial amplitude of the exponential decay, proportional to the water content; and (2) the constant $T2^*$ of the exponential decay, related to the mean size of water-filled pores and sensitive to the magnetic heterogeneities. Before the signal measurement, there is a delay called the dead time during which the SNMR signal cannot be measured because of the equipment design primarily focused on measurements of relatively long signals corresponding to mobile water (Legchenko et al., 2002; Legchenko & Valla, 2002).

Consequently, the SNMR does not measure the part of the water content related to relaxation times shorter

than the dead time (Flinchum et al., 2019; Müller-Petke et al., 2011). To have more details on the method, see, for example, Legtchenko (2013).

The 3D SNMR investigation applied on the OZNS experimental site comprises a set of ten 1D soundings measured independently using coincident Tx/Rx square loops of 50 m by side, with 2 turns of wire, 16 pulses for each sounding from 50 to 4500 A ms with 200 to 300 stacks and a dead time value of 40 ms. Figure 3 shows the position of these loops. To improve 3D resolution, loops are overlapped. The acquisition was done with the Numis POLY instrument (from IRIS instrument). We processed each sounding independently with the NumPro and SAMOVAR softwares with (1) a notch filtering of the 50 Hz frequencies and harmonics, (2) a 10 Hz bandpass, and (3) a stack optimization to improve the signal-to-noise ratio. Then, these data are gathered into a 3D data set and inverted to provide a 3D SNMR water content inverse model (Chevalier et al., 2014; Legchenko et al., 2011).

The inversion was done with only an optimization of the signal amplitude because of an insufficient signal-to-noise ratio for an inversion of complex signals. The 3D inverse model is composed of $10 \times 10 \times 2 \text{ m}^3$ cells down to a depth of 60 m. The NMR response of the 3D water-content inversion results fits the data with an RMSE of 16.19 nV, corresponding to a water content error of
<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /><figcaption>**FIGURE 3** Localization of the geophysical measurements on the investigated area. The data measured in some of the boreholes are borehole nuclear magnetic resonance (NMR), borehole electrical resistivity and density data. ERT, electrical resistivity tomography; IP, induced polarization; SNMR, surface nuclear magnetic resonance.</figcaption></figure>

1%–2% in the first 20 m following an SNMR error evaluation proposed by Legchenko et al. (2006). The signal amplitude depends on sounding location and varies between 155 nV and 280 nV.

## Borehole nuclear magnetic resonance (BNMR)

The principle of the BNMR method is similar to the SNMR one but with significant differences. (1) BNMR uses a higher controlled primary field at 8.2 T (instead of the natural geomagnetic field of about 47 µT at Vilamblain) and a consequently higher Larmor frequency of 350 MHz for the equipment used. (2) BNMR uses the Carr-Purcell-Meiboom-Gill sequence. It consists of a pulse injection to provide a 90° rotation of the longitudinal magnetization in the transverse plane and then numerous pulses at 180° to refocus the signal in many

echoes. A 'spin echo' NMR signal is observed for each refocusing pulse with a general decay corresponding to the *T2* constant instead of the *T2*^*^ constant usually obtained with SNMR (Behroozmand et al., 2015; Walsh et al., 2013). In BNMR, because of a higher Larmor frequency value and of a short delay between the pulses, the dead time is negligible. Consequently, BNMR measures all the water content and relaxation time values. The BNMR logs were measured by the NMRSA Company with a tool of 60 mm diameter in the boreholes SC05-6-7-8. For each depth, the BNMR data consists of a *T2* relaxation times distribution with a partial water content for each relaxation time.

The *T2* relaxation times distribution (or *T2* distribution) is cut off at different relaxation times to define three types of water content: the free fluid index (FFI) or moveable water content and the bound volume index (BVI) or bound water content. Morriss et al. (1997) defined cut-off values on laboratory by saturating and desaturating
carbonate samples to, respectively, 33 ms for the BVI and 92 ms for the FFI. The second value varies for carbonate rocks with vugs having longer relaxation times. The BVI for clay is at 3 ms (Dunn et al., 2002). We applied two cut-off times to our relaxation times distributions to distinguish three types of water content: the clay water content (T2 < 3 ms), the bound water content (3 ms < T2 < 100 ms) and the moveable water content (100 ms < T2). From this T2 distribution, we also calculated the T2ML value as the T2 logarithmic mean value of the distribution weighted by the partial water contents following Walsh et al. (2013).

