# Induced polarization applied to landslides. Part 1: imaging hydraulic barriers

Clément Casotti, André Revil, A Ghorbani, M Abdelfattah, M Guerini, F Hoblea, Gilles Ménard, Z Su, S Qiang, J Berthet, et al.

► To cite this version:

Clément Casotti, André Revil, A Ghorbani, M Abdelfattah, M Guerini, et al. Induced polarization applied to landslides. Part 1: imaging hydraulic barriers. Geophysical Journal International, 2025, 242, 10.1093/gji/ggaf218. hal-05298119

HAL Id: hal-05298119

https://hal.science/hal-05298119v1

Submitted on 5 Oct 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Induced polarization applied to landslides. Part 1: imaging hydraulic barriers

C. Casotti,<sup>1,2</sup> A. Revil,<sup>2</sup> A. Ghorbani,<sup>3</sup> M. Abdelfattah,<sup>2,4</sup> M. Guerini,<sup>5</sup> F. Hoblea,<sup>2</sup>

G. Ménard,<sup>2</sup> Z. Su,<sup>6</sup> S. Qiang,<sup>7</sup> J. Berthet,<sup>8</sup> P. Laroche,<sup>9</sup> C. Lansigu,<sup>10</sup> T. Houtteville<sup>1</sup> and
J.M. Côme<sup>1</sup>

Accepted 2025 June 12. Received 2025 June 5; in original form 2025 February 24

## SUMMARY

Water content and pore fluid pressure increases have been recognized as important drivers of shallow landslides, especially through the role of strong rainfalls promoting gravitational instabilities. Less recognized is the role of vertical hydraulic barriers impeding the flow of ground water at the feet of areas prone to landslides. Induced polarization is a non-intrusive geophysical technique able to image hydraulic properties of the shallow subsurface. Recently developed petrophysical models bridging the gap between hydraulic and electrical properties of soft sediments, soils and rocks have been developed. Thanks to these relationships, this geophysical method can be used to image the water and clay contents of the formations and their permeability. Therefore, induced polarization can be used to image the occurrence of vertical permeability barriers. We focus our approach on a large landslide that occurred in March 1931 (reactivated in 1971–1972) above Le Châtelard village (Bauges, France). This landslide started inside a kilometer-scale syncline hosting clayey formations and moraines. We performed a 2.2 km profile crossing the syncline and the sliding area including resistivity, induced polarization and self-potential measurements. In addition, 22 samples were taken from the different formations outcropping at the field site including limestones, sandstones and clayey formations. The petrophysical investigations are combined with the field data to image the water content and cation exchange capacity as well as their permeability. The data set shows the existence of a vertical permeability barrier at the bottom of the landslide corresponding to the tight Urgonian limestone formation. We combine the permeability distribution, the resistivity and self-potential data by forward modelling the groundwater flow and electrokinetic response. We then invert the self-potential measurements to refine the image of the Darcy velocity distribution. The results show a strong upflow of the ground water just above the Manauds canyon where several gravitational instabilities occured in the past.

**Key words:** Electrical properties; Permeability and porosity; Electrical resistivity tomography (ERT); Induced polarization; Hydrogeophysics.

## 1 INTRODUCTION

In the last decades, we have seen a clear increase of the occurrence of shallow landslides in response to the extreme rainfall events

associated with climate change (e.g. Gariano & Guzzetti 2016). This is not surprising since shallow ground water flow and pore pressure can be strong ingredients in the development of such gravitational instabilities (Miller & Sias 1998; Whiteley et al. 2019).

<footnote n="1"><sup>1</sup> GINGER CEBTP, 78990 Élancourt, France</footnote>

<footnote n="2"><sup>2</sup> Université Savoie Mont-Blanc, EDYTEM UMR CNRS 5204, 73376 Le Bourget du Lac, France. E-mail: andre.revil@univ-smb.fr</footnote>

<footnote n="3"><sup>3</sup> Naga Geophysics, 73000 Chambéry, France</footnote>

<footnote n="4"><sup>4</sup> Geology Department, Faculty of Science, Port Said University, Port Said 42522, Egypt</footnote>

<footnote n="5"><sup>5</sup> Department of Earth Sciences, University of Turin, Via Valperga Caluso, 35, 10125 Turin, Italy</footnote>

<footnote n="6"><sup>6</sup> College of Safety and Engineering, Anhui University of Science and Technology, Huainan 232001, China</footnote>

<footnote n="7"><sup>7</sup> Key Laboratory of Surficial Geochemistry of Ministry of Education, School of Earth Sciences and Engineering, Nanjing University, Nanjing 210023, China</footnote>

<footnote n="8"><sup>8</sup> Styx4D, 19 rue lac Saint André, 73370 Le Bourget du Lac, France</footnote>

<footnote n="9"><sup>9</sup> ONF, 2 bis Av. du Général Leclerc, 94700 Maisons-Alfort, France</footnote>

<footnote n="10"><sup>10</sup> Parc des Bauges, Av. Denis Therme, 73630 Le Châtelard, France</footnote>
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Test site located above the Le Chatelard village in Savoie, France. (a) Overview of the Châtelard syncline, showing the layout of the time-domain induced polarization geophysical profiles. The profiles start near the town of Le Châtelard at 737 m above sea level (m a.s.l.) and extend up to the crest of Mont Julioz at 1672 m a.s.l. The landslide area is outlined with a light plain line. The line AB denotes the position of the geophysical profile. (b) Mitigation structures, including dams, have been constructed to reduce risk. (c) In 1931 March 12, multiple hamlets were carried along the slope during a gravitational instability event (Michaud infrastructures moved alongside the landslides in 1931, credit service RTM, Restauration des Terrains de Montagnes, 1931 March 16). TDIP stands for Time Domain Induced Polarization.</figcaption></figure>

It naturally follows that the permeability distribution of the sediments is of paramount importance to understand the occurrence of such events. The existence of subvertical permeability barriers can play a strong role in the increase of fluid pore pressure and water content in response to sudden rainfalls (see Revil et al. 2020; Fig. 1).

Geophysical methods play an increasingly critical role in describing the shape and properties of lithofacies in the subsurface of the earth (e.g. Guzzetti et al. 1999; Hack 2000; Flageollet et al. 2004; Colangelo et al. 2006; Walter & Joswig 2008; Schmutz et al. 2009; Chambers et al. 2010). Furthermore, petrophysical relationships can be used to transform imaged geophysical parameters (like the electrical conductivity or the seismic velocities) into valuable hydraulic properties of interest such as water content and permeability (e.g. Titov et al. 2002, 2024; Revil et al. 2024a). In this context, geoelectrical methods have proven to be very sensitive to ground water flow (Colangelo et al. 2006; Arosio et al. 2018; Hojat et al. 2019), water and clay contents (Perrone et al. 2014), and permeability (e.g. Revil et al. 2020).

The induced polarization method has recently appeared to be a suitable non-intrusive investigation method to better understand the subsurface of the Earth (Slater 2007; Cassiani et al. 2009; Schön 2011; Flores Orozco et al. 2020). It has been used to characterize shallow landslide characterization (Marescot et al. 2008; Revil et al. 2020; Flores Orozco et al. 2022; Ali et al. 2024; Wahida et al. 2024). Induced polarization can be considered as an extension of

the classical Electrical Resistivity Tomography method that has been used for over three decades to image the subsurface of the Earth (e.g. Olhoeft 1981a, b; Weller et al. 1996).

Induced polarization has a long history in geophysics (see for instance Schlumberger 1920; Bleil 1953; Seigel et al. 2007) and colloidal electrochemistry where it is known using distinct terminologies such as low-frequency dielectric enhancement or impedance spectroscopy (Dukhin & Shilov 1974; Fixman 1980; Leroy et al. 2017). The interpretation of electrical conductivity tomography can be done using the petrophysical models developed by Archie (1942) and later Waxman & Smits (1968). Induced polarization measures non only the conductivity of rocks and sediments but can be also used to obtain an image the normalized chargeability, which characterizes the ability of porous media to store electrical charges when applying an external electric field (Olhoeft 1981a, b). In absence of metallic particles (especially semiconductors such as pyrite and magnetite), the main low-frequency polarization mechanism is associated with the existence of the electrical double layer coating the surface of the grains (e.g. Schurr 1964; Fixman 1980; Titov et al. 2004). A model called the dynamic Stern layer model (Schurr 1964; Revil 2012; Revil et al. 2017; Bücker et al. 2019) has been successfully used in the last decade to explain laboratory and field data including for landslides (e.g. Revil et al. 2020; Flores Orozco et al. 2022). For metal-rich porous media, the readers are directed to Florsch et al. (2011, 2012); Gurin et al. (2015, 2019); Manrique et al. (2024), and references therein.
<figure><img src="image_3.png" /><figcaption>**Figure 2.** Sketch of the geological cross-section along with the position the geophysical profile AB with the Urgonian syncline in which gravitational instabilities occur including mud flows. The Hauterivian formation is formed by a succession of marls and limestones (adapted from Dupire 2016). The occurrence of various landslides underlines the role of the Manauds canyon in focusing the mud flows over the alluvian fan of The Granges.</figcaption></figure>

The two questions we want to answer are (i) how can we combine induced polarization, petrophysics, clustering techniques and geology to enhance our understanding of the role of water in shallow landslides? and (ii) Can we couple electrical resistivity tomography, induced polarization, and self-potential data to image the flow of the groundwater? We focus our investigations on a large landslide located above the village of Le Châtelard located in the Bauges Massif, Savoie, France (Figs 1–3). In March 1931, a large-scale landslide affected the area close and above the village (Gex 1931; Hoblea et al. 2008). This landslide involved ~six million cubic meters of sliding materials (Fig. 3). Following this event, a vast programme was undertaken in the 30 s to limit the infiltration of rain water by digging ~12 km-long network of shallow ditches that drain the entire area (Fig. 3). The draining has served its purpose since no large landslides have occurred since March, 1931 except of an event in 1971–1972 and a partial and sporadic reactivation of the landslide since 2015. In the companion paper, we will apply the newly developed strategy to the 3-D imaging of a vast landslide in the Triève formation (Isère, France), to a different geology.

# 2 BACKGROUND

## 2.1. Field site

The test site used in this paper is located within the commune of Le Châtelard, in the Bauges Massif, located in Savoie, France (Fig. 2). This area corresponds to the central part of the Bauges subalpine range formed at the front of the Alpine chain. Marls and limestones were deposited on the Ligurian-Piemontese ocean floor during the Jurassic and Cretaceous periods (170–100 Myr ago). The investigated area is dominated on its NE side by two parallel ridges with the prominent Urgonian formation composed by very tight limestones. The two prominent ridges in the topography represent the two edges of an Urgonian syncline (Fig. 3).

