# Marine karst environment characterization using joint geophysical and geotechnical data

Judith Dusart, Pascal Tarits, Sara Bazin, Rocio Isorna, Jean-françois d'Eu

► To cite this version:

Judith Dusart, Pascal Tarits, Sara Bazin, Rocio Isorna, Jean-françois d'Eu. Marine karst environment characterization using joint geophysical and geotechnical data. Near Surface Geophysics, 2022, 20 (4), pp.349-364. 10.1002/nsg.12217. hal-04984096

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# Marine karst environment characterization using joint geophysical and geotechnical data

Judith Dusart¹,²*, Pascal Tarits¹,², Sara Bazin¹, Rocio Isorna³ and Jean-François d'Eu²

¹European Institute for Marine Studies (IUEM), Plouzané, France, ²Mappem Geophysics SAS, Saint-Renan, France, and ³France Energies Marines SAS, Plouzané, France

Received April 2021, revision accepted May 2022

## ABSTRACT

Submarine karstic environments are complex and challenging to study. Seismic investigations usually have difficulty getting geological information because of a lack of penetration due to the high reflectivity of the calcareous substratum. To circumvent this problem, we studied how to combine marine electrical resistivity tomography (MERT) with geotechnical data to investigate the porosity structure from the geotechnical to the geophysical scale. We applied the technique to the submarine karstic plateau of Banc de Guérande (Saint-Nazaire, France), which is mainly composed of hard calcarenite and sandy pockets. We obtained sections of two-dimensional resistivity models from the MERT data inversion. We used existing geotechnical data on extracted cores at several boreholes close to the MERT profiles using a multi-sensor core logging (MSCL) bench. We used porosity proxies derived from Archie's law and porosity data from the MSCL inferred from gamma density measurements on the core to combine the data of very different scales (metre for MERT and centimetre for MSCL). The comparison between measurements showed a good similarity between *in situ* MERT and borehole MSCL data at depths greater than ~10 m below the seafloor. A larger difference was observed close to the seabed, where the MERT porosity was higher than the MSCL porosity. The extraction of water-saturated cores and the numerous core fractures could explain this difference near the surface. The results were analysed with respect to the scale difference between geophysical and geotechnical data. The conclusions suggested that the difference between MERT and MSCL porosities could be testified from the local heterogeneity of the soil and indicated whether the surrounding substratum was more porous (and thus fractured or dissolved) than the core or vice versa. The study highlighted the necessity of an excellent collocation of the data to retrieve reliable information from the comparison between geophysical and geotechnical data.

**Key words:** Electrical resistivity tomography, Geotechnical, Porosity, Shallow marine, Site characterization.

## INTRODUCTION

Near-surface geophysical methods can provide useful subsurface information in karst regions to determine the limits and extent of the karst system, the structural discontinuities

<footnote>*E-mail: judith.dusart@mappem-geophysics.com</footnote>
(fractures, epikarsts), preferential pathways and/or concentrated infiltration and cavities (empty and filled ones). Chalikakis *et al.* (2011) reviewed the main techniques tested on terrestrial karst systems and evaluated their ability to assess each of these characteristics. However, a karst area remains a difficult environment for any geophysical exploration. In fact, selecting the best-suited geophysical method is not always straightforward due to the highly variable and unpredictable target characteristics (Chalikakis *et al.*, 2011).

In marine environments, evidence suggests that coastal regions shallower than ~130 m have been subjected to repeated alternations between subaerial and marine conditions during the frequent glacio-eustatic sea-level changes that occurred throughout the Quaternary, with extensive environmental changes occurring between glacial and interglacial periods (Yokoyama *et al.*, 2000; Camoin *et al.*, 2004; Fujita *et al.*, 2010). Consequently, repeated subaerial and submarine processes have modulated the geomorphology of shallow coastal regions (Kan *et al.*, 2015).

This phenomenon can create submarine karsts resulting from rock dissolution (carbonate substratum) caused by water circulation during subaerial exposure prior to submergence (Bonem, 1988; Courrèges, 1997). When the sea level rises, faults, dolines, sinkholes and caves are filled with saturated sediments brought by the sea currents. Karstification is stopped when the salinity is high (rock submerged by sea-level rise), except in coastal areas where saltwater and freshwater meet ('mixing corrosion'; Courrèges, 1997). The karst substratum is highly heterogeneous, showing numerous fractures and variable densities. As such, this type of marine environment is a geological challenge in regard to soil imaging and building offshore infrastructures.

Marine karsts were identified and studied around the world: along the eastern Adriatic coast of Croatia (Surić, 2002; Surić, 2005); Nagura Bay on Ishigaki Island (southwestern Japan) using multi-beam bathymetric surveys (Kan *et al.*, 2015); the Tremiti Islands Archipelago (Northern Puglia) using bathymetric and side scan surveys (Miccadei *et al.*, 2011); offshore the Apulian Margin (southern Adriatic Sea, Italy) using multibeam bathymetry, chirp sub-bottom profiler, side-scan sonar surveys (Taviani *et al.*, 2012); the Lošinj Channel in the north-eastern Adriatic Sea using seismic surveys and core data (Brunović *et al.*, 2020); off Marseille (France) using dredging, core extraction and seismic surveys (Blanc, 2010); and the Medoc peninsula (France) using geological observations and diving (Courrèges, 1997). Globally, the French Bay of Biscay is calcareous (Guilcher, 1958) and susceptible to formation of submarine karsts with sea-level variations.