## Borehole electrical resistivity (BER)

The BER method measures the electrical resistivity of a medium in a volume of a few centimetres around a borehole. The resistivity measurement consists in measuring the quadrature component of the secondary EM field at a coil distant from a primary field-transmitting coil. The SEMM Logging Company's tool has a diameter of 38 mm and two coil spacings of, respectively, 510 and 810 mm. For each borehole (SC05-6-7-8-9), the data set consists of two resistivity curves in function of depth. Because of borehole effects and low sensitivity of the tool for high resistivities, the short spacing data are usually noisy and the long spacing ones only are valorized. Resistivity measurement uncertainty for this spacing is evaluated on a repeatability basis at about 5%.

## Density logging

Gamma-gamma density logging is an active-nuclear measurement applied to determine the formation's bulk densities. In our study, we interpret a variation of density in a limestone as a variation of porosity. The SEMM Logging Company's tool uses two detectors making it possible to correct borehole effects. Thus, compensated gamma-gamma signals respond to variation in electron density which is directly related to the bulk density variation in most subsurface environments (Serra & Serra, 2003). The measurement is limestone calibrated with an uncertainty of about 2%.

## Electrical resistivity tomography (ERT) and induced polarization (IP) measurements

The ERT principle is to measure the media electrical resistivity distribution in response to the injection of an electrical current. The measurement consists of injecting an electrical current between two electrodes and measuring the potential between two other electrodes. By increasing the distance between transmitter and receiver, we measure media electrical resistivity for increasing volume and depth. The IP uses the electri-

cal phenomenon by which the subsoil temporally stores the electrical charges after stopping the injection; the measured parameter is called the chargeability. The difference between both methods is when the ERT method measures the voltage in a steady state, and the IP method measures the voltage decay during a transient state. The data measured by ERT and IP are, respectively, an apparent electrical resistivity and an apparent chargeability inverted into, respectively, an electrical resistivity and a chargeability. For more details about these methods, see, for example, Singha et al. (2022).

We measured 8 profiles of 48 electrodes with spacings of, respectively, 2.5 m between the electrodes and 5 m between the profiles. The measurements were done in a 3D dipole-dipole configuration with the Syscal Pro and Syscal Pro Switch instruments (from IRIS Instrument). The pulses have a maximum voltage of 800 V injected during 2 s with a total of four measurement cycles. We filtered the data with the softwares Prosys II (IRIS Instrument) and Matlab codes for the IP data. The 3D data inversion was done with the software BERT 3D using a smoothness-constrained Gauss-Newton inversion described by Günther et al. (2006) with a regularization based on L2 norm (e.g., Rücker (2011)). The electrical resistivity inverse model has a $\chi^2$ error of 3.48 and a relative RMS of 7.5%. After inversion, we cut off the deep part of the model on the basis of the coverage value (Günther, 2004) (or cumulative sensibility) at a value of $10^{-2}$.

## Data analysis

The data is analysed and interpreted into two aspects: (1) a lithological aspect to characterize the vadose zone limestone heterogeneities at a field scale, with a multi-scale qualitative analysis of the whole data; and (2) a water content and porosity analysis to propose a new water content model of the site at a field scale. For the lithological interpretation, to interpret jointly the ERT/IP and SNMR 3D models, we gathered and resampled them into one 3D model with three parameters (resistivity, chargeability, water content). Then, we interpreted together the inverted models with the borehole results by extracting log results from the 3D model at the position of each borehole.

For the water content and porosity interpretation, we based our analysis on a modified version of the conceptual porosity model proposed by Lubczynski and Roy (2005) relating the hydrologically defined water content types, the measured parameters to estimate them and how the SNMR method can contribute to this model with the measured water content. We simplified this model by neglecting clay content and unconnected porosity (Figure 4) to build our multiscale water content model. We interpret the SNMR water content, the BNMR water content and the saturated BER porosity calculated from
<figure><img src="image_10.png" /></figure>

<table><caption>TABLE 1 Archie's law parameters for the limestone of the OZNS site calculated by Abbas et al. (2022).</caption><thead><tr><td>Elevation</td><td>a</td><td>m</td><td>n</td><td>ρ<sub>f</sub> (Ω m)</td></tr></thead><tbody><tr><td>111–116 m</td><td>0.6</td><td>1.47</td><td>2</td><td>20</td></tr></tbody></table>

<figure><img src="image_11.png" /><figcaption>FIGURE 4 Conceptual model of porosity modified after Lubczynski and Roy (2005) in the unsaturated and saturated zones.</figcaption></figure>

Archie's law in a multiscale analysis. In the saturated zone, we discuss the BNMR water content and Archie porosity regarding the evaluation of the effective porosity. In the vadose zone, we discuss the respective BNMR and SNMR water content regarding the capillary water. We evaluate and compare the specific yield values to values from literature.

## Archie porosity from BER data in the saturated zone

We apply the Archie model proposed by Abbas et al. (2022) at the borehole scale on our site in the context of a heterogeneous limestone. The bulk resistivity $ρ$ is related to the porosity $φ$, and the saturation $S_w$ of the geological formation, taking in account the electrical resistivity of the fluid $ρ_f$ (Ω m), a and m being empirical parameters related to the tortuosity and cementation, and n, the saturation exponent through the following Archie (1942) relation.

