High sampling rate measurement and data treatment for mobile investigations: Kinematic Electrical Resistivity Tomography (KERT)

Geoderma 284 (2016) 22–33

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High sampling rate measurement and data treatment for mobile investigations: Kinematic Electrical Resistivity Tomography (KERT) Olivier Guerrero a,⁎, Jean-François Lataste a, Antoine Marache a a

Univ. Bordeaux, UMR 5295 I2M, GCE Department, 33405 Talence Cedex, France

a r t i c l e

i n f o

Article history: Received 23 December 2015 Received in revised form 4 August 2016 Accepted 7 August 2016 Available online xxxx Keywords: Electrical resistivity tomography High sampling rate measurement device Device for mobile investigations Data treatment De-noising data On-the-go sensors

a b s t r a c t This paper presents an innovative system which adapts Electrical Resistivity Tomography (ERT) for fast investigation on long transects. The device consists in a set of on-the-go sensors allowing high sampling rate measurement for mobile prospections. The weak contact between the mobile sensors and the soil, to allow fast investigations, induces very noisy raw datasets. Kinematic Electrical Resistivity Tomography (named KERT) is then associated with a data treatment process. A two-step process reveals the information contained in the datasets. The first focuses on the procedure to remove noise through the use of a low-pass filter. The assessment of cutoff frequency for smoothing is deduced from a Fast Fourier Transform (FFT) analysis, thus the value is adapted to the site and the prospection. The second phase consists in calibration of the KERT on a conventional static ERT. At this point, a classical static ERT was used as a reference, and directed on a reduced part of the KERT transect. The estimation of a factor of calibration (Xc) to correct bias revealed the resistivity variations along the entire transect and in depth. In the last part of the paper, the validation of the investigation method and data treatment methodology is performed on a real case study: a 450 m transect is investigated in 5 min (mean speed: about 6 km/h), integrating 10 depths of investigation. The steps of data processing are detailed to show the final results, consisting in a zonation along the transect. © 2016 Elsevier B.V. All rights reserved.

1. Introduction In geophysical prospection, advances in technologies now allow equipment to conduct extensive surveys in a relatively short time (Lund et al., 1999; Blais, 2004; Christensen and Sorensen, 2001). They include developments in high sampling rate measurement devices for geophysical prospection in the fields of archaeological exploration (Clomont, 2008; Tabbagh, 1992; Dabas et al., 2000), civil engineering (Neiderleithinger et al., 2015), geological surveys (Peyraube et al., 2012), and soil science (Coulouma et al., 2012). The idea is that these devices should respond to different expectations in terms of utility, whether for the prospection of soils for urban development plans, for the location of underground structures (Lew, 1997), or for geological surveys on a large scale (Meric, 2006; Friedel et al., 2006), etc. In this context, classical electrical resistivity tomography (ERT) can be a very interesting tool. Its sensitivity to water and/or clay content and lateral resistivity variability can bring a lot of advantages. This technique has many applications (Samouëlian et al., 2005). Numerous case studies have proved its high level of performance in measuring surfaces or boreholes provided by images in each considered zone (Taillet et al., ⁎ Corresponding author. E-mail address: [email protected] (O. Guerrero).

http://dx.doi.org/10.1016/j.geoderma.2016.08.007 0016-7061/© 2016 Elsevier B.V. All rights reserved.

2014). This zoning of surface soils makes it easier to define the variability of physical properties of a certain material such as the variation in clay content (De Benedetto et al., 2011; Tabbagh et al., 2000) or geometrical structures (Buvat et al., 2014; Guerrero et al., 2013; Chaplot et al., 2010; Besson et al., 2004). The major limitation of ERT prospection in fieldwork conditions is the relatively poor horizontal resolution with increased electrode spacing. Hence, applying this in a larger area can lead to difficulties. Implanting each electrode is time consuming, another source of difficulties encountered during ERT prospection. In addition, the following concerns should be seriously considered during fieldwork; sensitivities and abilities of several electrode configurations in relation to their differences in spatial resolution; tendency for artefacts to appear in images; deviation from the true model resistivity; and interpretable maximum depth. Following these restrictions, ERT seems to have limited potential in performing a high sampling rate measurement prospection. Over the last thirty years, advances in geophysical prospection have been focused on the adaptation of electrical methods in order to conduct soil structure mapping and to discern its physical characteristics (Samouëlian et al., 2005; Loke et al., 2013). Using the high sampling rate measurement device in geophysical prospection, the time of exploration can be directly correlated to the travel speed of the device. In this case, a great majority of the measurements techniques are towed, or at