In 1931 March 12, a landslide affected the whole area and occurred two weeks after exceptional rainfalls. Despite the absence of casualties, this event received a considerable attention across Europe at that time. Tensional fractures began to appear in October, 1930. In January, 1931, following snowmelt and increased runoff, these fractures widened significantly and started capturing surface water from several torrents and rivers (Gex 1931).
<figure><img src="image_4.png" /><figcaption>**Figure 3.** Geomorphological map of the landslide showing the directions of the gravitational instabilities together with the rock and erosional escarpments. We can also see the network of drainage ditches used to drain the water from strong rainfalls before infiltrating the ground. AB denotes the position of the geophysical survey (resistivity and induced polarization).</figcaption></figure>

Tight carbonates (especially the Urgonian and Nummulitic formations) and sandstones (Flysch) are found within the syncline (Fig. 3). The alteration of softer alumino-silicate-rich formations (such as the Melleta Shale) located inside the syncline led to the development of clay-rich soils in the center of the syncline that can lead to their gravitational instability, especially because of the upward flow of groundwater as discussed in the last part of the paper. The slope instability observed in this area was believed to be associated with a combination of factors:

(1) The asymmetrical configuration of the syncline, shaped by the steep dip of the fold to the west, has resulted in an unstable landscape prone to erosion. The western Urgonian ridge, culminating at Mont Chabert (1475 m a.s.l.), is less pronounced than the ridge in the eastern flank (Mont Julioz ridge, 1672 m a.s.l.). This topographical setting (with strong slopes ~25 per cent) promotes differential erosion rate with creeks and torrent eroding the interior of the syncline and contributing to gravitational instability of the area.

(2) The investigated area was significantly shaped by the Last Glacial Maximum (around 20 000 years ago) when glaciers from the Mont-Blanc region advanced over the Bauges range. As these glaciers retreated, they deposited morainic materials, including blocks and clayey pebbles. These permeable and loose deposits (sometimes with a thickness of ~100 m, Gex 1931) lie over older

blue clay formations (Gex 1931). This configuration induces sharp permeability contrasts, favouring the accumulation of water and the formation of transient perched aquifers. It may also be responsible for natural sliding surfaces facilitating downslope movements.

(3) The occurrence of episodic strong rainfalls that have been accentuated recently by climate change. The year 1930 and the beginning of 1931 were characterized by heavy rainfalls while 1928 and 1929 were very warm and dry, which may have weaken the cohesion of the morainic materials and favored rapid infiltration during subsequent wet periods (Gex 1931).

(4) In addition to these climatic and stratigraphic factors, field observations reveal the presence of localized water emergence zones, hydrophilic vegetation, and areas of persistent saturation across the landslide body, even though an artificial drainage network was implemented after the 1931 event. These surface indicators reflect inefficient drainage and suggest that part of the water does not follow shallow flow paths but instead originates from deeper groundwater circulations. This deeper flow may be facilitated by a system of fractures and joints, potentially influenced by a north-south axial fault affecting the core of the overturned syncline near 1300 m a.s.l. (ONF 2016). Such conditions favour the development of overpressures at depth, which can play a key role in the periodic reactivation and kinematic behaviour of the landslide.
<table><caption>**Table 1.** Petrophysical properties of the 22 samples used in this study. The CEC is expressed in meq/100 g (1 meq/100 g = 963.20 C kg⁻¹ in SI units) and is obtained using the cobalthexamine method. The surface conductivities and formation factors are determined by plotting, for each sample, the (in-phase) conductivity of the material (at 1 Hz) as a function of the conductivity of the pore water (in a log/log space). The main clay mineral is illite (Doudoux *et al.* 1999).</caption><thead><tr><th>Full name</th><th>Lithology</th><th>Porosityφ (−)</th><th>Grain densityρ<sub>g</sub> (g cm<sup>-3</sup>)</th><th>CEC(meq/100g)</th><th>F(−)</th><th>σ<sub>S</sub>(10<sup>-3</sup> S m<sup>-1</sup>)</th></tr></thead><tbody><tr><td>F2 (1)</td><td>Sandstone</td><td>0.14</td><td>2.70</td><td>6.845</td><td>24.6</td><td>4.211</td></tr><tr><td>F3 (1)</td><td>Sandstone</td><td>0.18</td><td>2.70</td><td>7.807</td><td>21.4</td><td>10.46</td></tr><tr><td>F41 (1)</td><td>Sandstone</td><td>0.10</td><td>2.70</td><td>6.845</td><td>26.6</td><td>12.00</td></tr><tr><td>F42(1)</td><td>Sandstone</td><td>0.13</td><td>2.70</td><td>6.845</td><td>70.2</td><td>5.113</td></tr><tr><td>F43(1)</td><td>Sandstone</td><td>0.080</td><td>2.70</td><td>6.845</td><td>22.5</td><td>5.13</td></tr><tr><td>F51(1)</td><td>Sandstone</td><td>0.082</td><td>2.70</td><td>6.845</td><td>47.91</td><td>4.334</td></tr><tr><td>F53(1)</td><td>Sandstone</td><td>0.050</td><td>2.70</td><td>6.845</td><td>67.4</td><td>5.503</td></tr><tr><td>G11(2)</td><td>Blue clay</td><td>0.103</td><td>2.65</td><td>5.262</td><td>76.1</td><td>6.809</td></tr><tr><td>G33(2)</td><td>Blue clay</td><td>0.0907</td><td>2.65</td><td>5.005</td><td>43.3</td><td>4.104</td></tr><tr><td>H21(3)</td><td>Limestone</td><td>0.075</td><td>2.80</td><td>3.251</td><td>237.7</td><td>2.399</td></tr><tr><td>H22(3)</td><td>Limestone</td><td>0.120</td><td>2.80</td><td>3.251</td><td>367.1</td><td>3.332</td></tr><tr><td>N (4)</td><td>Limestone</td><td>0.0868</td><td>2.80</td><td>0.914</td><td>333.6</td><td>0.501</td></tr><tr><td>SE4 (5)</td><td>Carbonate</td><td>0.0700</td><td>2.80</td><td>6.754</td><td>236.2</td><td>9.75</td></tr><tr><td>SE21 (5)</td><td>Carbonate</td><td>0.14</td><td>2.80</td><td>5.091</td><td>246.2</td><td>10.436</td></tr><tr><td>U1 (6)</td><td>Limestone</td><td>0.089</td><td>2.80</td><td>0.563</td><td>548.2</td><td>0.519</td></tr><tr><td>U2 (6)</td><td>Limestone</td><td>0.071</td><td>2.80</td><td>0.352</td><td>178.7</td><td>0.629</td></tr><tr><td>B2 (7)</td><td>Shale</td><td>0.50</td><td>2.70</td><td>31.02</td><td>27.2</td><td>-</td></tr><tr><td>FS2 (1)</td><td>Sandstone</td><td>0.43</td><td>2.70</td><td>20.64</td><td>2.661</td><td>23.573</td></tr><tr><td>M1 (8)</td><td>Moraine</td><td>0.850</td><td>2.80</td><td>2.613</td><td>1.803</td><td>9.114</td></tr><tr><td>RI (9)</td><td>Clayey material</td><td>0.475</td><td>2.70</td><td>1.390</td><td>-</td><td>-</td></tr><tr><td>SED (9)</td><td>Clayey material</td><td>0.470</td><td>2.70</td><td>16.40</td><td>25.56</td><td>4.441</td></tr><tr><td>M2 (8)</td><td>Moraine</td><td>0.620</td><td>2.80</td><td>11.98</td><td>1.712</td><td>21.14</td></tr></tbody></table>

(1) Flysch formation.

(2) Gault formation corresponding to a green sandstone.

(3) Hauterivian formation.

(4) Nummulithic formation.

(5) Senonian formation.

(6) Urgonian formation.

(7) Bartonian shale.

(8) Moraines.

(9) Materials from the landslide (clays and clayey moraines).

(*) CEC value used by default for the flysch.

<table><caption>**Table 2.** Petrophysical properties of 22 samples used in this study. In-phase conductivity, quadrature conductivity and normalized chargeability values at 25 °C. The normalized chargeability $M_n$ is computed from the difference of the in-phase conductivity between 10 mHz and 10 kHz. $σ_w$ represents the pore water conductivity (here reported at 25 °C).</caption><thead><tr><th>Full name</th><th>σ' 10 mHz(10<sup>-3</sup> S m<sup>-1</sup>)</th><th>σ' 10 kHz(10<sup>-3</sup> S m<sup>-1</sup>)</th><th>M<sub>n</sub>(10<sup>-3</sup> S m<sup>-1</sup>)</th><th>σ' 32 Hz(10<sup>-3</sup> S m<sup>-1</sup>)</th><th>σ' 32 Hz(10<sup>-5</sup> S m<sup>-1</sup>)</th><th>σ<sub>w</sub> (25 °C)(S m<sup>-1</sup>)</th></tr></thead><tbody><tr><td>F2</td><td>6.625</td><td>7.240</td><td>0.615</td><td>7.070</td><td>9.87</td><td>0.071 18</td></tr><tr><td>F3</td><td>12.12</td><td>13.49</td><td>1.374</td><td>13.04</td><td>21.82</td><td>0.071 18</td></tr><tr><td>F41</td><td>11.99</td><td>14.40</td><td>2.415</td><td>14.09</td><td>10.71</td><td>0.071 18</td></tr><tr><td>F42</td><td>6.494</td><td>7.841</td><td>1.347</td><td>7.590</td><td>15.56</td><td>0.071 18</td></tr><tr><td>F43</td><td>7.42</td><td>8.13</td><td>0.71</td><td>7.90</td><td>10.06</td><td>0.071 18</td></tr><tr><td>F51</td><td>5.500</td><td>5.965</td><td>0.465</td><td>5.785</td><td>7.55</td><td>0.071 18</td></tr><tr><td>F53</td><td>5.963</td><td>7.008</td><td>1.045</td><td>6.818</td><td>8.97</td><td>0.071 18</td></tr><tr><td>G11</td><td>5.915</td><td>7.223</td><td>1.308</td><td>7.043</td><td>34.29</td><td>0.071 18</td></tr><tr><td>G33</td><td>4.610</td><td>5.733</td><td>1.123</td><td>5.490</td><td>4.70</td><td>0.071 18</td></tr><tr><td>H21</td><td>2.161</td><td>2.278</td><td>0.116</td><td>2.192</td><td>1.40</td><td>0.071 18</td></tr><tr><td>H22</td><td>3.065</td><td>3.276</td><td>0.212</td><td>3.211</td><td>0.20</td><td>0.071 18</td></tr><tr><td>N</td><td>0.576</td><td>0.718</td><td>0.141</td><td>0.687</td><td>0.48</td><td>0.071 18</td></tr><tr><td>SE21</td><td>9.40</td><td>10.08</td><td>0.680</td><td>10.05</td><td>23.62</td><td>0.071 18</td></tr><tr><td>SE43</td><td>9.846</td><td>10.24</td><td>0.399</td><td>10.16</td><td>6.13</td><td>0.071 18</td></tr><tr><td>U1</td><td>0.044</td><td>0.100</td><td>0.056</td><td>0.101</td><td>0.04</td><td>0.071 18</td></tr><tr><td>U2</td><td>0.334</td><td>0.361</td><td>0.027</td><td>0.342</td><td>0.05</td><td>0.071 18</td></tr><tr><td>B2</td><td>149</td><td>151</td><td>2.062</td><td>150</td><td>0.20</td><td>1.684</td></tr><tr><td>FS2</td><td>23.66</td><td>26.85</td><td>3.198</td><td>24.60</td><td>19.94</td><td>0.027 81</td></tr><tr><td>M1</td><td>44.05</td><td>48.51</td><td>4.464</td><td>44.33</td><td>28.00</td><td>0.0638</td></tr><tr><td>RI</td><td>27.46</td><td>30.45</td><td>2.989</td><td>28.69</td><td>35.11</td><td>0.048 31</td></tr><tr><td>SED</td><td>32.53</td><td>35.23</td><td>2.700</td><td>32.29</td><td>30.65</td><td>0.077 32</td></tr><tr><td>M2</td><td>76.40</td><td>82.79</td><td>6.398</td><td>76.63</td><td>10.09</td><td>0.1123</td></tr></tbody></table>
<table><caption>**Table 3.** Petrophysical properties of the 22 samples used in this study. In-phase conductivity, quadrature conductivity and normalized chargeability values at 25 °C. The normalized chargeability $M_n$ is computed from the difference of the in-phase conductivity between 1 Hz and 1 kHz.</caption><thead><tr><th></th><th>Full nameσ' 1 Hz(10<sup>-3</sup> S m<sup>-1</sup>)σ' 1 kHz(10<sup>-3</sup> S m<sup>-1</sup>)M<sub>n</sub>(10<sup>-3</sup> S m<sup>-1</sup>)σ' 32 Hz(10<sup>-3</sup> S m<sup>-1</sup>)σ' 32 Hz(10<sup>-5</sup> S m<sup>-1</sup>)</th><th></th><th></th><th></th><th></th></tr></thead><tbody><tr><td>F2</td><td>6.95</td><td>7.16</td><td>0.21</td><td>7.07</td><td>4.18</td></tr><tr><td>F3</td><td>12.49</td><td>13.28</td><td>0.79</td><td>13.04</td><td>11.5</td></tr><tr><td>F41</td><td>13.42</td><td>14.34</td><td>0.93</td><td>14.09</td><td>11.1</td></tr><tr><td>F42</td><td>7.367</td><td>7.76</td><td>0.39</td><td>7.59</td><td>9.06</td></tr><tr><td>F43</td><td>7.645</td><td>8.04</td><td>0.39</td><td>7.90</td><td>6.17</td></tr><tr><td>F51</td><td>5.611</td><td>5.89</td><td>0.27</td><td>5.78</td><td>3.97</td></tr><tr><td>F53</td><td>6.553</td><td>6.92</td><td>0.37</td><td>6.82</td><td>4.65</td></tr><tr><td>G11</td><td>6.674</td><td>7.15</td><td>0.48</td><td>7.04</td><td>7.56</td></tr><tr><td>G33</td><td>5.172</td><td>5.63</td><td>0.46</td><td>5.49</td><td>5.36</td></tr><tr><td>H21</td><td>2.099</td><td>2.23</td><td>0.13</td><td>2.19</td><td>1.95</td></tr><tr><td>H22</td><td>3.137</td><td>3.24</td><td>0.11</td><td>3.21</td><td>0.90</td></tr><tr><td>N</td><td>0.644</td><td>0.70</td><td>0.06</td><td>0.69</td><td>0.55</td></tr><tr><td>SE21</td><td>9.989</td><td>10.06</td><td>0.07</td><td>10.05</td><td>1.63</td></tr><tr><td>SE43</td><td>10.098</td><td>10.19</td><td>0.09</td><td>10.16</td><td>0.85</td></tr><tr><td>U1</td><td>0.092</td><td>0.10</td><td>0.012</td><td>0.100</td><td>0.04</td></tr><tr><td>U2</td><td>0.342</td><td>0.35</td><td>0.01</td><td>0.34</td><td>0.19</td></tr><tr><td>B2</td><td>150.26</td><td>150.63</td><td>0.37</td><td>150.40</td><td>6.64</td></tr><tr><td>FS2</td><td>43.60</td><td>46.11</td><td>2.51</td><td>44.33</td><td>52.3</td></tr><tr><td>M1</td><td>75.62</td><td>79.18</td><td>3.55</td><td>76.63</td><td>78.1</td></tr><tr><td>RI</td><td>27.66</td><td>29.88</td><td>2.22</td><td>28.69</td><td>52.6</td></tr><tr><td>SED</td><td>23.77</td><td>25.83</td><td>2.06</td><td>24.60</td><td>47.5</td></tr><tr><td>M2</td><td>32.00</td><td>33.54</td><td>1.54</td><td>32.29</td><td>31.9</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>**Figure 4.** Picture of selected representative core samples. The investigated collection of rock samples and unconsolidated sediments comprises carbonates and siliciclastic materials with a total of 22 samples. Some of the carbonate rocks are very tight with connected porosities less than 10 per cent.</figcaption></figure>