The fluid resistivity was measured in boreholes with a calibrated sensor. They defined the a and m values (Table 1) with an inversion process using BER measurements in boreholes and water content simulated by Isch et al. (2022) at the date of BER measurement. The n value is fixed at 2.

To be able to use Archie's law in the Beauce limestone context, they hypothesized that limestone of the OZNS site can be assimilated to a sediment with grain sizes middle to coarse, close to sand grain sizes. They did the calculation at the depth of the fractured limestone where they assumed that the clay content and the associated surface conduction can practically be neglected. This assumption is supported by the value of 90% of CaCO3 measured by Aldana et al. (2021) in unaltered

samples (see Figure 2). In presence of clay, Archie's model overestimates the porosity by not considering the contribution of clay minerals in the electrical conductivity values and accounting that contribution as water-filled porosity. The Waxman and Smits (1968) model, a modified version of Archie's model taking in account the clay contribution, is more adapted in presence of clay. Oguntade et al. (2025) compared the BNMR water content and saturated porosities calculated with both Archie and Waxman and Smith's models and BER data in a sandstone aquifer. In comparison to BNMR water content measured in different boreholes, they calculated similar saturated porosities with the model of Waxman and Smith and porosities four to six times higher with the model of Archie, confirming the assumption of a porosity overestimate from Archie's model in presence of clay. The effectiveness of Archie's law for evaluating an effective porosity requires a homogenous inter-granular porosity and pore size. The Beauce limestone has a heterogeneous porous network with various connectivity and body size. Müller-Huber et al. (2015) discuss the effect of a variable pore radius on the porosity and on the cementation exponential factor m for limestone samples compared to sand and sandstones samples. They studied two types of limestone samples: the first ones with vugs and fractures and the second one with an inter-granular porosity. As the m value, calculated by Abbas et al. (2022) from 111 to 116 m, is consistent with the values of Müller-Huber et al. (2015) for samples of limestone with vugs and fractures, we consider that we can reasonably use their Archie model for valuing a water content.

In the aquifer, the porosity is saturated ($S_w$ = 1), and we assume that the saturated Archie porosity is equal to the saturated total porosity and that can be compared to the total BNMR water content. Moreover, as BER and BNMR data were not measured in the same time (respectively in May and in September) and with the same water table level (respectively of 112 and 111 m), we do the comparison between BER and BNMR data only below 111 m corresponding to the lower water table level measured in September and to a depth where both data are in fully saturated conditions.

## The SNMR and BNMR water content

We attempt to valorize together the SNMR and BNMR water content differences. To date, to the knowledge of the authors, there is no simple and general way to use both the BNMR and SNMR data together. The main
<figure><img src="image_12.png" /></figure>

reasons for that are the different investigated volumes, the dead time effect on the SNMR measurements and the differences of Larmor frequencies between BNMR (350 kHz) and SNMR (2 kHz).

As an example, Knight et al. (2012) with a dead time value of 10 ms, corrected the magnetic heterogeneities component of SNMR T2*, cut off the BNMR T2 distribution at 10 ms and recalculated the BNMR T2ML. After that, they found a correlation between the respective corrected T2* and T2ML values. Müller-Petke et al. (2011) with a dead time value of 40 ms, decided to cut off the BNMR T2 distribution at 30 and 80 ms, recalculated the BNMR total water content and simplified the vertical profile into a blocky structure. Then they compared these values to the SNMR water content inverted using various filtering and inversion methods. They found that with their best inversion method, the inverted SNMR water content has a good correlation with the BNMR water content cut off at 80 ms. Flinchum et al. (2019) generated an SNMR response by forward modelling the BNMR T2ML and water content data and inverted this response to obtain a simulated SNMR water content and T2*. The simulated SNMR values show a good agreement with the BNMR values. They are coherent qualitatively with the measured SNMR values, inverted after correcting the magnetic heterogeneities component T2*, with an underestimation of the values by the measured SNMR data. In our case, an attempt to calculate SNMR response and results based on BNMR water content and T2 distribution gave reasonable water content values but contrasted T2ML and T2* values (not presented).

For the present work, we only discuss the dead-time and volume effect. First, we interpret the total BNMR distribution. Then, after testing different cut-off values (not presented), we set the cut-off at 40 ms to calculate the total BNMR water content corresponding to T2 > 40 ms and compare it to the water content measured with SNMR.

# RESULTS AND DISCUSSION

## Lithological variations

### Lithological variations at the metric to decametric scale

Figure 5 shows two horizontal slices of the 3D model at two elevations: 120 m, in the vadose zone, and 110 m, in the saturated zone.