Our study focuses on the use of several datasets (geophysical and geotechnical data) to better characterize the challenging karst geology in an area expected to host a large wind farm (Fig. 1). Two geophysical methods were applied to obtain geological nature and geometry information on the substratum at a large scale: multichannel ultra-high-resolution (UHR) seismic imaging and marine electrical resistivity tomography (MERT). They were complemented by multibeam bathymetry (1 m resolution) and geotechnical investigations using multisensor core logging (MSCL).

## GEOLOGICAL SETTING

The study area (Fig. 1) is located on the South-Armoricán passive margin, 10 km off the Saint-Nazaire coastline in the Bay of Biscay. It consists of a calcareous platform gently dipping (<1%) towards the south-west, named Banc de Guérande' (EDF-Re, 2016). It belongs to a wide group of underwater 'plateaus', whose age ranges from Lutetian to Bartonian (Vanne, 1977). A palaeovalley is observed in the north-eastern part of the site and is approximately 1.5 km wide and 6 km long. The bathymetry of the study area ranges between -12 and -25 m below law astronomic tide (LAT) (Fig. 1).

The regional geology within the Saint-Nazaire site consists of bioclastic calcarenite from Lutetian-Bartonian (Figs. 2 and 3), with a thickness ranging from 10 to 29 m. This calcarenite bank outcrops most of the study area and overlies Ypresian sand (Fig. 3). The transition with Ypresian sands is very gradual and extends over several metres (Fugro, 2015b). Shells consist of benthic foraminifera (Nummulites), which belong to the Lutetian-Bartonian stages. This unit appears to be subjected to dissolution, as many pluri-millimetre to centimetre voids were observed (Fugro, 2015b). The thickness of each geological unit is highly variable in the study area (Fig. 3).

The Ypresian glauconitic sand appears to be very dense and is locally slightly cemented. The sand is generally fine, well graded and mostly composed of quartz grains. Several sequences of interbeds of silt and clay layers are observed in the deepest part of this formation.

Quaternary palaeochannel infill sediments are present on the northern border of the rock massif. The Banc de Guérande is covered by a thin layer of very coarse sediments. Geotechnical investigations (Fugro, 2014a, 2014b) have highlighted a high lateral variability of the sediment thickness and nature due to the uneven seabed. The thickness of this layer varies from 0 to 0.75 m. The sediments mainly consist of sandy coarse gravels with cobbles of weak to medium strong calcarenite. Below, the first metres present sediments with a
<figure><img src="image_3.png" /><figcaption>**Figure 1** (a) Location of the study area. (b) Map of the study area with the locations of the studied boreholes. The bathymetry is from SHOM using the Bathyelli references. (https://data.shom.fr/donnees).</figcaption></figure>

high content of fine particles, including very dense silica sand interbedded with thick beds of medium- to extremely high-strength clay. Below 10 m below seafloor (BSF), the sediments mainly consist of sand with a few clayey silty intercalations (Fugro, 2015b).

Across the Guérande plateau, the seafloor has a very irregular surface (Fig. 1b). Local depressions are observed within the study area (Fugro, 2015a; Fig. 1(b)). The current erosion surface on top of the Banc de Guérande is very rough in appearance due to karstification occurring during extensive periods of emergence or subaerial exposure that took place after its lithification. These bathymetric features are typical of

karst environments. Rocky rugged bathymetry was observed in similar submarine karsts (Miccadei *et al.*, 2011; Taviani *et al.*, 2012; Kan *et al.*, 2015). Circular rocky depressions filled with sand can be assimilated to dolines resulting from the dissolution or collapse of sinkholes due to karstification during subaerial exposure.

## AVAILABLE DATA

### Geotechnical data

Several geotechnical campaigns were carried out in the study area in 2015 (Geotek, 2015; Fugro, 2015b). Forty-nine
<figure><img src="image_4.png" /><figcaption>**Figure 2** Simplified geology (from the French BRGM database http://geoservices.brgm.fr/wms-c.html) and location of the geophysical and geotechnical data studied in this paper.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 3** Example of a section displaying the main geological features of the study area (adapted from EDF-Re, 2016). The base of the transitional dolomitic sand (green area) is only known from the boreholes and cannot be inferred from the seismic datasets because of a lack of penetration (denoted by question marks). The location of this line is indicated by a blue dashed line in Figure 2.</figcaption></figure>

30 m-long boreholes were drilled across the study area, and 12 cores were extracted and analysed in the laboratory using an MSCL bench (Geotek, 2015). This device is equipped with different sensors, providing, among others, linescan photogra- phy and measurements of gamma density, X-ray radiography and electrical resistivity. Sensors were calibrated prior to core measurements. The core diameter was 100 mm, and the length of the core run was typically 1.5 m.