Understanding the complex interplay of local geology, glacial deposits and hydrogeology is crucial for assessing slope stability in the study area. Given these challenges, induced polarization tomography provides a valuable method for investigating these factors. The basics of induced polarization are discussed in the next section.

## 2.2. Induced polarization

Induced polarization is a geophysical galvanometric technique that can be used to image the subsurface down to a depth of few kilometers. In this section, we provide a fundamental petrophysical model called the dynamic Stern layer model to understand induced polarization at the scale of a representative elementary volume of a rock sample (see Revil 2012, 2013a, b). In frequency-domain induced

polarization, we measure the amplitude and phase of the complex impedance. Thanks to a geometrical coefficient accounting for the position of the electrodes and boundary conditions, we can recast the amplitude and the phase of the impedance into a complex conductivity,

$$ \sigma^*(\omega) = \sigma'(\omega) - i\sigma''(\omega), \quad (1) $$

where $\sigma'(\omega)$ and $\sigma''(\omega)$ denote the in-phase and quadrature conductivity, respectively, and $\omega$ denotes the angular frequency (in rad/s) associated with the injected current. The quantities $\sigma'(\omega)$ and $\sigma''(\omega)$ describe conduction and polarization properties of the porous material, respectively, and can be determined in a broad frequency range (typically 1 mHz–100 kHz). In this paper, we do not consider the full description of the complex conductivity spectra but we focus on two
<figure><img src="image_6.png" /><figcaption>**Figure 5.** Selected spectra for six rock samples from the test site. Sample U2 corresponds to a tight Urgonian carbonate rock. The carbonate and limestone formations are represented with blue colours while the clay-rich formations (shales, clay-rich conglomerates, sandstones) are shown in red. MW corresponds to the high-frequency Maxwell-Wagner polarization. CEC stands for Cation Exchange Capacity.</figcaption></figure>

parameters, one describing the conduction and one describing the polarization of the material. The in-phase conductivity is approximated below by the instantaneous (high-frequency) conductivity

$\sigma_{\infty}$ (S m$^{-1}$), which can be written as (Revil et al. 2017),

$$ \sigma'(\omega) \approx \sigma_{\infty} = \frac{\sigma_w}{F} + \sigma_s^{\infty}, \qquad (2) $$
<figure><img src="image_7.png" /><figcaption>**Figure 6.** Conductivity of the core samples versus the conductivity of the pore water (NaCl, 25 °C). (a) 2 carbonate samples. (b) Two siliciclastic samples with surface conductivity higher than for carbonates. The fit of the data is used to determine the formation factor and the surface conductivity, which are reported in Table 1. The yellow area corresponds to the range of pore water conductivities measured at four springs observed in the field along the geophysical profile AB.</figcaption></figure>

where $\sigma_w$ denotes the pore water conductivity (S m⁻¹) (i.e. the conductivity of the pore water saturating the pore space of the porous body and dependent on salinity and temperature). The quantity F (dimensionless) is called the formation factor and is a textural property of the porous medium. It is related to the (connected) porosity $\phi$ (dimensionless) by a power law relationship $F = \phi^{-m}$ called Archie's law (Archie 1942) with m (dimensionless) being the first Archie exponent (porosity or cementation exponent). The quantity $\sigma_S^\infty$ (in S m⁻¹) in eq. (2) is called the excess conductivity or (instantaneous) surface conductivity. It denotes the additional conductivity component associated with electrical double layer coating the surface of the grains in presence of water in the pore space of the porous body.

Since the dependence of the in-phase conductivity with the frequency is small (less than 10 per cent), eq. (2) can be used to describe the conductivity at any frequency. In order to obtain, from laboratory experiments, the values of the (intrinsic) formation factor F and the value of the (instantaneous) surface conductivity $\sigma_S^\infty$, we can

measure the conductivity of the porous material at different salinities (hence different pore water conductivities). Then, we apply a nonlinear regression in the log-log domain (logσ', logσw) using eq. (2) to retrieve these two parameters. We will return to this point below.

The other property of interest is the normalized chargeability, which describes the ability of the porous material to polarize. This parameter can be determined from the (small) frequency dependence (dispersion) of the in-phase conductivity as the difference between the in-phase conductivity from a high frequency and a low frequency separated by several decades. In the frequency range investigated in this paper (10 mH, 45 kHz), it is the sum of two distinct polarization processes. The first one is associated with the polarization of the electrical double layer coating the grains (induced polarization effect) and the second one is called the Maxwell-Wagner polarization and is related to the discontinuity of the displacement current at the interface of the phases forming the porous composite. Therefore, we write the quadrature conductivity as,

$$\sigma''(\omega) \approx \sigma''_{\text{IP}}(\omega) + i\omega\epsilon_{\infty}, \quad (3)$$

where $\sigma''_{\text{IP}}(\omega)$ describes the contribution associated with induced polarization and where the dielectric constant $\epsilon_\infty$ corresponds to the low-frequency apparent dielectric constant of the Maxwell-Wagner polarization mechanism. In order to keep the model simple and because we are dealing with low-frequency measurements in the field (<10 Hertz), we let aside the description of the Maxwell-Wagner polarization in this paper.

Assuming now that the material is self-similar that is, its heterogeneities follow a fractal-like spatial distribution without a characteristic length scale, we expect a relatively flat spectrum for the quadrature conductivity $\sigma''_{\text{IP}}(\omega)$. In this case, the spectra are usually described by the so-called Drake or Constant Phase Model (see Van Voorhis et al. 1973). Generally speaking, the phase spectra are not flat but flat enough for the Drake model to apply reasonably well. Considering the quadrature conductivity at the geometric mean frequency of two frequencies $f_1$ and $f_2$ and the normalized chargeability being defined as the difference between the in-phase conductivity at the frequency $f_2(> f_1)$ and the in-phase conductivity at the lower frequency $f_1$, the quadrature conductivity and the normalized chargeability are related to each other by (Van Voorhis et al. 1973; Revil et al. 2017) $\sigma''_{\text{IP}}(\sqrt{f_1 f_2}) \approx M_n(f_1, f_2)/\alpha$, where $\alpha \approx (2/\pi) \ln A$ and A denotes the number of decades between $f_1$ and $f_2$. For instance, for the frequency range 10 mHz and 100 Hz corresponds to four decades, $A = 10^4$ and we obtain $\alpha \approx 6$. These assumptions lead to a constant quadrature conductivity model,

$$\sigma''(\omega) \approx \frac{M_n}{\alpha}. \quad (4)$$

In order to complete the petrophysical model, we need now relationships between the surface conductivity and the normalized chargeability and both the textural properties of the porous material and electrochemical properties characterizing the surface of the grains. According to the dynamic Stern layer model developed by Revil (2012), the surface conductivity and the normalized chargeability can be written as,