At 120 m (vadose zone), the SNMR water content is homogeneous with a water content of 0%–1%. On the electrical slices, excepting for the southern and northern boundaries, the global electrical resistivity has a mean value of 250 Ω m, with an anomaly of 120–160 Ω m in the zone Z2. The global chargeability has a mean value

of 1.5 mV/V with an anomaly of mean 2–2.6 mV/V in the zone Z2. The electrical resistivity and chargeability anomalies are coherent spatially and define the zone Z2. The zone Z1 has a low water content, a high electrical resistivity and a low chargeability, whereas the zone Z2 has a low water content, a lower electrical resistivity and a higher chargeability than in the zone Z1. We interpret Z1 as a weathered, fractured limestone and Z2 as a more clayey, more weathered, fractured limestone.

At 110 m (saturated zone), the electrical resistivity and the chargeability are homogeneous with average values of, respectively, 400 Ω m and 1 mV/V. On the SNMR water content slice, the global water content is 10% with two anomalies: the first one in Z2 with a water content of 5%–8% and the second one in Z1 with a mean water content of 15%–22%. We interpret the SNMR water content variations as porosity variations: Z1 as a karstified/fractured limestone and Z2 as a less porous, less karstified, fractured limestone. This interpretation explains the water content variations. However, this is not coherent with the electrical data because there are no anomalies in the saturated zone where we expect a decrease of resistivity due to the increase of the weathered/fractured porosity.

In order to precise our observations and interpretation, we analyse the data along the NS section (Figure 6) defined in Figure 5, which crosses the 3D model and some of the boreholes.

In the vadose zone, the 2D electrical resistivity and chargeability sections show (Figure 6) as follows:

- A conductive and chargeable upper layer with a resistivity less than 150 Ω m and a chargeability higher than 3 mV/V. This layer shows a significant deepening in Z2 that constitutes the anomaly. BER resistivity imaging confirms this deepening. Extracted electrical resistivity logs (Figure 6b) precise the depth ranges of the deepening in Z2 mainly from 125 m to 118 m where the values difference of electrical resistivity and chargeability between Z1 and Z2 are better expressed.

- The conductive cover overlays a more resistive (400 Ω m) and less chargeable (lower than 1 mV/V) layer, from 125 m to 118 m down to the base of the sections without any visible change when crossing the water level.

The SNMR water content variations, in the vadose zone, show a progressive increase of SNMR water content from 116 m to the saturated zone in Z1 and from 114 m to the saturated zone in Z2 (Figure 6b). Two effects can explain this increase of water content and may act together: (1) the water content in the capillarity fringe and/or water retention in the vadose zone. (2) The smoothing effect of inversion at the top of the water layer (=mainly the saturated zone).
<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /><figcaption>**FIGURE 5** Horizontal slices of the 3D model in the vadose zone (top, Z = 120 m) and in the aquifer (bottom, Z = 110 m). The parameters are the SNMR water content (left), the electrical resistivity (centre) and the chargeability (right). The white dots are the boreholes. The grey squares show the zones 1 and 2 with anomalies. The valorized boreholes SC05-6-7-8-9 (black dots) are located on the SNMR horizontal slice (Z = 110 m). ERT, electrical resistivity tomography; IP, induced polarization; SNMR, surface nuclear magnetic resonance.</figcaption></figure>

In the saturated zone, there is a large difference of SNMR water content between both zones, from 15%–22% in Z1 to 5%–8% in Z2 (Figure 6a). As previously interpreted, we explain these water content differences as a difference of porosity with a higher fracturing in Z1 than in Z2.

We can interpret the conductive layer as a clayey or weathered limestone with an increase of weathering/clay content in Z2 that explains the deepening of the conductive and chargeable layer. We interpret the resistive layer as a fractured limestone with a higher fracturing in Z1 than in Z2 that explains the SNMR water content variations.

## Data analysis at the borehole scale

Figure 7 shows the BNMR total water content, the density logs and the BER, as well as the corresponding resistivity log extracted from the 3D model at the respective borehole locations. We identify three layers with various behaviours:

1. From 130 m to 120 m, for all boreholes, we observe a general increase of density (from 1.5 to more than 2.0), a high BNMR total water content of 20%–30% (130–124 m) followed by a decrease to about 12% (124–120 m). For SC06 (Z1), we observe a continuous
<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /><figcaption>FIGURE 6 (a) SNMR water content vertical section (top), electrical resistivity vertical section with electrical conductivity logs from boreholes (left to right: SC06-SC05-SC07-SC09) (centre), chargeability vertical section (bottom), extracted from the 3D model. The blue line is the water table. The vertical black line and black dashed line are the positions of the 1D logs extracted from the 3D model in each zone. The white lines are the electrical resistivity isolines at 150 and 350 Ω m. The dashed white line is the chargeability isoline at 3 mV/V. (b) 1D logs extracted from the 2D profiles: solid lines for the zone 1 and dashed lines for the zone 2. The black line is the water table. SNMR, surface nuclear magnetic resonance.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>FIGURE 7 (a) Electrical resistivity extracted from the 3D model at the position of the boreholes SC05-6-7-8-9. (b) Electrical resistivity logs of boreholes SC05-6-7-8-9; the resistivities higher than 300 Ω m are out of the sensitivity range of the tool and are not presented. The black line is a synthetic model based on the borehole data, and the grey line is the electrical resistivity tomography (ERT) inversion result of this model. (c) Density logs of boreholes SC05-6-7-8-9. (d) Borehole nuclear magnetic resonance (BNMR) total water content logs of boreholes SC05-6-7-8. The blue dashed line is the water table. The black dashed lines are the limits of the interpreted layers.</figcaption></figure>
<figure><img src="image_18.png" /></figure>

uous increase of the BER (50–150 Ω m), for SC09 (Z2), a relatively stable BER about 40 Ω m (130–124 m) followed by a deeper increase up to about 150 Ω m. This variation is coherent with the conductive anomaly in Z2 previously described in the 3D model and illustrated by SC09 in Figure 7a. We attribute the discrepancies between depth limits of BER and 3D ERT to the smoothing effect of inversion.

2. From 120 m to 112 m, for all boreholes, we distinguish a slight BER decrease (160–140 Ω m) from 120 to 116 m and then a quite constant value of 200–300 Ω m (116–112 m), a quite constant density (mean of 2.2 g/cm³) and BNMR total water content (mean of 12%) along the whole horizon.

3. From 112 m to the borehole base, a progressive increase of BNMR total water content up to a mean value of 26% in the saturated zone, a rapid decrease of the electrical resistivity down to, in the saturated zone, 100 Ω m for SC06 and 140 Ω m for SC09. The density shows a slight decrease to a mean value of 2 g/cm³ at the top of the saturated zone and then larger variations.

Boreholes SC05-08 characteristics are somewhere close to Z1 characteristics, elsewhere close to Z2 characteristics and thus define an intermediate zone, Zi, between Z1 and Z2.

Figure 8 shows the BNMR data of the boreholes SC06 (Z1) and SC07 (Zi and representative of SC05-7-8) with the BNMR distributed water content, the BNMR T2ML and the SNMR total water content.

In the saturated zone, the borehole SC06 (Z1) has a higher T2ML value (mean of 165 ms, Figure 8e) than the boreholes SC05-7-8 (Zi) (mean of 35 ms). Similar values for the boreholes SC05-7-8 (Zi) in Figure 8e justify that SC07 only is presented as representative of the boreholes SC05-7-8 in Figure 8d for comparison with SC06 (Figure 8c). BNMR mobile water is predominant in the SC06 saturated zone (Z1, Figure 8c), whereas BNMR bound water is predominant in the SC07 saturated zone (Zi, Figure 8d).

We interpret the Layer 2 in the deep vadose zone as a slightly fractured limestone. The layer is spatially homogeneous from SC06 to SC05-7-8. Making the hypothesis that the Layer 3 has the same lithology as the Layer 2, the density should increase with the saturation. However, we observe no change in density or a slight decrease. Thus, we infer an increase of porosity associated with an increase of fracturing with depth, below 112 m. This explains both the water content increase associated to an electrical resistivity decrease, whereas the increase in saturation and porosity plays concurrently for a density almost unchanged.

Spatially, in the saturated zone, we interpret the differences of T2ML, BNMR water content type, BER

and density as a difference of porosities and fracturing between Z1 and Zi. Z1 has larger pores interpreted as larger fractures and karstification than Zi with less fractures. This interpretation is coherent with a lower resistivity in Z1 than in Zi and in Z2. This lower resistivity is, however, not sensed at the decametric scale (Figure 7a).

We explain this incoherence as a lack of vertical resolution of the 3D model at this depth. A simple model based on BER resistivities (black line in Figure 7b) indeed shows that a low resistivity layer between 112 and 104 m elevation (coherent with the regionally known Gatinais marl) cannot be imaged (grey line in Figure 7b) with the dipole-dipole measurement and inversion schema applied in the present study.

The SNMR water content (Figure 8a) and BNMR total water content (Figure 8b) have the same variations but a shift value of mean 12%. The dead-time effect on SNMR data could explain the water content shift.

## Interpretation summary

As a synthesis, Figure 9 proposes a new lithological model of the site, based on geophysical parameters heterogeneities revealed at the multi-decametric and borehole scales and interpreted as lithology. During the interpretation at both scales, the logs were divided into two main parts:

1. A conductive and chargeable layer with an SNMR water content of 0% from 130 m to 125–120 m interpreted as a clayey weathered limestone, with a deepening in Z2.