O. Guerrero et al. / Geoderma 284 (2016) 22–33

least linked to movable devices. Pulling the device implies a development of existing techniques to adapt to the new measurement process (Jakosky, 1938; Hesse et al., 1986; Panissod et al., 1998). Most of the methods and measuring devices developed have mainly aimed at mapping large surfaces or obtaining the transect of physical properties via surveys like kinematics. The use of kinematics leads to the rapid achievement of a large number of measurements. At present, a number of resolutions exist in terms of equipment to generate continuous geoelectrical surveys. ARP (Automatic Resistivity Prospection), operated by Geocarta, is used for the recognition of archaeological zones (Panissod et al., 1997; Dabas, 2009). ARP is a motorized system that allows 3 simultaneous measurements of apparent resistivity, representing 3 volumes of investigation (Dabas, 2009). Materials with the same technical basis of geoelectrical measurement also exist in Denmark, such as the PACES (Pulled Continuous Electrical Sounding System) developed by the University of Aarhus (Christensen and Sorensen, 2001), or in the USA with the Veris 3100 Soil EC Mapping System developed by Veris Technology (Lund et al., 1999). Recently, there has been the Geophilus Electricus (Lueck and Ruehlmann, 2013) for mapping the top-soil in five depths of investigation (0–1 m). All these approaches are focused on soil mapping, in terms of apparent resistivity. The value of ERT is its ability to invert data in order to assess a model for true resistivity distribution. In this study the classical ERT was developed in order to reach high sampling rate measurement approaches. This enhanced ERT device can allow easier actual installation on site. It can allocate investigations on transect along large spatial scale in the field. The adaptation of the common geophysical methods in a geophysical prospection with on-the-go sensors aims to exploit the characteristics of several methods of electrical investigation to avoid the obligation of a continuous contact between the ground and the electrodes (Shima et al., 1996). Kinematics Electrical Resistivity Tomography (KERT) allows the measurement of apparent resistivity transects in ten depths of investigation, with a classical ERT format. The data are then inverted to produce a true resistivity 2D tomography. In this, the existing equipment allow to obtain an apparent resistivity transect within several pseudo depth, while KERT prospection allow to obtain an tomography with true inverted resistivity through the use of onthe-go sensors and a high sampling rate measurement approaches. Two dimensions are taken into account in the development of the measuring device. In addition, interpretation of the data is provided. Compared to common geophysical prospection, kinematic geophysical prospection generates a higher noise level. This high proportion of noise is mainly associated with the electrical coupling between mobile sensor and topsoil. Prior to the interpretation of the data, there is a preprocessing of measures phase, aimed at analyzing and correcting them. To address the noise concern, several approaches are possible. The first approach is to limit the bias. In the present case, use of classical static probes would be the solution. However, this is not compatible with high rate investigation. The second approach consists in data filtering to remove noise. Various tools can be used, for instance statistics: while the mean and the variance can serve to highlight the main trends of the measures, a filtering of outliers can be put in place relative to the thresholds (Macnae et al., 1984; Bellanger and Aigrain, 2006; Doucet and Johansen, 2010; Ferahtia et al., 2012) above which (maximum and minimum values) the measurements are filtered. Filtering can be also performed by rejecting property variations due to too large gradients (Starck et al., 1989). Temporal or spatial approaches to datasets are a second possibility. These highlight areas (space) or durations (time) in which the studied variable presents variations qualified as regular. The data processing serves to smooth (Fullana, 2002) the series of data showing unrealistic changes in the studied property, e.g. wet sand (prospected by drilling) connected to a resistivity of 10,000 Ω. The first studies on the treatment of smoothing geophysical data were carried out on time data, such as time electromagnetic measurements (Reninger, 2012). A classical treatment method for processing noise data aims to make the data discrete in terms of frequencies (Köhler