$$\sigma_S^\infty = \frac{1}{F\phi} B \rho_g \text{CEC}, \quad (5)$$

$$M_n = \frac{1}{F\phi} \lambda \rho_g \text{CEC}, \quad (6)$$
<figure><img src="image_8.png" /><figcaption>**Figure 7.** Intrinsic formation factor versus porosity and fit with Archie's law. (a) Clay-rich rocks with data from El Alam *et al.* (2024), Bernard *et al.* (2007), Revil *et al.* (2022) and Zhang *et al.* (2023). (b) Carbonate rocks. Most of the data are from Panwar *et al.* (2021) with the crosses representing the dolomite core samples from Halisch *et al.* (2014, symbol +) consisting of large crystals with some dissolution structures (with more than 90 per cent dolomite) and the Aquitian Danian dolomite core samples investigated by Cerepi (2004, symbol ×).</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>**Figure 8.** Normalized chargeability (determined as the difference between the in-phase conductivity between 10 mHz and 10 kHz) and the quadrature conductivity at the geometric mean of the two frequencies (32 Hz). The soil sample data are from Revil et al. (2017) and the volcanic rock data are from Revil et al. (2022). The granite data are from an unpublished study. The theoretical value predicted by the Constant Phase Model is 8.8.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Figure 9.** Surface conductivity versus (partial) normalized chargeability. The crosses correspond to the Tushka clay-rich carbonates from Egypt (Halish et al. 2014). For these carbonates, the quadrature conductivity was transformed into partial normalized chargeability for the frequency range 1 Hz–1 kHz using $\alpha = 4.4$ (corresponding to three decades in frequencies). The carbonate may have a broad range of R-values between 0.01 for pure calcite to R = 0.10 (like for siliciclastic materials) for clay-rich carbonates.</figcaption></figure>

where $\phi$ (dimensionless) denotes the connected porosity, B (in m$^2$s$^{-1}$V$^{-1}$) and $\lambda=R B$ (in m$^2$s$^{-1}$V$^{-1}$) denotes two effective mobilities of the counterions in the double layer coating the surface of the grains, $\rho_g$ the mass density of the grains (2700 kg m$^{-3}$ for silico-clastic materials and 2900 kg m$^{-3}$ for carbonates and limestones), and CEC denotes the Cation Exchange Capacity of the material (mostly associated with clay minerals). From eqs (5) and (6), the ratio between the normalized chargeability to the surface conductivity is given by (Revil 2012, Revil et al. 2017),

$$ \frac{M_n}{\sigma_S} = \frac{\lambda}{B} \equiv R, \qquad (7) $$

where R is a non-dimensional parameter independent of temperature and saturation or textural properties.

Induced polarization measurements can also be performed in the time-domain. We usually use time-domain induced polarization with a period of 1 s for the injection of the electrical current. The chargeability is determined by integrating an early window of the voltage decay curve after shutting down the electrical current. Then the normalized chargeability is obtained by the product of the conductivity with the chargeability. We will compare below in Section 2.3 the normalized chargeability obtained from frequency-domain measurements to those obtained with time-domain measurements.

## 2.3. Samples description and petrophysical results

We collected 22 samples that are representative of the different facies present along the geophysical survey. The petrophysical data are reported in Tables 1–3 and a picture of some of the core samples can be seen in Fig. 4. Sampling was carried out in outcrops surrounding the geophysical profile shown in Fig. 2. The CEC was obtained with the cobalthexamine method (Ciesielski et al. 1997; Aran et al. 2008) and the porosity by measuring the volume of the core samples, and both their dry and saturated weights. The cobalt-hexamine is a classical titration method used to determine the CEC in agriculture. The exchange between the solution and the porous material is characterized by the change of concentration of cobalt in the solution by spectrocolorimetry of the coloured Cohex ions at 425 nm. In the following analysis, we mix this petrophysical study with other literature data since the dynamic Stern layer model should be universal and not site specific.

To determine the electrical conductivity of the pore water under field conditions, we measured water samples collected from various springs along the slope intersecting the geoelectrical profile using a Hanna Dist-3 field conductivity meter. The Hanna Dist-3 is a low-range electrolytic water-proof field conductivity meter than can measure up the water conductivity to 2000 µS cm$^{-1}$ making it ideal to monitor a variety of water quality applications. Temperature correction was applied to standardize all conductivity values to 25 °C, ensuring consistency with laboratory conditions. Additional Inductively Coupled Plasma Mass Spectrometry analyses conducted at the EDYTEM laboratory (https://edytem.osug.fr/) revealed ion exchange processes between the spring water and the clay formations, notably sodium retention and calcium release. This confirms the influence of clay minerals on water chemistry and helps explain the variability in measured conductivities, which range from 300 to 800 µS cm$^{-1}$ (i.e. 0.03 to 0.08 S m$^{-1}$) across the valley. For comparison with the field data, our 22 vacuum-saturated rock samples were saturated with water from the field exhibiting a pore water conductivity of 712 µS cm$^{-1}$ (25 °C).

We performed frequency-domain induced polarization measurements over the frequency range 10 mHz–45 kHz at three salinities
<figure><img src="image_11.png" /><figcaption>**Figure 10.** Surface conductivity versus the normalized CEC defined as the CEC divided by the tortuosity of the pore space (product of the formation factor by the connected porosity). The data set comprises volcanic rocks from shield and stratovolcanoes (Zhang *et al.* 2023), bentonite (El Alam *et al.*, 2024), and the data from this work (carbonates, sandstones and shales).</figcaption></figure>

(pore water conductivity of 0.1, 1.0 and 10.0 S m⁻¹, T = 25 °C, NaCl). The measurements were acquired with the ZELSIP04-V02 impedance meter developed in Germany by Egon Zimmermann (see Zimmermann *et al.* 2008, 2019). In Fig. 5, we show complex conductivity spectra at the lowest pore water conductivity. The clayey materials are characterized by both high in-phase and quadrature conductivities while the carbonates are characterized by lower in-phase and quadrature conductivities. This contrast reflects the higher porosity and CEC of clayey materials compared to the lower values observed in carbonates (see Table 1).

In Fig. 6, we show four selected examples of (in-phase) conductivity versus the pore water conductivities at three salinities. Using eq. (2) and these data, we can determine the formation factor *F* and surface conductivity σs∞ for each core sample as described above. These results are reported in Table 1. In Fig. 7, we plot the formation factor versus the porosity and fit the data using Archie's law to determine the porosity (cementation) exponent *m*. A value of *m* = 2.1 ± 0.2 is consistent with both the current dataset and literature data. In Fig. 8, we plot the normalized chargeability versus the quadrature conductivity. The normalized chargeability is determined from the dispersion of the in-phase conductivity between two frequencies (here 10 mHz and 10 kHz) and the quadrature conductivity at the geometrical mean of the two frequencies (i.e. ~33 Hz). The slope can be predicted from the theory (eq. 4

with $\alpha \approx (2/\pi) \ln A$) and the predicted slope from Constant Phase Model agrees with the one obtained by fitting the data. The theory also predicts a linear relationship between the surface conductivity and the normalized chargeability which is confirmed by the data displayed in Fig. 9. These results indicate that for pure calcite we have *R* = 0.01 while for clay-rich sediments (including clay-rich carbonates), we have *R* = 0.10 (see Panwar *et al.* 2021).

Finally the surface conductivity is proportional to the CEC divided by the tortuosity of the pore space and given by the product of the formation factor and the connected porosity (i.e. *F* *φ*, see Fig. 10). The data are consistent with a value of the apparent mobility *B*(Na⁺, 25 °C) = 3.1 ± 0.3 × 10⁻⁹ m⁻²s⁻¹V⁻¹ while the apparent mobility is given by $\lambda = BR$ according to eq. (7).

A key aspect is the comparison between normalized chargeability from field time-domain induced-polarization and laboratory frequency-domain induced-polarization measurements. Indeed the normalized chargeability obtained from frequency-domain measurements is obtained using several decades in frequency (ideally from DC to infinite frequencies for the induced polarization contribution to polarization). In order to get the same normalized chargeability, the time-domain induced polarization measurements should be done with a current injected over the following time window [-∞, 0]. In reality, we use [-T, 0] with T = 1 s. This implies that only the fraction corresponding to the smallest grains are
<figure><img src="image_12.png" /><figcaption>**Figure 11.** Statistical summary of normalized polarization responses based on 1000 Cole–Cole models with the complex conductivity relaxation time taken in the following interval $\tau \in[0.007\ 85, 0.383\ 35]$ s and the Cole–Cole exponent $c \in[0.28, 0.41]$. (a) In phase ($\sigma'$, solid line) and quadrature ($\sigma''$, dashed line) components of the complex conductivity spectra. The grey-shaded area indicates the envelope encompassing 85 per cent of the computed models, and the black line shows the median response. (b) Time-domain decay curves computed using the same set of models. The solid black line corresponds to the median response for a truncated injection of 1 s, $M_{T=1s}(t)$, while the dashed black line shows the median ideal decay, $M_{T=\infty}(t)$. Grey areas represent the 85 per cent confidence interval around each response. The frequency-domain and time-domain normalized chargeabilities are properly defined in Appendix A.</figcaption></figure>

polarized and therefore the normalized chargeability is smaller than for $T = +\infty$. An analysis of the amplification factor is done in Appendix A for the specific Cole–Cole model in complex conductivity (the Cole–Cole model is a complex conductivity/resistivity model broadly used in electrical and dielectric properties of porous media and colloids). Fig. 11 shows that for a Cole–Cole complex conductivity model with a random selection of the Cole–Cole parameters inside a range prescribed by the experimental data, the decay curve for the field-selected induced polarization parameters ($T = 1$ s, dead time of 0.1 s) is substantially smaller than the true normalized chargeability by a factor 5 to 10. This factor is called the amplification factor $a$ (see Appendix A). In order to connect the normalized chargeability obtained with such a small period $T = 1$ s and the normalized chargeability obtained from frequency-domain measurements, we develop a specific dedicated experimental dataset. In order to do so, we use the ABEM-LS2 12-channels field resistivity meter to perform time-domain measurements on the same sample as frequency-domain measurements but with the same acquisition parameter as used in the field (period of 1 s and dead-time of 0.1 s). The comparison between the two values of the normalized chargeabilities is shown in Fig. 12, where we plot our dataset alongside

data from other studies that applied the same methodology, including the published results of Piolat *et al.* (2025). A general trend indicates that an amplification coefficient of $a = 10$ is required to scale the field data to match the laboratory frequency-domain measurements. With this information in mind, we adopted the flowchart shown in Fig. 13 to interpret the field data as discussed further in the next section of this paper.

# 3 FIELD SURVEY

## 3.1. Field investigations

In order to better understand the architecture of the landslide, we performed a 2.2 km long profile using an ABEM-LS2 equipment and an electrode spacing of 20 m. We use stainless steel electrodes, a primary current injection period $T = 1$ s between the electrode pairs AB, and a full waveform acquisition of the secondary voltages at the electrode pairs MN. The position of the profile is shown in Fig. 3. The data were filtered using standard deviations and deviations from neighbouring measurements in the pseudosections
<figure><img src="image_13.png" /><figcaption>**Figure 12.** Comparison between frequency-domain and time-domain induced polarization laboratory data. (a) Electrical resistivity. (b) Normalized chargeability. For the frequency domain measurements, the normalized chargeability is determined from the dispersion of the in-phase conductivity between 10 mHz and 1 kHz and for the time-domain data, current injection of *T* = 1 s, dead time 0.1 s and 10 windows of 0.1 s (chargeability determined on the first window after the dead time). The granite data are from (Piolat *et al.* 2025) and Toarcian core data are from an unpublished study. The frequency-domain and time-domain normalized chargeabilities are properly defined in Appendix A.</figcaption></figure>

of the apparent resistivities and chargeabilities. Additionally, for the apparent chargeability decay curves (see examples in Fig. 14), measurements were discarded when the quality of the exponential fit, assessed using the coefficient of determination *r*², was below a critical threshold.