2. From 120 m to 110 m, the geophysical interpretation of the 3D SNMR water content and electrical resistivity shows a resistive layer with a higher water content in Z1 than in Zi and Z2 in the saturated zone. We first interpret this layer as a fractured limestone, with a higher fracturing area in Z1 than in Z2 in the saturated zone. The geophysical interpretation of the borehole data allows us to precise the lithological interpretation with a slightly fractured limestone from 120 m to 112 m and a fractured limestone from 112 m to 110 m, with a karstification in Z1.

This model, interpreted as lithology, complements and improves the previous lithological description from samples. Indeed, the limestone heterogeneities at a metric scale are integrated as fractures, karst conduits and clayey limestone. These heterogeneities are larger than the sample representative volume and thus not visible at a sample scale. However, it is necessary to take them into account in the perspective of hydrological modelling of the site vadose zone.
<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /><figcaption>**FIGURE 8** (a) SNMR water content extracted from the 3D model at the position of the boreholes SC05-6-7-8-9. (b) Total borehole nuclear magnetic resonance (BNMR) water content of the boreholes SC05-6-7-8. Note the scale difference between the BNMR and SNMR water content. (c and d) BNMR water content distribution of the boreholes SC06 (Zone 1) and SC07 representative of the boreholes SC05-7-8 (intermediate zone). (e) BNMR T<sub>2ML</sub> of the boreholes SC05-6-7-8 related to the mean pore size. The blue horizontal line is the water table. The black dashed lines are the limits position of the interpreted layers.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>**FIGURE 9** Lithological model based on the geophysical interpretations at the multi-decametric and borehole scales in comparison to the site geology illustrated here as a lithology synthetized from Aldana (left) (Figure 2). The blue line is the water table.</figcaption></figure>
<figure><img src="image_22.png" /></figure>

<table><caption>TABLE 2 Borehole nuclear magnetic resonance (BNMR) total water content compared to the Archie porosity calculated from borehole electrical resistivity (BER) and Archie's law in the saturated fractured limestone.</caption><thead><tr><th></th><th></th><th>BNMR total water content (%)</th><th>BER (Ω m)</th><th>BER porosity (Archie) (%)</th></tr></thead><tbody><tr><td rowspan="2">Aquifer</td><td>SC06-Z1</td><td>25</td><td>100</td><td>23</td></tr><tr><td>SC05-7-8-Zi</td><td>25</td><td>120</td><td>21</td></tr></tbody></table>

## Water content analysis

### Comparison of the BNMR water content and the Archie porosity in the saturated fractured limestone at the borehole scale

Table 2 presents the mean BNMR total water content calculated in the saturated zone for the borehole SC06 (Z1) and the boreholes SC05-7-8 (Zi). The mean BER data evaluated for the same depth range and the corresponding Archie porosities calculated using Archie's model developed by Abbas et al. (2022) are also presented.

We observe that BNMR total water content values and BER water content (=BER porosity for full saturation) are close to each other. In saturated zone, in agreement with the model of Figure 4, we interpret the BNMR water content as well as the Archie porosity as an evaluation of the effective porosity. The difference of 2%–4%, if significant, might be explained by the non-connected porosity contributing to the BNMR water content but not to BER.

### Comparison of the SNMR and BNMR water content

Figure 10 shows the BNMR water content distribution and the summed BNMR water content for T2 lower than 40 ms (red curves) for the boreholes SC06 (Figure 10a) and SC05-7-8 (Figure 10b). Figure 10c shows the BNMR total water content (dot), the BNMR total water content summed for the T2 values higher than 40 ms, and the SNMR total water content. Although we do not consider SNMR and BNMR water content values directly comparable, the similarity of log shapes tells us they describe the same phenomena, and we attempt to value them together to build our water content model of the Beauce limestone.

In the vadose zone, we observe a BNMR water content > 40 ms decay from 111 m to 113 m and variations with values smaller than 5% above 113 m. This decay above the water table, attributed to the capillarity fringe, is 1.5 m thick, the same value as the one simulated by Aldana et al. (2021) on the basis of lab measurements. The variations above are coherent with retention water in the vadose zone (Isch et al., 2022). We also observe a good agreement with the SNMR total water content variations in the vadose zone: a smooth decay above the water table and water content variations with values

smaller than 5% above. In the upper part, we note that the maximum SNMR and BNMR water content corresponds to the upper altered layer (L1, Figure 9) where lithology changes with higher clay content and possibly massive limestone at its base (Figure 2), which may favour some perched aquifer or a relatively higher retention water content. We attribute the smoother SNMR water content decay above the water level both to the inversion and to the capillarity fringe. Given that the result of a smooth inversion is to have a smoother water content increase above the top of an aquifer and a decrease curve below the bottom of the aquifer, the consequence is to have an increase of water content above the top of the aquifer that can be attributed to both the smoothing inversion effect and to the water in the capillary fringe. A better estimator to evaluate a result is the water volume or water column, corresponding to the product of a water content in a layer with the thickness of that layer (Legtchenko, 2013).