Resistivity measurements on the Geotek MSCL were per- formed using a non-contact system. The sensor uses an induc-

tion method to measure the electrical resistivity of the sample (Jackson *et al.*, 2006). This sensor technique is limited to mea- suring low-resistivity samples (0.01–10 Ω·m) and is therefore suitable for marine environments. Electrical resistivity varies with temperature, so a correction to 20°C is applied in the pre- processing of the measured values using the MSCL process- ing panel and an empirical calibration relationship (Geotek, 2015). A factory calibration was provided for each resistivity sensor. This calibration is specific to cylindrical sample geom- etry and can be applied to rock or sediment cores. A series
of saline solutions were used at different concentrations to empirically calibrate the resistivity measurements. After these different calibration steps, the corrected resistivity values may be closer to representing the bulk electrical resistivity of the samples (Geotek, 2015) and thus can be directly compared to electrical resistivity tomography (ERT) measurements.

MSCL tests were able to provide data with every cen-
timetre along the core, as long as the core was not altered by
the extraction or during transportation to the laboratory. We
specifically studied 11 boreholes (Fig. 2).

The MSCL analysis was only conducted on the calcaren-
ite and calcarenite/sand transition cores. MSCL data artefacts
related to air gaps (fractures, non-intact core or core loss) were
removed, as well as resistivity data that could be strongly af-
fected by fractures or when an air gap was located around the
sensor. Whereas X-ray radiographs recorded in air gaps (i.e.,
fractures or non-intact core) were edited out of the final data,
data collected through intra-core voids (areas of high dissolu-
tion and/or poor cementation) remain within the dataset.

From the gamma density, the porosity was evaluated using calculations of water content and density. The porosity was estimated with direct measurements on rocky samples using buoyancy techniques (Franklin, 1979) and corresponds to the volume of the voids accessible to water (connected porosity).

We distinguish the natural rock and/or sediment poros-
ity, the dissolution voids created by the karstification process
and the fractures mainly caused by the collapse of the rock
when it is weakened by dissolution voids. The cores are also
partially affected by fractures caused by the extraction. This is
quantified by the solid core recovery (SCR) index (Annels and
Dominy, 2003), which has been estimated for each core and
evaluates the core quality (Zabidi and De Freitas, 2011): an
index within the range of 70-100% shows good quality; the
range 50-69% corresponds to moderate to weathered quality
and the range 0-49% to bad quality (highly fractured rock or
karsts).

Synthetic logs displaying results from geological and geotechnical descriptions, results of geotechnical and in situ tests as well as MSCL data were constructed for geological understanding purposes and comparison with geophysical data (e.g., Fig. 3).

Ultra-high-resolution multichannel seismic reflection

The seismic survey was carried out by Fugro Ocensismica in
2015 (Fugro, 2015a). The system consisted of a 20 cubic inche
sleeve gun source and a 48 channel Geometrics Solid streamer

as a receiver. Each group was composed of 16 hydrophones,
and the group interval was 3.125 m. The sampling interval
was 0.250 ms, and the maximum fold was 48. Streamer depth
and position were monitored by a tail buoy with a GPS track-
ing system towed from the end of the streamer and three depth
controllers (compass birds) installed along the streamer.

The processing workflow included a demultiple, a veloc-
ity analysis carried out every 250 m, a normal moveout correc-
tion, a post-stack Kirchhoff time migration and filtering using
the time-variant Butterworth filter. The final processed data
have a horizontal resolution of ~1.6 m, a vertical resolution
of ~5 m and a very variable penetration depending on the soil
nature.

Marine electrical resistivity tomography

Marine electrical resistivity tomography acquisition

In situ electrical resistivity probes or remote electromagnetic
techniques are often used to determine the sediment porosity
and electrical properties (formation factor, etc.) of the subsur-
face. These techniques circumvent some of the obvious prob-
lems caused by coring disturbance. They proved to be effi-
cient in evaluating bedrock quality (Dahlin and Loke, 2018),
identifying groundwater pathways in a karst coastal aquifer
(O'Connell et al., 2018) or detecting and characterizing frac-
tured zones in bedrock (O'Connell et al., 2018; Tassis et al.,
2020). These studies highlighted the major difficulty for geo-
electrical surveys in marine environments, which is the high
conductivity of the water column and thus the loss of electric
current into the water. But they also showed that resistivity
measurements are an efficient and promising tool to charac-
terize complex and highly heterogeneous geologies.

In our study, we carried out in 2016 a MERT survey
along some of the seismic lines (Fig. 2) with the MAPPEM
acquisition system (Tarits et al., 2012). In contrast to most
studies, where electromagnetic systems were first developed
for terrestrial applications and then adapted to marine envi-
ronments (Rucker and Noonan, 2013; Ronczka et al., 2017;
Dahlin and Loke, 2018), the MAPPEM system has been specif-
ically developed for marine site investigation since 2015 and
is thus able to deal with the water column, the contrast at the
sea/soil interface and challenging marine contexts (Tarits et al.,
2012; Flamme et al., 2020). The system was configured with
a dipole-dipole layout. We acquired 90 km of MERT sections
along 20 lines. In this study, we focused on 11 lines.