These filtered data (resistivity and polarization) were then in-
verted using the open-source package pyGIMLi, employing an

inversion based on the generalized Gauss–Newton method (see
Günther *et al.* 2006 for details). We first inverted the resistivity
data using a discretization with 7532 cells accounting for the topog-
raphy. The iterations are stopped when the root mean square error
is smaller than a prescribed value. The inversion process penalizes
the roughness of the inverted model and the inversion is stopped at
iteration 5. Then we inverted the apparent chargeability data using
<figure><img src="image_14.png" /><figcaption>**Figure 13.** Flow chart to obtain the water content and CEC tomograms from the electrical conductivity and normalized chargeability tomograms. The amplification factor *a* = 10 is used only for the CEC tomogram but not to the water content tomogram. The pore water conductivity *σ*<sub>w</sub> can be obtained through its measurement of the pore water conductivity in boreholes. The values of the two mobilities occurring in the equations, *B* and *λ*, are given in Table 4 at 25 °C.</figcaption></figure>

the resistivity model obtained at the previous step. Again, the inversion process penalizes the roughness of the inverted model and the inversion is stopped at iteration 4.

In addition to the resistivity and induced polarization data, we
performed a self-potential survey along the profile with a spacing
of 20 m between the measurements. The self-potential method is a
passive geophysical technique where the electrical potential distri-
bution is associated with natural currents occurring in the ground
(Revil & Pezard 1998; Revil et al. 2001). We use non-polarizable
PbPbCl₂ electrodes and a 100 MOhm-input impedance voltmeter
with a sensitivity of 0.1 mV. We did not use bentonite to improve
the contact between the electrodes and the soil because of the good
moisture content of the ground at the time of the measurements.

3.2. RESULTS

The inverted resistivity and normalized chargeability tomograms as
well as the SP data are shown in Fig. 15. The cross-plot between
the inverted normalized chargeability and conductivity is shown in
Fig. 16 with and without the use of the amplification factor dis-
cussed in Section 2.3. In this figure, we also added the data from
the frequency-domain measurements using the core samples of the
different facies observed at this site. The results confirm that the

need of the correction factor to get the correct normalized charge-
abilities from the time-domain induced polarization measurements
using the small period (T = 1 s) as in for the field measurements.

In order to apply facies-dependent petrophysical transforms to
interpret the field data, we use a clustering algorithm as done re-
cently by Revil *et al.* (2024b) in order to separate the carbonate
facies from the siliciclastic facies. We apply an iterative K-means
clustering approach using the *scikit-learn* library (Pedregosa *et al.*
2011). This algorithm partitions the data into *K* groups by mini-
mizing the variance within each cluster, based on Euclidean dis-
tance to the cluster centroids. The input features are the logarithm
of the electrical conductivity and the logarithm of the normalized
chargeability, both standardized prior to clustering to ensure equal
weighting. Although the main objective is to distinguish between
two main facies (carbonates and siliciclastics), we opted for a two-
step approach starting with *K* = 3, which allows us to better account
for transitional or mixed facies. This intermediate step improves the
robustness of the facies separation. Initially, we cluster the data with
*K* = 3, identifying two well-defined facies and a third, mixed cluster.
A second clustering step is then applied to this mixed cluster with
*K* = 2, allowing us to assign each subgroup to one of the initial fa-
cies. This approach enhances the discrimination of complex facies.
The results are shown in Figs 16 and 17 where we observe a net
separation between the facies. For instance, the Gault formation,
<figure><img src="image_15.png" /><figcaption>**Figure 14.** Apparent chargeability decay curves for various quadrupoles ABMN associated with the different formations shown in Fig. 2 (field data). We note, as expected, that the chargeability of the shale is close to $M = R = 100$ mV V⁻¹ (i.e. $R = 0.10$, see Fig. 9) while the chargeability of the carbonates is close to $M = R = 10$ mV V⁻¹ ($R = 0.01$, see Fig. 9) implying the strong role of surface conductivity in controlling the rock conductivity in both types of formations in agreement with what is shown in Fig. 6.</figcaption></figure>

which is a sandstone, is well-recovered while sandwiched between two carbonate formations, namely the Urgonian and the Senonian formations (see Fig. 2). Finally, we apply the petrophysical transforms developed in Section 2 (see Fig. 13) to obtain the tomograms of the water content and CEC (see Fig. 18) using the two following petrophysical transforms (see Piolat et al. 2025)

$$ \theta = \left[ \frac{1}{\sigma_w} \left( \sigma_{\infty} - \frac{M_n}{R} \right) \right]^{1/m}, \qquad (8) $$

$$ \text{CEC} = \frac{a M_n}{\theta^{m-1} \rho_g \lambda}. \qquad (9) $$

We then perform a cross-plot between the water content values and the CEC values to compare the field data to the laboratory data and we can see in Fig. 18 that we have very good relationships between the tomograms and the laboratory measurements.

The last step is to obtain the permeability distribution from the CEC and water content. For the carbonates, we use the relationship between the permeability $k$ (in m²) and the formation factor $F$ (dimensionless) as determined in Panwar et al. (2021, their fig. 12),

$$ \log k = c - dm \log \theta, \qquad (10) $$

with $c = -9.7 \pm 0.4$ and $d = -2.5 \pm 0.2$. The value $m = 2.1$ yields $\log k = -9.7 + 5.3 \log \theta$. For siliciclastic materials, we determined the permeability $k$ (in m²) using the following relationship (Soueid

Ahmed et al. 2020b)

$$ k \approx \frac{k_0 \theta^6}{(\rho_g \text{CEC})^2}, \qquad (11) $$

with $k_0 = 10^{4.30}$ in SI units (C² m⁻⁴), $\theta$ is unitless, and the CEC is here expressed in C kg⁻¹ (note that 1 cmol/kg = 1 meq/100 g = 963.20 C kg⁻¹ in SI units) and $\rho_g$ denotes the grain density (in kg m⁻³). The choice of using two distinct equations for the permeability prediction is motivated by the fact that both models were derived from large experimental data sets representative of specific lithologies (siliciclastic and carbonate rocks). Eq. (10) was calibrated using carbonate samples by Panwar et al. (2021), while eq. (9) was developed based on measurements from clay-rich sandstones (Sen et al. 1990). Applying each model within its domain of validity ensures that the estimated permeability values are as geologically consistent as possible. With these two relationships, the permeability tomogram is shown in Fig. 19.

The derived tomograms of water content, CEC, and permeability must be interpreted with caution for several reasons. First, are derived from inverted conductivity and normalized chargeability tomograms, which are regularized using smoothness constraints. Second, the petrophysical transforms used to derive water content, CEC, and permeability introduce additional sources of uncertainty.
<figure><img src="image_16.png" /><figcaption>**Figure 15.** Geophysical survey. (a) Self-potential profile. (b) Electrical conductivity tomogram. (c) Normalized chargeability tomogram obtained from the chargeability tomogram and the conductivity by performing a multiplication cell-to-cell of the two quantities. The tomograms show the finite element mesh used for both the forward and inverse modelling.</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>**Figure 16.** Cross-plots between the normalized chargeability and the electrical conductivity from the fielm survey and comparison with the value of the dimensionless parameter R. (a) Cross-plot without any correction for the normalized chargeability. (b) Cross-plot using the amplification coefficient for the normalized chargeability. In this figure, we also show the clustering approach applied on the electrical conductivity and normalized chargeability inverted data. The goal is to separate the carbonate facies from the siliciclastic facies using the clustering approach.</figcaption></figure>

We followed the uncertainty propagation methodology presented by Moser et al. (2025), treating separately the siliclastic and carbonate cases. For the water content, we differentiate the previous eq. (8) with respect to $\sigma_w$, R and m. For the CEC, we differentiate eq. (9) with respect to a, $\theta$, m, $\rho_g$ and $\lambda$. Finally, for the permeability, we differentiate with respect to m, $\theta$, c and d for the carbonate case and $k_0$, $\theta$, CEC and $\rho_g$ for the siliciclastic case. For each of the three parameter (q, CEC, k), the Relative Standard Deviation (RSD) is

computed as,

$$RSD_{\theta,CEC,k}(\text{parameter}) = \frac{\partial(\theta, \text{CEC}, k)}{\partial(\text{parameter})} \cdot \frac{\text{std}(\text{parameter})}{\theta, \text{CEC}, k}, \quad (12)$$

where std(.) stands for the standard deviation for a given parameter. The standard deviations used are summarized in Table 4, and the results are presented in Table 5. The analysis confirms that water content is particularly sensitive to the uncertainty in pore
<figure><img src="image_18.png" /><figcaption>**Figure 17.** Tomogram of the two electrofacies determined from the clustering approach. We choose only two clusters to apply the clustering approach in order to differentiate the carbonates from the siliciclastic formations (sandstones, shales and other clay-rich formations).</figcaption></figure>

water conductivity $\sigma_w$, with a RSD of approximately 22 per cent in the siliciclastic case, consistent with the findings of Moser *et al.* (2025). Additionally, the use of a newly introduced scaling parameter *a* ($M_n$ scaling factor), which corrects for the discrepancy between time-domain and frequency-domain induced polarization measurements, introduces a non-negligible uncertainty in CEC estimates (RSD $\approx$ 20 per cent). The assumed standard deviation of this parameter ($\pm$2) remains high and would benefit from further calibration through systematic time-domain and frequency-domain comparison of the normalized chargeabilities.

Permeability exhibits the highest overall uncertainty, primarily due to its strong dependence on the uncertainty of water content in the siliciclastic case, and on the loosely constrained empirical coefficients *c* and *d* for the carbonate case. However, the advantage of the carbonate model lies in its reduced sensitivity to $\theta$. Relative uncertainties for water content, CEC, and permeability are about 1.3 times higher in carbonates than in siliciclastic facies. This difference can be attributed to the lower values of $M_n$ and $\sigma$.

Geophysical imaging reveals two key hydraulic barriers (Figs 19 and 20). The first hydraulic barrier, formed by the Nummulitic limestone, overlain by reworked landslide materials, is characterized by water-saturated soils and hygrophilous vegetation, confirming its role as a barrier. The second hydraulic barriers, composed of the purer Urgonian limestone, acts as a structural barrier, forming a ridge that blocks water and landslide movement, directing water and sediment flow through the Manauds canyon. Upstream, an impermeable formation of Bartonian–Stampian blue clays, also acts as a barrier but is absent downstream due to its heterogeneity (Fig. 20). Indeed some of the syncline formation are heterogeneous and imply asymmetries of electrical properties. These three formations, despite distinct electrical properties, serve as critical hydraulic

barriers within the syncline, as demonstrated by the petrophysical modelling presented in this study.

## 4 GROUND WATER FLOW MODELLING

In this discussion, we come back to the role of hydraulic barriers in the development of some shallow landslides. The existence of permeability barriers (seals) impeding the flow of water downstream below an area susceptible of a gravitational instability may play a strong role in the occurrence of landslides. Indeed, the increase of the water content (hence the weight of the sediments) and the pore pressure are two ingredients that can trigger shallow landslides in response to extreme rainfalls that are more and more associated with climate change. If geophysics can play a role in evaluating the permeability structure and flow field in the subsurface (see recently Revil *et al.* 2024a), then it will play an increasing role in the coming decades in monitoring areas prone to landslides and may guide the strategic implementation of targeted drainage systems.