Moreover, the vadose zone water content measured by BNMR and not by SNMR corresponds to the water situated in small pores with too short relaxation times to be measured by SNMR. We interpret and attribute this water content as an evaluation of the capillary water in the vadose zone. The corresponding average value of 12% (wBNMR < 40 ms) is consistent with the water content value measured in saturated conditions on rock samples by Aldana (2019), at a scale representative of the matrix porosity and the capillary water. In the aquifer, for the boreholes SC05-7-8, the BNMR water content larger than 40 ms represents half of the BNMR total water content, and the value is close to the SNMR water content with a mean water content of 12%. For the borehole SC06, the BNMR water content larger than 40 ms represents a larger part of the total water content with a value of 25% while the SNMR water content is only 16%. To explain the difference between the SNMR water content and the BNMR water content larger than 40 ms, we estimate the effect of a saturated karst conduit on the total water content regarding the volume explored. At the borehole scale, we interpret the difference between the boreholes SC05-7-8 and SC06 as a karst volume in SC06. Regarding the BNMR investigation volume (a few dm³), the difference between a water content of 12% (SC05-7-8) and of 25% (SC06) represents the volume of a 5 cm radius sphere which is coherent with some karst conduit observed during the big well digging. At the decametric scale, regarding the volume, assumed as a square with 50 m by side (size of the SNMR loop) and a
<figure><img src="image_23.png" /></figure>

<figure><img src="image_24.png" /><figcaption>**FIGURE 10** (a and b) Borehole nuclear magnetic resonance (BNMR) cumulated water content and BNMR water content related to the *T*₂ smaller than the dead-time (40 ms) for the boreholes SC06 and SC05-7-8. (c) Total BNMR water content (dot), BNMR water content related to the *T*₂ longer than the dead time (40 ms) (line) and SNMR total water content (dashed line). SNMR, surface nuclear magnetic resonance.</figcaption></figure>

3 m thickness, the difference between a water content of 12% (SC05-7-8, volume of 900 m³) and of 15% (SC06, volume of 1125 m³) represents a volume of 225 m³. That means a network of horizontal karst conduit of 0.1 m diameter and of 50 m long every 2.7 × 2.7 m². This is quite a lot but not unrealistic. Water-filled karstic cavities thus explain the varying water content measured at the decametric as well as the metric scale. Moreover, this karst evaluation is consistent with the small karst conduits observed on large samples during the big well digging and with the karstic developments observed with a camera inside the well around the groundwater table depth. Figure 11 synthetizes the results and proposes a conceptual model of water content and porosity based on the BNMR water content larger than 40 ms of SC05-7-8 in Zi. In this model, the specific yield value of 9% is consistent with the range of the literature values (7%–13%) for the Beauce limestone (Schnebelen et al., 1999). The 13% water content in the vadose zone corresponds to the capillary water, including the matrix porosity. It is compatible with the 15% water content measured on saturated core samples because the samples are representative of the matrix porosity and partly of the smaller fractures. The SNMR water content gives a good evaluation of the specific yield comprising fractures and karst conduits but may also include part of the

capillary water retained in smaller fractures. More or less important water content discrepancies from this model at the aquifer top can be explained by the occurrence or the lack of karstic cavities of decimetre size corresponding to karst observed during the well digging as explained before.

Legchenko et al. (2022) applied an SNMR water content monitoring during one hydrologic year on a site 1.5 km to the south of the OZNS observatory to study the vadose zone dynamic. Their results showed that during the infiltration process, the SNMR water column, product of the SNMR water content in a layer by the thickness of this layer, increases of about 200 mm to compare with a corresponding increase of the cumulated effective rainfall of about 600 mm. This water column accumulation occurs 3 months before the water table rise, during the recharge process.

Our SNMR and BNMR data were measured in September 2020 before the hydrogeological recharge. Let us estimate the effect of an increase of the water column during the recharge. In Figure 10c, the BNMR water content larger than 40 ms is of mean 6% from 111 to 113 m and of mean 2% from 113 to 120 m in the fractured limestone. Considering a water column increase of 210 mm, we obtain an increase of 3% of water content from 113 to 120 m in the vadose zone.
<figure><img src="image_25.png" /></figure>

<figure><img src="image_26.png" /><figcaption>**FIGURE 11** Schematic water content model of the Beauce fractured limestone based on the SC05-7-8 (Zi) borehole nuclear magnetic resonance (BNMR) water content > 40 ms. The black line is the water table. The capillary water, effective porosity and specific yield are based on the conceptual porosity model modified after Lubczynski and Roy (2005) (Figure 4).</figcaption></figure>

The water column increase value of 210 mm is close to Legchenko et al.'s (2020, 2022) results based on SNMR during the 1999–2000 recharge monitoring.