23

and Lorenz, 2005). In these studies, Fast Fourier Transform (FFT) analysis is used to determine the frequency spectrum of a series of measurements. The use of a low pass filter on the frequency spectrum serves to filter outliers (i.e. excessive gradients) and unrealistic data ranges with regard to the scale of prospection. A third approach to dealing with noise interpretation consists in the calibration of raw data on referenced values. This limits the interpretation of relative variations, whatever the absolute values. It is also possible only if the noise level is low relatively to the information level in the records, in other words: the noise/signal (N/S) ratio is sufficiently low. This paper presents an innovative ERT approach via a new device (KERT), accompanied by enhanced data treatment to smooth resistance data obtained through KERT prospection, and to calibrate it on a classical electrical resistivity tomography (limited in space). This study employed only the ERT device to develop a new geophysical method of investigation. With this methodology, KERT will be a method for large scale mapping, achieving accurate zoning of fields (adapted to pedological, archaeological or civil engineering applications according to measuring parameters, mainly probe spacing). First the device is presented along with the tools used for data treatment. Then, in the second part, the method is developed on a real site in order to capture all the real constraints of on-site prospection. The data processing is based on two main phases: (1) FFT analysis and (2) the determination of a corrective factor (Xc) to calibrate measurements of realistic ranges by a bias correction (on the basis of an ERT calibration measurement). In the third part, the validation of the method is performed on a second real site, independent from the first (used for development). In the last part some methodology aspects are discussed, before the concluding remarks. 2. Materials and methods 2.1. Technical parameters of the device KERT consists of a quad, referred to as traction vehicle in Fig. 1, towing movable electrodes called on-the-go sensors. The quad also carries the power and acquisition system (SyscalPro (Iris Instrument) and a computer). An optimized mode is available on the acquisition system allowing simultaneous measurement of 10 potential differences for some electrode arrays (Dipole-Dipole (DD), Wenner, Schlumberger). This makes it possible to adapt it to a device for mobile investigations. The configuration of the KERT device is dipole-dipole. The dipole-dipole array is composed of a couple of electrodes for current injection and ten pairs of electrodes for measuring the potential difference. For practical reasons and with regard to researches that are not developed in this paper, this device is currently developed with 50 cm probe spacing (a), limiting the depth of investigation to the first 2 m. This point could be easily changed to increase the depth of investigation. The KERT device is composed of 13 electrodes. The two first are current electrodes used for the injection of electrical current into the soil (labeled A and B). They are spaced by 1 interval labeled “a”, which here is equal to 50 cm. The 11 other electrodes (labeled P1 to P11) are potential electrodes, used to assess the potential drop along 10 intervals. This allows the calculation of apparent resistivity for various depths of investigation. As these depths are not real (not precisely known), we refer to “level” (ranking from 1 for the smallest probe spacing to 10 when the measuring probes are spaced by the 10 intervals), or else “pseudo depths” (linked to electrode spacing ranging here from 0.6a to 3a). The depths of investigation, estimated for inversion (Barker, 1989) from pseudo depths, are between 0.3 and 1.5 m. Mobile sensors are steel toothed wheels whose characteristics are studied in Guerrero (2014). Preliminary tests showed the outlier values of the first level of investigation (which corresponds to the smaller spacing between injection probes and potential probes). To improve the rough data in terms of noise quantity, the spacing between injection probes and first potential probes was fixed at 2a (i.e. 1 m). The initiation of the measurements

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O. Guerrero et al. / Geoderma 284 (2016) 22–33

a)

b) Fig. 1. The KERT device diagram and illustration in-situ, a) device as a whole, b) on-the-go sensors in dipole-dipole configuration with 50 cm interelectrode spacing and 10 levels of investigation.