The system comprised the main fish and a smaller one,
both forming an injection dipole transmitting a DC current of
25 A at low voltage and a streamer with 20 electric potential
<figure><img src="image_6.png" /><figcaption>**Figure 4** Example of raw data for line MERT_3. (a) Apparent resistivity section with the 19 dipoles formed by the 20 receiving electrodes. (b) Corresponding uncertainty section of the measurements.</figcaption></figure>

electrodes, forming 19 simultaneous receiving dipoles of various lengths. The system position was obtained from altitude, depth and bidirectional tilt sensors. The transmitter dipole was 10.9 m long. The 20 receivers were 4 m apart and located 11 m behind the transmitter. The system had a total length of 107.5 m and was towed at an altitude of about 5–10 m above the seafloor at 3–4 knots.

The depth of investigation (DOI) and the minimum vertical resolution depend on the size of the system and were approximately estimated as 20–25 m and ~5% of the depth, respectively. The data sampling (about every metre) and the receiver spacing (4 m) control the MERT horizontal resolution. Each sounding consisted of 19 electric potentials repeated with spatial sampling depending on the ship velocity (Fig. 4a). During the survey, the current injection rate was 0.5 s, thus 0.8-1.0 m at 3–4 knots (ship velocity). The uncertainty of each measurement was estimated from the standard deviation of the potential difference measured when the current was not injected (ambient noise). The uncertainty increased with the distance between the injection dipole and the receiver dipole and ranged between ~0.02% and ~0.70% (Fig. 4b).

## Data processing

Data processing was carried out using both built-in software and processing codes adapted to the MAPPEM system. The processing workflow consisted of attitude data cleaning to remove abnormal jumps and artefacts. Then, the location of each measurement was obtained from the combination of GPS

data on the ship and the layback continuously monitored (uncertainty of ~5 m). Taking stock of the acquisition of the simultaneous 19 potential differences and using the geometry of the system, we scaled the data into apparent resistivity (electrical resistivity of an equivalent homogeneous space).

For a given profile, the dataset consisted of the apparent resistivity values and their standard deviation as a function of the offset (distance between receiver and transmitter) and position along the profile (the standard deviation comes from repeated measurements divided by the geometric factor). The relationship between apparent resistivity and true resistivity is non-linear, and data inversion must be performed to recover the true resistivity as a function of depth and position. This operation was carried out using two-dimensional (2D) commercial inversion software (Res2DInv; Loke, 2004).

Electric-sounding data inversion is well known. Various algorithms exist in one, two and three dimensions (Loke, 2004; Sharma and Verma, 2015). Some algorithms include solutions for data acquired at the surface of the water (river, lake, sea) or on the bottom. In this study, we used the commercial software Res2DInv adapted to our dataset, allowing a suspended system within the water column and the option of generalized electrode positions (Loke, 2016). That version of the software enables 2D inversion of the large set of data (several thousands of data points per profile) with suspended sources and receivers and a variable depth-resistivity profile in the water layer.

All MERT lines (Fig. 2) were inverted using a grid size defined according to the maximum DOI, the minimum resolution and the results of the inversion tests. The thickness
of the first layer was 0.5 m, the increasing factor with
depth was 1.1, and the bottom depth was set to twice the
maximum DOI, which corresponds to about 45 m below
the acquisition system. The model grid had a total num-
ber of 32 layers. Above the seafloor and for MERT_1 to
MERT_3, the water layer could be split to include resistiv-
ity values measured with a conductivity temperature depth
(CTD) probe, in order to calibrate the model and deal with
the classical difficulty of a strongly conductive seawater layer
in marine electrical investigations (Dahlin and Loke, 2018;
Tassis et al., 2020). For lines MERT_4 to MERT_11, no CTD
values were available, and the resistivity of the water column
was set to 0.22 Ω·m. This value is constant vertically and hor-
izontally, and was averaged from CTD measurements carried
out in the water column for lines MERT_1 and MERT_3. Be-
sides, this water conductivity value proved to be a good av-
erage value, as it gave consistent inversion results for lines
MERT_4 and MERT_11 when compared to lines MERT_1
and MERT_3.

The inversion was tested for several normalization and regularization terms. Eventually, we used the L2-norm and a flatness filter directly applied to the model. We noticed that including the data standard deviations as error estimates in the inversion process improved the results by reducing artefacts in the models and reducing the root mean square (RMS) of the final resistivity models.

The survey lines were composed of 1621 to 4979 sound-
ings and thus were too long to be inverted at once with
Res2DInv. Each line was split into sub-sections of 1000 sound-
ings maximum that were inverted separately and then stitched
together. All inverted sections overlapped by 420 soundings
to create seamless profiles. The final RMS error was less than
1.5% for all sections.