A 2-D Darcy flow model, based on the finite element method, is built in COMSOL Multiphysics® to estimate the flow paths along the geophysical profile. We are especially interested in the area prone to the upflow of groundwater since such upflow can lead to the observed gravitational instabilities. This numerical simulation uses the permeability and water content distributions (assuming saturation) resulting from the combined resistivity and induced polarization data as described above. Fig. 21(a) shows the boundary conditions and the finite element mesh. A no-flow condition is applied at the bottom side of the computational domain. Its two sides have fixed hydraulic heads as boundary conditions. The surface has an atmospheric boundary condition ($p = 0, p$ fluid pressure). The model domain was discretized using a mesh of 27 009 tetrahedral
<figure><img src="image_19.png" /><figcaption>**Figure 18.** Tomograms of the water content and CEC for the entire survey. (a) Water content tomogram. (b) CEC tomogram. Note that the ranges of water content and CEC values are consistent with those reported in Table 1. Under the assumption of saturated conditions, the water content values can be interpreted as estimates of porosity. The area covered by the 1971–1972 landslides is shown in Fig. 2.</figcaption></figure>

Fig. 21(c) presents the flow paths (materialized by arrows) and the (colour-coded) Darcy velocity magnitudes on a logarithmic scale. We compute the self-potential profile at the ground surface from the results of this groundwater flow model. To do this, we assume that the self-potential signals result from the groundwater flow and an electrokinetic coupling effect associated with the drag of the electrical diffuse layer coating the surface of the grains (Ishido & Mizutani 1981). We have therefore assumed the absence of ore/redox component in the self-potential data. A comparison with the self-potential measurements is shown in Fig. 21(c). There is a fair agreement between the two indicating that the ground water flow model is probably a good prior model. The area is marked by a groundwater upflow in the region just above the West side of the syncline, in the area marked by wet soils and associated vegetation cover. It is likely that this upflow may have played a key role in the occurrence of landslides in this area. The current drainage of

the surface water (limiting the infiltration in the upper part of the syncline) may help in reducing the conditions favourable to landslides. The groundwater upflow is driven by the gravitational force associated with the hydraulic head gradient and is guided by the permeability distribution inside the syncline.

Finally, we invert the self-potential data using the strategy developed recently in Jardani *et al.* (2007, 2008) and especially in Revil *et al.* (2024a). It is summarized in Appendix B. The idea is to reduce the difference (using the L2 norm) between the computed self-potential data and the measured data by finding a suitable distribution of the Darcy velocity. We use the previous hydrogeological model as a prior model for the source current density and we invert the self-potential data using this prior source current density model and the resistivity distribution determined from the electrical resistivity tomography. The final result is shown in Fig. 22. We observe a strong upflow of the ground water in the area just above the lower
<figure><img src="image_20.png" /><figcaption>**Figure 19.** Permeability tomogram. This tomograms displays two areas of low permeability corresponding to the shales at the upfront of the landslide and the Urgonian formation at the bottom of the landslide area. This later is key to understand the built-up of the pore pressure and water content through the entire syncline during strong rain events. The area covered by the 1971–1972 landslides is shown in Fig. 2.</figcaption></figure>

<table><caption>**Table 4.** Electrical properties and physical parameters of the clean (clay-free) carbonates (mostly composed of calcite or aragonite) versus the properties of clay-rich materials.</caption><thead><tr><th rowspan="2">Property</th><th colspan="2">Siliciclastic case</th><th colspan="2">Carbonate case</th></tr><tr><th>Value</th><th>STD</th><th>Value</th><th>STD</th></tr></thead><tbody><tr><td>ρ<sub>g</sub> (kg m<sup>-3</sup>)</td><td>2700</td><td>100</td><td>2800 (1)</td><td>100</td></tr><tr><td>R (–)</td><td>0.10</td><td>0.01</td><td>0.010</td><td>0.001</td></tr><tr><td>B (m<sup>2</sup>s<sup>-1</sup>V<sup>-1</sup>)</td><td>3.1 × 10<sup>-9</sup></td><td>0.3 × 10<sup>-9</sup></td><td>1.0 × 10<sup>-8</sup></td><td>0.2 × 10<sup>-8</sup></td></tr><tr><td>λ (m<sup>2</sup>s<sup>-1</sup>V<sup>-1</sup>)</td><td>3.0 × 10<sup>-10</sup></td><td>0.7 × 10<sup>-10</sup></td><td>2.0 × 10<sup>-10</sup></td><td>0.5 × 10<sup>-10</sup></td></tr><tr><td>m (–)</td><td>2.1</td><td>0.2</td><td>2.1</td><td>0.2</td></tr><tr><td>σ<sub>ω</sub> (S m<sup>-1</sup>)</td><td>0.055</td><td>0.025</td><td>0.055</td><td>0.025</td></tr><tr><td>k<sub>0</sub> (–)</td><td>10<sup>4.3</sup></td><td>10<sup>4</sup></td><td>10<sup>4.3</sup></td><td>10<sup>4</sup></td></tr><tr><td>a (–)</td><td>10</td><td>2</td><td>10</td><td>2</td></tr><tr><td>c (–)</td><td>–</td><td>–</td><td>-9.7</td><td>0.4</td></tr><tr><td>d (–)</td><td>–</td><td>–</td><td>-2.5</td><td>0.2</td></tr></tbody></table>

<table><caption>**Table 5.** RSD (in per cent) estimated for each parameter involved in the calculation of water content θ, CEC, and permeability k, based on analytical error propagation using partial derivatives. For the siliciclastic case, representative values of the normalized chargeability and electrical conductivity were taken as M<sub>n</sub> = 1 × 10<sup>-4</sup> S m<sup>-1</sup> and σ = 3 × 10<sup>-2</sup> S m<sup>-1</sup> while for carbonates, we used M<sub>n</sub> = 3 × 10<sup>-6</sup> S m<sup>-1</sup> and σ = 1 × 10<sup>-3</sup> S m<sup>-1</sup>.</caption><thead><tr><th rowspan="2">Property</th><th colspan="2">Siliciclastic case</th><th colspan="2">Carbonate case</th></tr><tr><th>RSD θ (per cent)</th><th>RSD CEC(per cent)</th><th>RSD k (per cent)</th><th>RSD θ (per cent)</th><th>RSD CEC (per cent)</th><th>RSD k (per cent)</th></tr></thead><tbody><tr><td>σ<sub>w</sub></td><td>21.7</td><td>–</td><td>–</td><td>21.7</td><td>–</td><td>–</td></tr><tr><td>R</td><td>0.3</td><td>–</td><td>–</td><td>0.3</td><td>–</td><td>–</td></tr><tr><td>m</td><td>3.7</td><td>7.8</td><td>–</td><td>19.1</td><td>40.2</td><td>–</td></tr><tr><td>θ</td><td>–</td><td>23.8</td><td>129.9</td><td>–</td><td>23.8</td><td>60.8</td></tr><tr><td>ρ<sub>g</sub></td><td>–</td><td>3.7</td><td>7.41</td><td>–</td><td>3.7</td><td>–</td></tr><tr><td>λ</td><td>–</td><td>23.3</td><td>–</td><td>–</td><td>23.3</td><td>–</td></tr><tr><td>a</td><td>–</td><td>20.0</td><td>–</td><td>–</td><td>20.0</td><td>–</td></tr><tr><td>CEC</td><td>–</td><td>–</td><td>47.6</td><td>–</td><td>–</td><td>–</td></tr><tr><td>k<sub>0</sub></td><td>–</td><td>–</td><td>51.0</td><td>–</td><td>–</td><td>–</td></tr><tr><td>c</td><td>–</td><td>–</td><td>–</td><td>–</td><td>–</td><td>59.8</td></tr><tr><td>d</td><td>–</td><td>–</td><td>–</td><td>–</td><td>–</td><td>52.2</td></tr></tbody></table>
<figure><img src="image_21.png" /><figcaption>**Figure 20.** Hydrogeological representation. (a) Schematic cross-section of the numerical terrain model around the Nant des Granges landslide. (b) Schematic view of the effect of a permeability barrier on the water content. The terrain becomes oversaturated and loses cohesion, thereby favouring the occurrence of landslides. This effect is partially mitigated by the realization of a drainage network collecting the surface waters.</figcaption></figure>

part of the syncline in a consistent way with the presence of wet soils in this area. Such upflow of water may have a strong role in the occurrence of muddy landslides but this will need to be demonstrated using a coupled hydromechanical model, which is beyond the tasks of the current paper.

## 5 CONCLUSIONS

We showcase in this paper how the induced polarization technique can be used to image the architecture of a shallow landslide in its geological environment and the potential existence of hydraulic barriers that may play a role in their occurrence. We performed a 2.2 km induced polarization profile investigating the formation down to a depth of 220 m below the ground surface. In parallel, a petrophysical study was undertaken to study the connection between the electrical conductivity and normalized chargeability and hydraulic properties. The resulting petrophysical transforms are used to image the water content, the CEC, and the permeability of the formations forming a vast syncline in which the unstable gravitational area is nested. Since the electrical properties of limestones and carbonates are different from the properties of silici-clastic sediments (blue clay,

flysch, and shale), a clustering technique is used to separate the different facies in order to apply distinct petrophysical relationships. The final result demonstrates the existence of a vertical flow barrier downstream the landslide area associated with the Urgonian formation, which exhibits very low permeability and porosity. These results confirm those of Revil *et al.* (2020) in underlying the role of vertical permeability barriers associated with shallow landslides. Finally, we combine the permeability profile, the resistivity and self-potential data to invert the Darcy velocity distribution. The resulting fluid flow distribution shows a very strong and focused upflow of the ground water in an area characterized by wet soils and prone to landslides. In the context of an increasing frequency of extreme rainfall events, these results highlight the importance of geophysical methods for characterizing subsurface flow patterns and identifying hydraulically active zones that may play a critical role in the triggering or reactivation of slope instabilities. Such insights may support local authorities in designing risk mitigation strategies for vulnerable slopes. A complementary study is presented in the companion paper for a very different clayey formation, namely the Triève formation located in Isère (France).
<figure><img src="image_22.png" /><figcaption>**Figure 21.** Hydrogeological model (forward modelling). (a) Finite element mesh with the boundary conditions. We use the porosity (estimated as the water content at saturation) and permeability determined from the geophysical data. (b) Darcy velocity **u** (in m s⁻¹) distribution showing the upflow of water in the area associated with a wet soil and associated vegetation. (c) Comparison between the self-potential model resulting from the hydrogeological model (plain line) and the self-potential measurements (black dots).</figcaption></figure>
<figure><img src="image_23.png" /><figcaption>**Figure 22.** Inversion of the self-potential data and resulting groundwater flow problem. (a) Comparison between the self-potential data and the self-potential profile resulting from the self-potential inversion in terms of Darcy velocity distribution. (b) Distribution of the Darcy velocity **u** (in m s⁻¹) resulting from the inversion of the self-potential data accounting for the hydrogeological model as starting model and the electrical resistivity distribution.</figcaption></figure>
DATA AVAILABILITY

The data used in this manuscript are available upon request to the
corresponding author.

ACKNOWLEDGMENTS

We thank the group GINGER for its support. The PhD grant of Clément Casotti is supported by a CIFRE grant. AR thanks the CNRS for its support over the past years. The equipment used in this project was obtained thanks to the funding of the Auvergne-Rhône-Alpes region and FEDER through the IRICE project with the help of IRISK. IRISK is thanked for its strong support and fruitful discussions regarding gravitational instabilities over the years and especially Margot Bernard and François Nicot for their strong encouragements over the years. We also thank the PALLAS project (Banque de Développement) to fund some of the methodology used in this work. We thank V. Costabloz (ONF), C. Begorre, M. Dellinger, S.E. Kottabi, A. Fichot, S. Qiang, J. Richard, W. Bouits, L. Fabre, F. Lemot, J. Agziou and P. Gorrias from EDYTEM for their help in the field. We thank Egon Zimmermann for the construction of the ZELSIP04-V02 impedance meter in Germany. We thank the Editor Tina Martin and the two anonymous Referees for the quality of their comments that have helped us to improve the quality of our manuscript.