The coherence between this model estimating a seasonal recharge and the monitoring measured by Legchenko et al. (2020, 2022) shows that the water content measured by SNMR and BNMR >40 ms corresponds to the water and porosity contributing to the seasonal recharge. Then, we can now distinguish more clearly the part of porosities contributing:

- *To the seasonal recharge:* a water content of 10% attributed to the specific yield, to the fracture and karst porosity and to a small part of the capillary water and measured by SNMR and BNMR >40 ms

- *To the plurennial recharge:* a water content of 12% attributed to the capillary water, corresponding mainly to the matrix porosity and measured only by BNMR <40 ms.

Finally, this model is compatible with an SNMR water column increase during a recharge process, and we propose that this model may be used to preliminary simulate geophysical responses during a recharge event. It would then be a base for further improvement through a monitoring approach.

## CONCLUSION AND OUTLOOKS

A multimethod geophysical investigation combining 3D field survey and borehole measurements was applied

at a field scale on the OZNS observatory to characterize lithological and water content heterogeneities that may affect water flow in the vadose zone. The joint interpretation of the whole data shows at least three combinations of different lithological variations that may affect the hydrogeological phenomenon within the vadose zone and the underlying saturated aquifer: weathering, clay content, fracturing and karstification. These heterogeneities are related to variations in the limestone fracture's main porosity which is one of the main components controlling the annual aquifer recharge.

In addition to the lithological characterization, a schematic water content model of the Beauce limestone is proposed based on a multiscale analysis of the water content measured by BNMR, SNMR and the saturated porosity calculated from BER data and Archie's model. This water content model goes further into the site porosity description at a field scale by illustrating how the different limestone water-filled porosity—capillary water, specific yield, effective porosity—are sensed by geophysical investigations. In this limestone setting, (1) BNMR and BER data coupled to Archie's model in the saturated zone are estimators of the effective porosity, (2) SNMR and BNMR with relaxation time greater than 40 ms are sensitive mainly to the gravitational water, and (3) BNMR can distinguish capillary water from total porosity.

This model is compatible with the known regionally specific yield values, with laboratory evaluation of cores porosity and with a preceding dynamic estimation of the water column variation in the vadose
<figure><img src="image_27.png" /></figure>

zone during a hydrogeological recharge event based on SNMR measurement. Contrasted water content values are observed at the top of the saturated zone depending on the measurement scale and the location. Our model easily explains the observed water content variations by introducing water-filled karst network of decimetric size in agreement with karst direct observation (samples, cores and well camera). In addition, the coherence of this model with a dynamic evaluation of an annual recharge allows distinguishing the porosities components contributing to the annual recharge (fracture and karst porosity and a small part of the capillary water) and to the plurennial recharge (the capillary water, corresponding mainly to the matrix porosity). As these types of porosities are similar in other fractured and karstified carbonate aquifers but with different proportions, this methodology may be applicable and tested in other fractured and karstified carbonate aquifers to characterize the different porosities (matrix, fracture and karst conduit).

Finally, our water content model thus appears as a robust schematic model that could be used for simulating geophysical responses to a recharge event. As an outlook of the present work, multimethod monitoring, including SNMR, BNMR and BER measurements, is recommended to improve the vadose zone dynamic characterization initiated by previous works.

## ACKNOWLEDGEMENTS

The work presented here was carried out as part of a Ph. D. project partly funded by Centre-Val de Loire region under Grant n°2019-00136419 and the French Ministry of Higher Education and Research subsidy to BRGM. The material is partly based on work supported by the Centre-Val de Loire region PRIR program under Grant n°2020-00138753. The authors would like to thank French National Centre for Scientific Research for the access to the O-ZNS observatory field site. They thank Clara Jodry and Salma Ammor who contributed to the data acquisition.

## CONFLICT OF INTEREST STATEMENT

The authors declare no conflicts of interest.

## DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.

## ORCID

Clémence Ryckebusch https://orcid.org/0000-0002-4217-9956

Pauline Kessouri https://orcid.org/0000-0001-5649-989X

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**How to cite this article:** Ryckebusch, C. et al. (2025) Characterization of a heterogeneous limestone vadose zone based on a multimethod and multiscale geophysical approach. *Near Surface Geophysics*, 1–17. https://doi.org/10.1002/nsg.70026