The DOI was evaluated to be ~30 m below the
system. The DOI method used is described by Roy and
Apparao (1971). For our system, this DOI was evaluated to
be ~22 m below the system. Considering that (1) the pen-
etration was good for our dataset on the Guérande bench
and (2) our system is quite long compared to classical DC
systems (large offsets between dipoles), we followed the rec-
ommendation of Loke (2004) to use a factor of 1.3 on this
DOI to evaluate the real penetration, which is close to ~30
m. The effective penetration below the seabed depends on the
system altitude above the seabed. The greater the altitude is,
the shallower the penetration. In our dataset, the penetration
in the subsurface remained constant (close to ~25 m) along
the studied lines as the system was very stable in the water
column.

RESULTS

Seismic data

Overall, the data quality was satisfactory, even though
marginal weather conditions (wind, swell, currents) affected
the seismic survey. Below the seabed, the reflections could
hardly be identified and were masked by noise (Fig. 5a). In-
deed, the penetration was strongly reduced, possibly due to
strong acoustic scattering on the hard calcarenite.

We present the seismic lines SNA15001EW and SNA15002WE (Fig. 5a), where we can observe little information on the soil geometry and geological units. Geological layering cannot be interpreted by clear reflectors, but the variable seismic pattern indicates that the underground is not uniform. Several reflections can be identified, but the seismic data were unable to reveal cavities with good confidence.

Resistivity models

Globally, resistivity models show high soil heterogeneity
throughout the study area (Fig. 5b). The resistivity values
range between 0.18 Ω·m (seawater) and 20. Ω·m.

We present the interpreted models along lines MERT_1 and MERT_3 (Fig. 5b). Similar results are obtained for the other lines (see the additional data in the supplementary material), showing the same global trends, and they lead to the same geological interpretation.

The lateral heterogeneity of the resistivity model is partic-
ularly strong. The resistivity varies from 4 to 8 Ω·m between
-30 m LAT and -60 m LAT. Such strong lateral variations are
typical of karst environments (Nyquist et al., 2007; Muham-
mad et al., 2012; Carrière et al., 2013).

Besides, a low-resistivity layer is often observed be-
neath the seafloor, with resistivity values of less than 2 Ω·m
(Figs. 5 and 6a).

Multi-sensors core logging data

MSCL measurements were of good quality. We used the mea-
surements of resistivity and density, X-ray radiographs and
calculations of the SCR index.

Geotechnical reports mentioned highly fractured samples
(Geotek, 2015): grey hatching highlights them to help the
interpretation (Fig. 7). We can see that fractures are largely
present along the cores in the calcarenite layers. The SCR in-
dex (Fig. 8) shows that the best conserved cores after extrac-
tion are D02 and E03. The other cores are quite well conserved
and not much remoulded or fractured from part to part, but
<figure><img src="image_7.png" /><figcaption>**Figure 5** Top: seismic line SNA15001EW and MERT_1 line, both crossing the boreholes A11 and A13 locations. Bottom: seismic line SNA15002WE and MERT_3 line, crossing boreholes B07 and B09 locations. Each section displays the location and stratigraphy of the boreholes. (a) Seismic amplitude. (b) Electrical resistivity model. (c) The resistivity model is superimposed with the seismic amplitude. For boreholes A13 and B09, no MSCL data are available and thus they are not studied thereafter.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Figure 6** Zoom on the line MERT_1. (a) Resistivity section alone. (b) The resistivity section is superimposed with the acoustic amplitude from seismic data. The white dashed line shows the base of the low resistivity layer. The red dashed line embodies the transition to harder material based on both seismic and resistivity data.</figcaption></figure>

some core runs have an SCR of less than 30%, which corresponds to a poor-quality core.

The acquired electrical resistivity values on the MSCL bench once corrected for instrument drift and edited for non-intact zones, were of good quality. The resistivity values are converted into conductivity for easy comparison with porosity distributions. The conductivity profiles (orange in Fig. 7) range between 0.02 S/m and 0.05 S/m within the top 10 m BSFs, up to between 0.2 S/m and 0.3 S/m from 10 m BSF.

The X-ray radiographs show the variations in the core density (Fig. 7) and thus are sensitive to the presence of intraformational voids (cracks, fractures and karst dissolution voids would appear white) or core loss. In our data, X-ray radiographs testify for very numerous intraformational voids and highlight density differences within the core samples. The rock and sediment samples show a variable density profile downcore because of either denser beds or the occurrence of intra-core voids.

The trends observed in the MSCL porosity follow the variations in the MSCL conductivity (Fig. 7) and globally vary from 10% to 50% within the calcarenite layer (see, cores C03, D02 and E03 in Fig. 7). High-porosity values accompany high MSCL conductivity. In the superficial highly fractured calcarenite layer, the porosity tends to be quite low (down to 10% for core A11), but these values also coincide with highly frac-

tured core samples, which suggest that the measured porosity does not include all possible in situ voids.