was carried out by a wheel encoding the displacement of the whole device for positioning each measurement (i.e. odometer). This encoder wheel responds to the GPS imposed limitations in shaded areas i.e. under the trees which are present in the area. The accuracy of the encoder wheel reaches a centimeter, even at a speed of progression in the order of 5 to 8 km/h. The remote triggering of the injection current (AB) and the difference in potential measurement by all the pairs of electrodes (P1-P11) is thus carried out with a constant measurement step, despite the irregular speed of the device in the field. The constant measurement step can be set at least at 20 cm, with a speed of progression reduced b 3 km/h, and up to several meters with a speed of progression of 5 to 8 km/h. As the exploration is performed, a software package (Sysmar - Iris Instrument) creates the entire pseudo-section of apparent resistivity in real time. 2.2. Data processing Two steps are developed to successively smooth then calibrate data from KERT, leading to final values that are similar to those obtained by a static device, allowing interpretation with traditional tools. The two steps (de-noising and calibration) use data from a reference static ERT performed on a portion of the KERT transect, first to identify the “natural” variability of resistivities along the transect, and second to assess the resistivity ranges on the area. The first step of data processing is the smoothing of outlier values associated with random noise. In light of the studies already conducted in this context (Angelini and De Canditiis, 2000; Amato and De Feis, 2000; De Canditiis and De Feis, 2006), the geoelectric data smoothing analysis by Fast Fourier Transform (FFT) proves to be a relevant approach for

highlighting the frequencies and, therefore, the dimensions of the main geoelectrical structures measured. In this study, all the pseudo depths of investigation of the KERT are named level. Each level of the KERT is viewed as a set of data independent of other levels which is treated individually. Thus, in each level component, a KERT gives a series of data that can be represented by a frequency spectrum. Applying a treatment by FFT on a KERT transect yields the frequency spectrum in distance in which the unit of frequency is m−1 (Fig. 2), since the measurement points are sampled according to the distance travelled, with a step of measure α in meter. Fig. 2 represents the common data of apparent resistivity within the second level (same distance (x), same level (y)), between a KERT transect (length : 70 m, α = 0.5 m) and an ERT transect (length : 48 m, α = 1 m). The number of apparent resistivity data in a level of KERT is in this case 141, and only 48 data are in common with the ERT transect. The analysis of the frequency spectrum (Fig. 2) identifies the distribution of resistivities according to their frequency ranges. This representation corresponds to the resistivity variation linked to the wavelength of the measured phenomenon. Noise is classically characterized by very high frequency (short wavelength), particularly linked to the quality of the contact between probes and top-soils. Low frequencies, however, correspond to the different geoelectrical structures (larger for lower frequency). The use of an analysis by FFT consists in determining the low-pass frequency filter to remove the frequencies associated with the noise during the measurements. Then by performing an inverse Fourier Transform, the denoised signal is rebuilt. The discretization of the frequency spectrum depends on the step of measure (α) retained for the KERT measures. The determination of the threshold frequency of the

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a)

b) Fig. 2. a) noise signal for the second level of investigation using KERT, b) frequency spectrum of the apparent resistivity from the second level of investigation using KERT.

low-pass filter (fx) relies on the minimum size of heterogeneities to detect (λ). The relationship is described below (see Eq. (1)): fx ¼

1 λ:

ð1Þ

For instance, for fx = 0.25 m−1, the minimum size for soil structure which can be characterized is 4 m in length. Another approach is to determine fx relatively to the noise level. This approach is used as an indicator of decision making for choice of fx. This approach seems more relevant and better reflects the coherence of the studied site, compared with a more objective approach. This approach requires reasoning on a limited number of resistivity data (48 per level), but the results lead to 5 m wavelengths, which is significantly lower than the 48 m of the studied ERT transect. This approach is subject to discussion, but allows to orient the choice of the fx. The frequency that does not provide more information on the geoelectrical structures

can be considered as noise. The determination of this frequency threshold can be achieved objectively: the work is done on static ERT data, after which (according to similarity) we apply these observations to the kinematic survey (KERT). The analysis consists in degrading the reference signal (from static ERT) by successively decreasing the threshold frequency fx of the low-pass filter. Then an analysis of inverse Fourier transform is performed for each case with the aim of deriving the “percentage of variation (Δ%) between reference ERT and filtered ERT” as a function of fx, the percentage of variation being calculated on each point according to Eq. (2).