REFERENCES

Ali, B., Nanda, M., Zainal, M., Yanis, M., Syukri Surbakti, M., Idris, N. & Ismail, N., 2024. Application of ERT, IP and VLF-EM methods to investigate landslide-prone structures at archaeological sites in Lamreh, Aceh Besar, Indonesia, *Trends in Sciences, **21**(3), 7221.

Aran, D., Maul, A. & Masfaraud, J., 2008. A spectrophotometric measure-
ment of soil cation exchange capacity based on cobalthexamine chloride
absorbance, *C. R. Geosci.*, **340**(12), 865–871.

Archie, G.E., 1942. The electrical resistivity log as an aid in determining some reservoir characteristics, *Trans. AIME*, **146**, 54–62.

Arosio, D., Ivanov, V.I., Loke, M.H., Papini, M., Tresoldi, G. & Lanzi, L., 2018. A laboratory experience to assess the 3-D effects on 2D ERT monitoring of river l evees, *24th European Meeting of Environmental and Engineering Geophysics*, 2018, 1–5.

Bernard, M.-L., Zamora, M., Géraud, Y. & Boudon, G., 2007. Transport properties of pyroclastic rocks from Montagne Pelée volcano (Martinique, Lesser Antilles), *J. geophys. Res.*, **112**(B5), doi: 10.1029/2006JB004385.

Bleil, D.F., 1953. Induced polarization: a method of geophysical prospecting, *Geophysics*, **18**, 636–661.

Bücker, M., Flores Orozco, A., Undorf, S. & Kemna, A., 2019. On the role of Stern-and diffuse- layer polarization mechanisms in porous media, *J Geophys. Res. Solid Earth*, **124**(6), 5656–5677.

Cassiani, G., Kemna, A., Villa, A. & Zimmermann, E., 2009. Spectral induced polarization for the characterization of free-phase hydrocarbon contamination of sediments with low clay content, Near Surf. Geophys., 7(5-6), 547–562.

Cerepi, A., 2004. Geological control of electrical behaviour and prediction key of transport properties in sedimentary porous systems, *Colloids and Surfaces A: Physicochem. Eng. Aspects*, **241**, 281–298.

Chambers, K., Kendall, J.M., Brandsberg-Dahl, S. & Rueda, J., 2010. Testing the ability of surface arrays to monitor microseismic activity, *Geophys. Prospect.*, **58**(5), 821–830.

Ciesielski, H., Sterckeman, T., Santerne, M. & Willery, J.P., 1997. A comparison between three methods for the determination of cation exchange capacity and exchangeable cations in soils, *Agronomie*, **17**, 9–16.

Colangelo, G., Lapenna, V., Perrone, A., Piscitelli, S. & Telesca, L., 2006. 2D self-potential tomographies for studying groundwater flows in the

Varco d'Izzo landslide (Basilicata, southern Italy), *Eng. Geol.*, **88**(3-4), 274-286.

Doudoux, B., Barfety, J.-C., Vivier, G., Carfantan, J.-C., Nicoud, G. & Tardy, M., 1999. *Notice Explicative De la Feuille Albertville à 1/50 000*, Éditions du BRGM, Service Géologique National.

Dukhin, S.S. & Shilov, V.N., 1974. *Dielectric Phenomena and the Double Layer in Disperse Systems and Polyelectrolytes*, Wiley, New York.

Dupire, P., 2016. Forêt domaniale du Nant des Granges, Report, Office National des Forêts, Service départemental RTM, Report, 95pp., https://www.onf.fr//++amgt++A016038V//++zfiles++49894d59.

El Alam, J., Revil, A. & Dick, P., 2024. Induced polarization of clay-rich materials. 5. Influence of hyperalkalinity in bentonite, *Geophysics*, **89**(6), E267–E279.

Fixman, M., 1980. Charged macromolecules in external fields. I. The sphere, *J. Chem. Phys.*, **72**, 5177–5186.

Flageollet, J.-C., Malet, J.P., Maquaire, O. & Schmutz, M., 2004. Integrated investigations on landslides: example of the Super-Sauze earthflow. Mar-gottini, C., *Natural Disasters and Sustainable Development*, Chap. 14, pp. 213–238, Springer-Verlag.

Flores Orozco, A., Gallistl, J., Steiner, M., Brandstätter, C. & Fellner, J., 2020. Mapping biogeochemically active zones in landfills with induced polarization imaging: the Heferlbach landfill, *Waste Manage.*, **107**, 121–132.

Flores Orozco, A., Steiner, M., Katona, T., Roser, N., Moser, C., Stumvoll, M.J. & Glade, T., 2022. Application of induced polarization imaging across different scales to understand surface and groundwater flow at the Hofermühlehle landslide, *Catena*, **219**, 106 612.

Florsch, N., Llubes, M. & Téreygeol, F., 2012. Induced polarization 3-D tomography of an archaeological direct reduction slag heap, Near Surf. Geophys., **10**(6), 567–574.

Florsch, N., Llubes, M., Téreygeol, F., Ghorbani, A. & Roblet, P., 2011. Quantification of slag heap volumes and masses through the use of induced polarization: application to the Castel-Minier site, *J. Archaeol. Sci.*, **38**(2), 438–451.

Gariano, S.L. & Guzzetti, F., 2016. Landslides in a changing climate, *Earth Sci. Rev.*, **162**, 227–252.

Gex, F., 1931. L'éboulement du Chatelard (Bauges, 12 mars 1931), *Revue de Géographie Alpine*, **19**(2), 499–521.

Günther, T., Rücker, C. & Spitzer, K., 2006. Three-dimensional modelling and inversion of dc resistivity data incorporating topography. II. Inversion, *Geophys. J. Int.*, **166**, 506–517.

Gurin, G., Titov, K. & Ilyin, Y., 2019. Induced polarization of rocks containing metallic particles: evidence of passivation effect, *Geophys. Res. Lett.*, **46**, 670–677.

Gurin, G., Titov, K., Ilyin, Y. & Tarasov, A., 2015. Induced polarization of disseminated electronically conductive minerals: a semi-empirical model, *Geophys. J. Int.*, **200**(3), 1555–1565.

Guzzetti, F., Carrara, A., Cardinali, M. & Reichenbach, P., 1999. Land-
slide hazard evaluation: a review of current techniques and their ap-
plication in a multi-scale study, central Italy, *Geomorphology*, **31**(1-4),
181–216.

Hack, R., 2000. Geophysics for slope stability, *Surv. Geophys.*, **21**(4), 423–448.

Halisch, M., Weller, A. & Kassab, M.A., 2014. Impedance spectroscopy on carbonates, *International Symposium of the Society of Core Analysts*, paper SCA2014-039.

Hoblea, F., Cadilhac, L., Nicoud, G., Dodelin, C. & Lasserre, D., 2008. Hydrogéologie karstique du massif des Bauges : état des connaissances et contributions de Michel Lepiller aux recherches fondamentales et appliquées, *Journée Technique Du Comité Français de L'Association Internationale Des Hydrogéologues*, Comité Français de L'Association Internationale Des Hydrogéologues, Orléans, France, pp. 71–81.

Hojat, A., Arosio, D., Longoni, L., Papini, M., Tresoldi, G. & Zanzi, L., 2019. Installation and validation of a customized resistivity system for permanent monitoring of a river embankment, *EAGE-GSM 2nd Asia Pacific Meeting on Near Surface Geoscience and Engineering, April 2019*, Vol. 2019, pp. 1–5.
Ishido, T. & Mizutani, H., 1981. Experimental and theoretical basis of electrokinetic phenomena in rock-water systems and its applications to geophysics, *J. geophys. Res.*, **86**(NB3), 1763–1775.

Jardani, A., Revil, A., Bolève, A. & Dupont, J.P., 2008. Three-dimensional inversion of self-potential data used to constrain the pattern of groundwater flow in geothermal fields, *J. geophys. Res.*, **113**, B09204.

Jardani, A., Revil, A., Bolève, A., Dupont, J.P., Barrash, W. & Malama, B., 2007. Tomography of the Darcy velocity from self-potential measurements, *Geophys. Res. Lett.*, **34**, L24403.

Leroy, P., Weigand, M., Mériguet, G., Zimmermann, E., Tournassat, C., Fagerlund, F., Kemna, A. & Huisman, J.A., 2017. Spectral induced polarization of Na-montmorillonite dispersions, *J. Colloid Interface Sci.*, **505**, 1093–1110.

Manrique, I.I., Hermans, T., Caterina, D., Jougnot, D., Mignon, B., Masse, A. & Nguyen, F., 2024. Integrated methodology to link geochemical and geophysical-lab data in a geophysical investigation of a slag heap for resource quantification, *J. Environ. Manage.*, **349**, 119 366.

Mao, D., Revil, A., Hort, R.D., Munakata-Marr, J., Atekwana, E.A. & Kulessa, B., 2015. Resistivity and self-potential tomography applied to groundwater remediation and contaminant plumes: sandbox and field experiments, *J. Hydrol.*, **530**, 1–14.

Marescot, L., Monnet, R. & Chapellier, D., 2008. Resistivity and induced polarization surveys for slope instability studies in the Swiss Alps, *Eng. Geol.*, **98**, 18–28.

Miller, D.J. & Sias, J., 1998. Deciphering large landslides: linking hydrological, groundwater and slope stability models through GIS, *Hydrol. Process.*, **12**, 923–941.

Moser, C., Morra di Cella, U., Hauck, C. & Flores Orozco, A., 2025. Spectral induced polarization survey for the estimation of hydrogeological parameters in an active rock glacier, *The Cryosphere*, **19**, 143–171

Olhoeft, G.R., 1981a. Electrical properties of granite with implications for the lower crust, *J. geophys. Res.*, **86**(B2), 931–936.

Olhoeft, G.R., 1981b. Electrical properties of rocks, in *Physical Properties of Rocks and Minerals*, pp. 257–297, eds, Touloukian, Y. S., Judd, W. R. & Roy, R. F., McGraw Hill.

ONF 2016, *Étude de bassin de risque—Forêt domaniale du Nant des Granges, Septembre 2016. Missions d'intérêt général relatives aux actions de RTM, confiées à l'ONF par le Ministère de l'Agriculture, de l'Agroalimentaire et de la Forêt*, 36pp.

Panwar, N. et al. 2021. Induced polarization of carbonates, *J. Geophys. Res.-Solid Earth*, **126**, e2021JB022029.

Pedregosa, F. et al. 2011. Scikit-learn: machine Learning in Python, *J. Mach. Learn. Res.*, **12**, 2825–2830.

Perrone, A., Lapenna, V. & Piscitelli, S., 2014. Electrical resistivity tomography technique for landslide investigation: a review, *Earth Sci. Rev.*, **135**, 65–82.

Piolat, L. et al. 2025, Induced polarization of volcanic rocks. 8. The case of intrusive igneous rocks, *Geophys. J. Int.*, **241**, 1348–1372.

Revil, A., 2012. Spectral induced polarization of shaly sands: influence of the electrical double layer, *Water Resour. Res.*, **48**, W02517.

Revil, A., 2013a. Effective conductivity and permittivity of unsaturated porous materials in the frequency range 1 mHz–1 GHz, *Water Resour. Res.*, **49**, 306–327.

Revil, A., 2013b. On charge accumulations in heterogeneous porous materials under the influence of an electrical field, *Geophysics*, **78**(4), D271–D291.

Revil, A. et al. 2017. Complex conductivity of soils, *Water Resour. Res.*, **53**(8), 7121–7147.