## DISCUSSION

### Comparison between the datasets

The comparison between the seismic profiles and the resistivity models (Fig. 5) suggested that the best-defined seismic interfaces globally coincide with the transition between the upper low-resistivity layer of fractured calcarenite (between −20 m LAT and −30 m LAT; Fig. 6b) and a more resistive (>4 Ω·m) substratum below (weathered calcarenite lying on dolomitic sand). However, a more detailed comparison was not possible due to the lack of clear reflections in the seismic sections.

The first 5-m below the seabed has a moderate resistivity of 2 Ω·m (Fig. 5). The geotechnical logs revealed on most boreholes (see, boreholes A11, D02, E05, E11 or E13 in Fig. 7) that this superficial layer corresponds to highly fractured calcarenite characterized by the presence of possible seawater saturated sand pockets and karstification features, which are conductive media.

We extracted from the 2D resistivity sections the MERT resistivity values at the closest position from each borehole. We converted these values into electrical conductivity versus
<figure><img src="image_9.png" /><figcaption>Figure 7 Borehole data. For each borehole: conductivity measured on the core with MSCL (orange) and MERT (blue) to the left; porosity calculated from core data (grey), core porosity interpolated at MERT depths (red), MERT porosity inferred with Archie's law (blue), difference between MERT and borehole porosities (black) (middle); X-ray radiograph of the core (right), with highly fractured areas highlighted by grey hatching.</figcaption></figure>

depth (Fig. 7) to facilitate the comparison with porosity and with the MSCL data (conductivity and porosity). Thus, from now on, we refer to electrical conductivity instead of resistivity. The MERT conductivity profiles are reported in Figure 7.

The MERT profiles average conductivity over a scale of a few metres, whereas the MSCL measurements describe the parameters at a scale of some centimetres. They do not describe the same lithological scales, and a direct comparison may be misleading. However, since MERT values are an average over a larger volume, they should fall in the range of borehole scale values.

In Figure 7, we observe that the MERT conductivity values are in fair agreement (same trend, variations, although at different scales, and average values) with the MSCL data deeper than about 10 m BSF, thus for the units below the highly fractured calcarenite. In contrast, the MERT and MSCL conductivity generally have an opposite trend in the near seabed highly fractured calcarenite (Fig. 7). This observation is clear for boreholes B07, D02 and E03, and is generally observed for all boreholes. For superficial sediments,

the results of the MSCL measurements are not representative of the *in situ* state of the undisturbed sediment. However, the loss of pore fluid may also be due to the numerous fractures present in the superficial calcarenite layer, where the pore fluid is easily drained and can escape from the matrix grains. Both reasons could explain why the MERT conductivity is higher than the MSCL conductivity close to the seabed.

The whole area is subject to dissolution voids due to karstification taking place in the calcarenite substratum. These voids are then filled with saturated sediment that may be more porous than the surrounding rock. Therefore, areas containing karst cavities would likely appear more conductive than the surrounding substratum. The cavities that have been observed in borehole A11 are less than 1 m wide (Fugro, 2015b), but their redundancy is unknown. A cavity of such dimensions is marginally detectable by the MERT method, but the presence of such cavities could increase the bulk conductivity values, which is what we observe in the upper calcarenite layer of the MERT sections (Fig. 5c).
<figure><img src="image_10.png" /><figcaption>Figure 7 Continued</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Figure 8 Solid core recovery index for the studied boreholes (Fugro, 2015b).</figcaption></figure>

Combining MERT and MSCL resistivity to scale the heterogeneity

Combining MERT and MSCL data involves addressing the difference in scale as well as the distance between the borehole data and the closest MERT line. We consider two possible cases (Fig. 9): (1) the borehole is located beyond the MERT volume (Fig. 9a), and (2) the borehole is located within the volume resolved by the MERT (Fig. 9b). The MERT horizontal

resolution length (HRL) is about 2–3 m at best. This value comes from the lateral resolution of the resistivity model, which was calculated from the vessel speed and the array size (distances between emitting and receiving electrodes). Five boreholes are located within this range (B07, C03, F06, D02 and E03). The others are located between ~3 m and ~12 m from the MERT line (Fig. 10). We must keep in mind that the MERT HRL increases with depth (Fig. 10). However, for shallow depths (less than 10 m BSF), an HRL value of 2–3 m is a reasonable estimate to investigate how to compare geotechnical and geophysical data.

In case 1 (Fig. 9a), the MERT and MSCL conductivities are expected to be correlated depending on the local intensity of the heterogeneity. This case seems to occur for boreholes A03, E13, E15 and E05 (Fig. 7), which are located far from the MERT lines (between ~5 m and ~12 m). We observed large discrepancies between the MERT and MSCL conductivities (>0.3 S/m; see Fig. 7). Yet, conductivity values are similar for borehole A11 (Fig. 7), ~7 m away from the closest MERT line. This result is either circumstantial or the area is homogeneous across the distance between the borehole and the MERT line. The interpretation cannot go further without additional data (for instance, resistivity logging included in collocated Cone Penetration Test-Resistivity Cone Penetration Test (RCPT) boreholes as in Bazin and Pfaffhuber, 2013).