ρarj −ρafij
Δ% j ¼ 100  ρarj

ð2Þ

With Δ%j, the percentage of variation on the point j, ρarj the apparent resistivity on j on the reference static pseudo-section, and ρafij the

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apparent resistivity on point j on the filtered (with value f for low-pass filter frequency) pseudo-section. Δ% is the average value of Δ%j for each fx. In electrical prospection generally one can consider that 10% resistivity contrast corresponds to a significant contrast to detect a structure from the surrounding soil (Tabbagh, 1985). Considering the Δ% function of frequency, we can pick fx as the frequency value corresponding to Δ% = 10%. A filtering with a frequency lower than fx leads to keeping the measurement noise and intrinsic variability of soil, while a filtering frequency higher than fx leads to the erosion of information. Thus, the frequency higher than fx are removing because they are considered like bias (no pertinent information). Thereby, only the frequency lower than fx are keep to do an inverse Fourier transform. Once KERT data are de-noised, the second step of the KERT data processing is the calibration of resistivity values. Indeed, the average resistivity value on KERT is very high, due to the effect of contact resistance between moving probes and top-soils. As long as this resistance depends on the electrodes' characteristics, its value could be comparable for all the probes. Consequently, its contribution could be considered as a close constant for a constant spacing. Next, the data treatment in terms of calibration is defined level by level, with the determination of the calibration factor for each level. The static ERT performed on a portion of the KERT transect is the reference for completing this task. In practical terms, the objective is to determine an average shift within each level, between the apparent resistivity measured by KERT and ERT. We defined the calibration factor Xc that quantifies the shift between the apparent resistivity measured by a KERT and an ERT. The calibration factor Xc is obtained for each level of investigation by Eq. (3). Xc ¼

n logðρ 1 aKERT Þ ∑ n 1 logðρaERT Þ

ð3Þ

Thus, for a level of investigation, to calibrate data we obtain Eq. (4): 1 ρaERT ¼ ðρaKERT Þ =Xc

ð4Þ

with: n: number of comparable points within the level i. ρaKERT: smooth apparent resistivity at the x position, within the level i of a KERT. ρaERT: apparent resistivity at the x position, within the level i of an ERT. 2.3. Test sites Two test sites are considered: the first one for the development of the methodology, used for identification of the various measuring parameters influencing the prospection and the development of the data processing methodology; and the second site for the validation of the methodology developed in an independent context. The first site is located in Pessac (44° 47 ′52.81″N, 0° 36′ 34.35 ″ W), near Bordeaux in southwest France. The main geological surface of the site corresponds to colluvium of mixed origin (fluvial and wind) consisting of sand, gravel, and pebbles with a clay matrix. From the surface, the study area is composed of a backfill layer with varying thickness of about 0–1 m (Pratviel et al., 1978). This backfill layer is present only in the northern part of the site. In this specific part, a layer of sedimentary materials consisting of a succession of layers of gravel and sand to a depth of 5 to 10 m is present. All these Quaternary formations are on the surface of the calcareous substratum of the upper Miocene. The transect is 48 m in length, limited to the length of the static transect used as reference. The top–soil is covered by gravel and sparse grass. The second site is located in the south of Bordeaux (latitude longitude 44.745239° N 0.693154° W). The geology of the soil corresponds to the Dépée formation (Pratviel et al., 1978), consisting of sands and more or less homogeneous clay. The site is relevant as it has