Revil, A. et al. 2024b. Field investigation of serpentinite with induced polarization and the K-means clustering technique, *Geophys. Res. Lett.*, **51**(18), e2024GL08920.

Revil, A., Ehouarne, L. & Thyreault, E., 2001. Tomography of self-potential anomalies of electrochemical nature, *Geophys. Res. Lett.*, **28**(23), 4363–4366.

Revil, A., Ghorbani, A., Zhao, X., Mouyeaux, A., Barrère, L., Richard, J., Peyras, L. & Vaudelet, P., 2024a. Ground water flow paths using

combined self-potential, electrical resistivity, and induced polarization signals, *Geophys. J. Int.*, **239**, 798–820.

Revil, A. & Pezard, P.A., 1998. Streaming electrical potential anomaly along faults in geothermal areas, *Geophys. Res. Lett.*, **25**(16), 3197–3200.

Revil, A., Qi, Y., Panwar M. Gresse, N., Grandis, H., Sharma, R., Géraud, Y., Chibati, N. & Ghorbani, A., 2022, Induced polarization images alteration in stratovolcanoes, *J. Volcanol. Geotherm. Res.*, **429**, 107598.

Revil, A., Soueid Ahmed, A., Coperey, A., Ravanel, L., Sharma, R. & Panwar, N., 2020. Induced polarization as a tool to characterize shallow landslides, *J. Hydrol.*, **589**, 125 369.

Schlumberger, C., 1920. *Etude sur la Prospection Électrique Du Sous-sol, Gouthier-Villars, Paris.*

Schmutz, M., Guérin, R., Andrieux, P. & Maquaire, O., 2009. Determination of the 3D structure of an earthflow by geophysical methods: the case of Super Sauze, in the French southern Alps, *J. Appl. Geophys.*, **68**(4), 60–67.

Schön, J.H., 2011, *Physical Properties of Rocks: a Workbook*, Elsevier.

Schurr, J.M., 1964. On the theory of the dielectric dispersion of spherical colloidal particles in electrolyte solution, *J. Phys. Chem.*, **68**, 2407–2413.

Seigel, H., Nabighian, M., Parasnis, D.S. & Vozoff, K., 2007. The early history of the induced polarization method, *Leading Edge*, **26**, 312–321.

Sen, P.N., Straley, C., Kenyon, W.E. & Whittingham, M.S., 1990. Surface-to-volume ratio, charge density, nuclear magnetic relaxation, and permeability in clay-bearing sandstones, *Geophysics*, **55**, 61–69.

Slater, L., 2007. Near surface electrical characterization of hydraulic conductivity: from petrophysical properties to aquifer geometries—A review, *Surv. Geophys.*, **28**, 169–197.

Soueid Ahmed, A., Revil, A., Abdulsamad, F., Steck, B., Vergniault, C. & Guihard, V., 2020b. Induced polarization as a tool to non-intrusively characterize embankment hydraulic properties, *Eng. Geol.*, **271**, 105 604.

Titov, K., Abramov, V., Emelianov, V. & Revil, A., 2024. Induced polarization of volcanic rocks. Part 7. Kimberlites, *Geophys. J. Int.*, **236**, 233–248.

Titov, K., Kemna, A., Tarasov, A. & Vereecken, H., 2004. Induced polarization of unsaturated sands determined through time-domain measurements, *Vadose Zone J.*, **3**, 1160–1168.

Titov, K., Komarov, V., Tarasov, V. & Levitski, A., 2002. Theoretical and experimental study of time domain-induced polarization in water-saturated sands, *J. App. Geophys.*, **50**, 417–433.

Van Voorhis, G.D., Nelson, P.H. & Drake, T.L., 1973. Complex resistivity spectra of porphyry copper mineralization, *Geophysics*, **38**(1), 49–60.

Wahida, W., Lepong, P., Alamsyah, A., Djayus, D., Supriyanto, S., Hermawan, Q.F. & Amir, A., 2024. Analysis and evaluation of stability for the reactivated road landslide using electrical resistivity and induced polarization in Muara Badak district, East Kalimantan, Indonesia, *The 4th International Conference on Mathematics and Sciences (The 4th ICMSc), AIP Conf. Proc.*, Vol. **3095**, pp. 040002-1-040002-9.

Walter, M. & Joswig, M., 2008. Seismic monitoring of fracture processes generated by a creeping landslide in the Vorarlberg Alps, *First Break*, **26**, 131–135.

Waxman, M.H. & Smits, L., 1968. Electrical conductivities in oil-bearing shaly sands, *Soc. Pet. Eng. J.*, **8**(2), 107–122.

Weller, A., Seichter, M. & Kampke, A., 1996. Induced-polarization modelling using complex electrical conductivities, *Geophys. J. Int.*, **127**, 387–398.

Whiteley, J.S., Chambers, J.E., Uhlemann, S., Wilkinson, P.B. & Kendall, J.M., 2019. Geophysical monitoring of moisture-induced landslides, A review, *Rev. Geophys.*, **57**, 106–145.

Zhang, K., Chibati, N., Revil, A., Richard, J., Gresse, M., Xue, Y. & Géraud, Y., 2023, Induced polarization of volcanic rocks. 6. Relationships with other petrophysical properties, *Geophys. J. Int.*, **234**, 2376–2394.

Zimmermann, E., Huisman, J.A., Mester, A. & van Waasen, S., 2019. Correction of phase errors due to leakage currents in wideband EIT field measurements on soil and sediments, *Meas. Sci. Technol.*, **30**(8), 084 002.

Zimmermann, E., Kemna, A., Berwix, J., Glaas, W., Münch, H.M. & Huisman, J.A., 2008. A high-accuracy impedance spectrometer for measuring sediments with low polarizability, *Meas. Sc. Tech.*, **19**(10), 105 603.
## APPENDIX A. FREQUENCY- AND TIME-DOMAIN NORMALIZED CHARGEABILITIES

As explained in the main text, the normalized chargeability determined form the time-domain measurements is different from the normalized chargeability determined using the complex conductivity spectra. In this appendix, we further explain this difference using a complex conductivity Cole Cole model written as,

$$ \sigma^* = \sigma_{\infty} - \frac{M_n(\infty, 0)}{(1 + i\omega\tau)^c}, \qquad (A1) $$

$$ M_n(FD) \equiv M_n(\infty, 0) = \sigma_{\infty} - \sigma_0. \qquad (A2) $$

The time-domain response for an infinite charging time (current injected in the time window [-∞, 0] is obtained using the Mittag-Leffler function,

$$ M(t) = \frac{M_n}{\sigma_{\infty}} \sum_{k=0}^{\infty} \frac{(-1)^k \left( \frac{t}{(1-m)^{1/c}} \right)^{kc}}{\Gamma(1 + kc)}. \qquad (A3) $$

However in our laboratory time-domain experiments and field survey, the current is injected over a period T (i.e. in the time interval [-T, 0]). Since the system is linear and causal, we can use the superposition principle and the time-domain response is given by,

$$ M_{TD}(t, T) = M(t) - M(t - T). \qquad (A4) $$

Furthermore, the normalized chargeability is obtained by integrating the decay (normalized) voltage over a time windows following the dead time $t_1$, i.e.

$$ M_n(TD) = \sigma_{\infty} \int_{t_1}^{t_2} M_{TD}(t, T)dt, \qquad (A5) $$

with $(t_1, t_2) \ll \tau$. We use $t_2 - t_1 = 0.1s$. The amplification factor $a$ is defined as,

$$ a \equiv \frac{M_n(FD)}{M_n(TD)} \geq 1. \qquad (A6) $$

## APPENDIX B. GROUND WATER FLOW FROM SELF-POTENTIAL DATA

The self-potential generated by groundwater flow at the ground surface is calculated using the following set of equations:

$$ \nabla \cdot \mathbf{j} = 0, \qquad (B1) $$

$$ \mathbf{j} = \sigma_0 \mathbf{E} + \mathbf{j}_S, \qquad (B2) $$

$$ \mathbf{j}_S = \hat{Q}_v \mathbf{u}, \qquad (B3) $$

$$ \mathbf{E} = -\nabla \varphi, \qquad (B4) $$

$$ \log_{10} \hat{Q}_v = -9.2 - 0.82 \log_{10} k, \qquad (B5) $$

where eq. (B1) is the conservation of charge in the quasi-static limit of the Maxwell equations (j denotes the total current density in A m⁻²), eq. (B2) represents the expression of the total current density written as the sum of Ohm's law (E is the electrical field, in V m⁻¹) and the streaming current density associated with the drag of the charge density of the diffuse layer by the flow of the pore water, eq. (B3) represents the expression of the streaming current density which is the product of the effective charge density of the diffuse layer times the Darcy velocity u (in m s⁻¹), eq. (B4) provides the expression of the electrical field in terms of electrical (self-) potential φ in the quasi-static limit of the Maxwell equations, and finally eq. (B5) denotes the relationship between the effective charge density and the permeability k (in m²). Solving numerical the elliptic equation resulting from eqs (B1) and (B2), requires boundary conditions (i) we consider an insulating boundary condition at the ground surface and we pad the domain of interest with a 1 km thick layer on the sides and bottom to have the potential vanishing to zero far from the area of groundwater flow where electrokinetic coupling occurs. To satisfy the zero electrical potential boundary condition at infinity, a 1000-m-thick layer (with a conductivity of to 0.01 S m⁻¹) is used to pad the domain of interest. We used the conductivity obtained from the electrical resistivity tomography. Using this approach, we are able to compute the self-potential distribution resulting from a groundwater flow model as shown in Fig. 21.

In the next step, the electrical model described above is used for the inversion of self-potential data in order to refine the subsurface distribution of the Darcy velocity that would agree with the measured self-potential distribution. In order to find the source current density $j_s$ that fits the self-potential data (knowing the electrical conductivity), we minimize the following cost function $C_λ$ defined as (Jardani et al. 2008; Mao et al. 2015):

$$ C_{\lambda} = \|\mathbf{W}_{d}(\mathbf{K}\mathbf{m} - \mathbf{d})\|^2 + \lambda \|\mathbf{W}_{m}(\mathbf{m} - \mathbf{m}_{0})\|^2, \qquad (B6) $$

where d is vector of N elements corresponding to the self-potential data measured along the profile, λ denotes the regularization parameter determined using L-curve criterion, W_d is a square diagonal weighting N × N-matrix, m is the vector of 2M-model parameters, m_0 is the reference model obtained at the previous step (hydrogeological-consistent current density model), W_m is first order differential Laplacian operator (2M-1 × 2 M)-weighting matrix (penalizing therefore the roughness of the inverse problem), and K = (K_{ij}^x, K_{ij}^z) denotes the N × 2 M kernel matrix (for horizontal and vertical components x and z) and corresponding to the Green functions of the problem. The solution of this linear problem is given by the minimum of the objective function (∂C_λ/∂m = 0) is given by:

$$ \mathbf{m}^* = [\mathbf{K}^T (\mathbf{W}_d^T \mathbf{W}_d) \mathbf{K} + \lambda (\mathbf{W}_m^T \mathbf{W}_m)]^{-1} \cdot (\mathbf{K}^T (\mathbf{W}_d^T \mathbf{W}_d) \mathbf{d} + \lambda (\mathbf{W}_m^T \mathbf{W}_m) \mathbf{m}_0). \qquad (B7) $$

In the final step, the Darcy velocity u is determined using m* and eqs (B3) and (B5) using therefore the relationship between the excess charge density and the permeability.