In case 2 (Fig. 9b), the borehole is located inside the volume defined by the MERT HRL. The MERT conductivity value is a weighted average of the actual conductivity over the HRL volume. Obviously, if the medium was homogeneous at the HRL scale, both the MERT and MSCL conductivity values should be similar. Thus, differences observed between MERT and MSCL conductivity profiles should be related to incomplete core recovery at the borehole site or to heterogeneity in the calcarenite layer (or both).

Figure 8 shows the recovery rate for all studied boreholes. The recovery is very variable. The cores are mainly composed of calcarenite, sand and pore fluid, namely, seawater. We, therefore, approximate the substratum as a simple three-phased rock model and use the equivalent medium theory based upon Archie's law (1942) to express its conductivity:

$$ \sigma_{\text{MERT}} = \sigma_w S_{\text{water} \in \text{sand}}^n V_{\{\text{water}+\text{sand}\}}^m \in \text{calcarenite} \quad (1) $$

with $\sigma_w$ water conductivity, $S_{\text{water} \in \text{sand}}$ water fraction in the sand, $n$ water volume exponent, $V_{\{\text{water}+\text{sand}\}}$ calcarenite volume fraction of the compound {water+sand} in the calcarenite voids, $m$ volume exponent. However, too few data are available to assess all the terms properly, in particular, there
<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /><figcaption>Figure 9 Cartoon describing the location of the borehole with respect to the MERT HRL volume (see the text for details). (a) The borehole is located outside the MERT HRL volume. (b) The borehole is located inside the MERT HRL volume.</figcaption></figure>

are no in situ borehole conductivity measurements. Thus, we simplified this equation by melding calcarenite and sand in a single highly resistive phase:

$$\sigma_{\text{MERT}} = \sigma_{w} \phi_{\text{MERT}}^{m}. \qquad (2)$$

The value $\phi_{\text{MERT}}$ is now the volume fraction of voids containing seawater (pores, fractures, cavities) and hence the equivalent porosity of the soil at the MERT scale. When the core recovery was successful, such as at boreholes E03 or D02, the differences between $\sigma_{\text{MSCL}}$ and $\sigma_{\text{MERT}}$ should reflect the heterogeneity of the soil. Since the MERT conductivity models average the soil conductivity over the HRL volume, we can synthesise $\sigma_{\text{MERT}}$ them as follows:

$$\sigma_{\text{MERT}} = \frac{1}{V_{\text{HRL}}} \int \sigma(r) F_{\text{pos}}(r) dV_{\text{HRL}}, \qquad (3)$$

where $F(r)$ is the averaging kernel and $r$ is the position within the HRL volume.

This equation tells us that $\sigma_{\text{MERT}}$ is a value within the range of possible soil conductivity values $\sigma_{\text{BH}}$ measured at the borehole scale. However, at the borehole drilled within the

HRL volume, this conductivity is likely to be different from $\sigma_{\text{MSCL}}$ since the latter is a value measured after core extraction. Instead, it is preferable to use the MSCL porosity as a proxy of $\sigma_{\text{BH}}$ compared to $\sigma_{\text{MERT}}$. Now, we can estimate the implication of observing $\sigma_{\text{MERT}} < \sigma_{\text{BH}}$ or $\sigma_{\text{MERT}} > \sigma_{\text{BH}}$ through the comparison between the MERT volume fraction $\phi_{\text{MERT}}$ calculated with equation (2) and the MSCL porosity, which is an estimate of the borehole volume fraction $\phi_{\text{BH}}$. When $\sigma_{\text{MERT}} < \sigma_{\text{BH}}$, the MERT volume fraction $\phi_{\text{MERT}}$ of cavities or voids on average is less than at the borehole $\phi_{\text{BH}}$ ($\phi_{\text{MERT}} < \phi_{\text{BH}}$). Conversely, when $\sigma_{\text{MERT}} > \sigma_{\text{BH}}$, on average, the volume of cavities or voids is larger than what is observed at the borehole ($\phi_{\text{MERT}} > \phi_{\text{BH}}$).

When the recovery is poor on average, an additional effect should be taken into account. The missing material corresponds mostly to a loss of pore fluid during extraction. Consequently, the lost volume of pore water induces a bias in the MSCL porosity and should contribute to the observed difference between the porosity measured in the recovered material of the core and the porosity inferred from the MERT conductivity. Using equation (2) with $\sigma_{w} = 4.5$ S/m (from CTD
<figure><img src="image_16.png" /><figcaption>**Figure 10** Difference between the MERT and MSCL (BH) porosities for all boreholes. Colour according to the distance between the borehole and the closest MERT line. Boreholes located within the HRL volume (B07, C03, F06, D02 and E03) are plotted in bright colours. Boreholes located outside the HRL are plotted in pale colours.</figcaption></figure>

measurements in the water column) and $m = 2$, we can infer the volume fraction $\phi_{\text{MERT}}$. Typical values for $m$ may range from 1.8 to 2.1 (Lee and Collett, 2006); thus, the volume fraction uncertainty ranges from 4% to 7% for $\phi_{\text{MERT}}$ between 0.2 and 0.6.