homogenous surface soil of several meters, with no multiple variations in horizontal structures. The study area is a pathway in a forest of about 450 m in length with a slight slope from north to south. The topsoil is mainly composed of sand. 3. Results In this part, the development of the analysis of KERT data is proposed. Results are integrally elaborated on the first test site. 3.1. Raw data Fig. 3 shows the result after an inversion of the apparent resistivity (ρapp) of the KERT prospection campaign with regard to the reference ERT performed at the same coordinates, and under the same conditions (same date, same array, same settings, etc.). The ranges obtained varied strongly, showing 50 to 5000 Ohm.m with the ERT, and higher values for KERT. At this step, the resistivities on KERT are outside of plausible values. Comparing these raw data obtained in terms of relative variation to the ERT reference, it can be observed that KERT has lateral variations in resistivity ranges, with strong values between 0 and 30 m and lower values beyond. For depth as a factor, the ERT presents (in its first 24 m) a decrease in resistivity, however, for the KERT, this gradient is increasing. The large variation in ρ for two neighboring measures in the KERT case does not highlight the geometries of heterogeneities. From a qualitative point of view, these measures are not relevant to the materials observed on site. This reflects the strong disturbance of the measurements, indicates a strong bias in the measurements. These disturbances can be interpreted as noise related to the measurements, i.e. the intrinsic quality of the contacts of the on-the-go sensor (Guerrero, 2014). The analysis of the data from a KERT prospection emphasizes that measured resistivity cannot be directly interpreted through the traditional tools normally used for this type of measurement (Loke and Barker, 1996). The purpose of this paper is not to identify the causes of this difference (bias) between the apparent resistivity data of ERT and KERT, but to develop a method for treating apparent resistivity data of KERT to make these as interpretable measures. 3.2. FFT filtering for smoothing data An analysis is performed of the percentage of variation for the determination of the cutoff factor for the low pass. The graph in Fig. 4 presents a curve showing three domains: the first (fx b 0.2 m−1) where the curve presents a high negative slope translating the extensive erosion of data for a frequency filter that is too low; the second (0.2 b fx b 0.4 m−1) where there is only a weak influence of fx on Δ%, meaning a low influence of the exact fx value for filtering; and the third (fx N 0.4 m− 1) curve shows a sharp negative slope translating the decrease in measurement noise (generally associated with higher frequency). This curve clearly shows low frequency limits before significant erosion of data (0.2 m−1) and the high frequency limits of measurement noise (0.4 m− 1). Furthermore, relatively to the analysis of Δ%, and the threshold of 10% (as the threshold for significant resistivity change - Tabbagh, 1985), it is observed (Fig. 4) that if fx N 0.2 m−1, the erosion of data from ERT is b10%. If fx b 0.2 m−1, there is a deviation between the reference and the filtered tomography N 10%. In this case, with fx = 0.2 m−1 the inverse Fourier transform serves to smooth the noise, keeping an accurate dataset. If fx is lower, the inverse Fourier transform causes a loss of information. To illustrate the influence of this method of smoothing geoelectrical data, we can study the evolution of the correlation coefficient (Table 1) between the apparent resistivity of an ERT and a smoothed KERT with different filter frequencies (0.35 m−1; 0.2 m−1; 0.1 m−1; 0.05 m−1). The calculation of the correlation coefficients between the apparent resistivity of an ERT and a smoothed KERT shows the main variations in

O. Guerrero et al. / Geoderma 284 (2016) 22–33

27

Fig. 3. Comparison of true resistivity, obtained after the inversion of ERT and raw KERT data.

the apparent resistivity related to the ERT observed within the KERT transect once the geoelectrical data are smoothed. In Fig. 5, it also follows that the smoothing of the KERT data makes analysis possible as it presents same trend in terms of apparent resistivity, but not the same value ranges. This data smoothing highlights geophysical structures larger than 5 m. Fig. 5 allows comparison of apparent resistivity transects, for the same level (pseudo depth) for KERT and ERT. The data presented are obtained after smoothing by FFT analysis with the application of a 0.2 m−1low-pass filter. Within a level of exploration (level 2), the expected measurements (ERT) and the effective measurements (KERT), expressed as a logarithm, show a relatively constant offset. This smoothing of the measurements by the FFT inverse analysis emphasizes that KERT data contain information in terms of relative variations in resistivity, allowing consideration of the zoning along the transect. This led to the proposal of the calibration factor. 3.3. Calibration of smoothed KERT relatively to reference ERT Fig. 6 is a representation of the relations between the apparent resistivity of the KERT and the ERT. This illustrates the impact of the different processing on the data. This figure shows the measurement values of apparent resistivity smoothed by FFT grouped into 5 major classes, each corresponding to a level of investigation. These apparent resistivities are described (average) for each level by Eq. (2), with the values of