We shall note that the use of the Archie law implies having information about the soil's nature (especially the clay content) and the water saturation. Thus, the availability of geotechnical data (e.g., boreholes) is particularly important to obtain reliable and contextually adapted porosity information and to validate our methodology.

We calculated the MERT volume fraction for all boreholes and showed the difference between the MSCL and MERT volume fractions ($\Delta\phi = \phi_{\text{BH}} - \phi_{\text{MERT}}$) in Figure 10. We focus on boreholes E03, B07, C03, F06 and D02, which

are located within the HRL. The recovery at borehole F06 is very poor, at B07 and C03 average, and E03 and D02 very good (Fig. 8). The X-ray fluorescence logs (Fig. 7), the SCR index calculation (Fig. 8) and core observations (Geotek, 2015) show that cores B07 and F06 are heavily fractured, whereas cores C03 and D02 are only fractured in the upper calcarenite layer (Fig. 7).

For borehole C03, $\phi_{\text{MERT}}$ and $\phi_{\text{BH}}$ are similar ($\Delta\phi$ small) within the first 7 m of BSF, but then $\phi_{\text{BH}}$ tends to be greater than $\phi_{\text{MERT}}$ ($\Delta\phi > 20\%$) down to about 13 m of BSF.

For B07 and D02, $\Delta\phi$ can reach about -20% in the upper 6 m, suggesting an underestimation of porosity at the borehole scale compared to the HRL scale. A similar conclusion may be drawn for boreholes C03 and E03 (for the latter, this observation is true down to -11 m BSF). In contrast, for F06, $\Delta\phi$ reaches +20% in the upper 4 m, suggesting an overestimation of porosity at the borehole scale compared to the HRL scale. Furthermore, for all the boreholes within the HRL, we observe $\Delta\phi > 0$, which means that the MSCL porosity is systematically greater than the MERT porosity. This suggests that at the scale of HRL volume, the surrounding calcarenite is less porous (porosity of ~20%) than what was suggested by MSCL measurements at the borehole.

The interpretations of the overall heterogeneity within the HRL volume hold for boreholes D02 and E03 since the recovery is very good there. For B07 and C03, and worse for F06, the interpretation of the volume fraction differences is complicated because of the missing material unless $\sigma_{\text{MERT}} < \sigma_{\text{BH}}$; thus, $\phi_{\text{MERT}} < \phi_{\text{BH}}$. When $\sigma_{\text{MERT}} > \sigma_{\text{BH}}$ part or all of the difference may be attributed to the missing water or water and sand. Of course, the recovery varies with depth, and some of the interpretations drawn for these boreholes may hold when the recovery is good at depth.

## CONCLUSION

We investigated the combination of MERT with geotechnical data to complete the partial geological information retrieved by seismic data that could not penetrate deeply into a highly reflective calcarenite. The 2D resistivity models provided a framework to describe the variability of the lithology structure. Combining the vertical MERT resistivity profiles closest to the boreholes and the MSCL data, we showed that for boreholes within the MERT lateral resolution volume, we could draw information about the porosity at both the borehole and geophysical scales.

The study was limited by the heterogeneity of the area, which imposed a requirement for excellent collocation be-
tween the datasets to perform reliable comparisons and in-
fer better information on the substratum characteristics. Most
of the boreholes were more than 3 m away from the closest
MERT section, which limited the interpretation of the results.

Moreover, the analysis of the whole results was based
upon the hypothesis that the MERT conductivity values pro-
vided by the models were a weighted average of the actual
conductivity over the HRL volume. This is a good first ap-
proximation, but cannot be exactly true in some cases of com-
plex geology: low- or high-resistivity features located off the
recorded line can influence the inversion result and make it ap-
pear in the 2D cross sections. This can potentially be circum-
vented by running a three-dimensional (3D) inversion, which
would be more sensitive to the soil heterogeneity in all direc-
tions. Testing 3D inversions in a similar approach would be
very interesting to improve the comparison between MERT
conductivity models and MSCL conductivity data but may be
limited by the lack of data in a 3D configuration.

This study shows encouraging results and demonstrates
the fruitfulness of combining MERT and MSCL surveys as
they bring complementary observations. On the way forward,
we recommend that an effort is made on the collocation of
the different datasets in such a heterogeneous context. The
analysis would also benefit from MERT lines crossing at the
borehole location. Finally, the generalization of in situ resis-
tivity logs (such as RCPT boreholes) along MERT lines would
considerably improve the porosity model for the study area.

ACKNOWLEDGEMENTS

We thank EDF-Renouvelables for providing geotechnical data
and allowing us to publish them. Part of this work benefited
from France Energies Marines and National Research Agency
grant ANR-10-IED-006 (GEOSISMEM Project).

DATA AVAILABILITY STATEMENT

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

ORCID

Judith Dusart ID https://orcid.org/0000-0003-1909-5583

Sara Bazin ID https://orcid.org/0000-0001-6478-7760

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