the calibration factor Xc increasing with depth. The factors Xc are calculated for each level of investigation of a KERT comparable to that of an ERT, requiring that the KERT and ERT measurement values are carried out at the same coordinates. To determine the calibration factors Xc, we compare a KERT and en ERT made at the same position. By the characteristics of the surveys, we can compare 45 values of apparent resistivity per level of exploration. The calibration factors Xc are quantified in Table 2. On this site, we note that the coefficients evolve from 1.29 to 3.14 according to the levels. In an ideal case, with no calibration needed, the Xc values would be equal to 1. The coefficients of variation of calibration factors Xc are constant according to the different levels of investigation. The increase in the Xc values as a function of the level (i.e. depth of investigation) shows that biases increase with depth.

3.4. Study of improved resistivity data With an analysis of the RMSE (Root Mean Square Error) factor we assessed (Eq. (5)) the effects of various data treatments on the KERT apparent resistivity prospection, in relation to the apparent resistivity of the reference ERT. The relative comparison of RMSE allows quantification of the evolution of apparent resistivity after each processing step (Table 3). The choice of this indicator is based on the fact that the RMSE highlights the large differences between the ERT and KERT resistivities within the same level. The average noise level (variability) of an ERT is evaluated by repetition of the measurement, and then by an analysis of the differences recorded. This gap between the same measurement values of apparent resistivity is an indicator of a variability of the measurements, giving a signification level of variation. Two sets of measurements have been successively acquired by leaving the device in place between the two sequences of measurement for determining the noise inherent in ERT measures. Table 3 represents the RMSE resulting from the comparison between the two sequences of ERT

Table 1 Correlation between the apparent resistivity of the reference ERT and the KERT, depending on the different frequencies of smoothing. Threshold frequency of the low-pass filter (m−1)

Fig. 4. Loss of information due to smoothing by low-pass filter.

Correlation. Coefficient.

Raw data

0.35

0.2

0.1

0.05

0.6558

0.84

0.92

0.91

0.88

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O. Guerrero et al. / Geoderma 284 (2016) 22–33

Fig. 5. Result of a smoothing process with a low-pass filter frequency of 0.2 m−1 within the second level of investigation.

(Reference), the comparison between the ERT of reference and the raw KERT, the smoothed KERT (FFT), and the smoothed calibrated KERT (CFFT). sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 RMSE ¼ : N

i¼N

∑ ðρiaERT −ρiaKERT Þ2 i¼1

ð5Þ

with: N: number of apparent resistivity data. ρiaERT: ERT apparent resistivity. ρiaKERT: KERT apparent resistivity. The analysis of the RMSE as well as of the average apparent resistivity and the coefficient of variation (CoV) can illustrate two influences of different treatments performed when measuring the apparent resistivity. Firstly, the study of CoV illustrates that smoothing by low-pass filter of the apparent resistivity reduces the measurement bias significantly. Secondly, in terms of the RMSE, it emerges that the calibration of the KERT apparent resistivity yields variations in resistivity comparable to those measured by the reference ERT and also in the comparable ranges. Fig. 6 illustrates the apparent resistivities according they are raw data (from KERT) or processed data (FFT and calibration), in function of reference data (from ERT). It is shown the improvement of measured resistivity due to the data processing, the final coefficient of correlation is 0.87. The treatments of the KERT data (FFT smoothing and calibration)

help to make the KERT raw data useful for interpretation (Fig. 7). By comparing the two sections, it appears that that the lateral zoning of geo-electrical structures obtained with processed KERT is consistent with ERT. One can note the two distinct zones along transect: before 25 m where the top-soil structures are highly resistive (N500 Ohm.m), and after 25 m where the top-soil is more conductive (100 to 300 Ω.m). The deeper part of the transect presents very low resistivities (b100 Ω.m) all along. These spatial distributions are qualitatively the same with the two devices. Nevertheless there is a resistivity range's shift between KERT and ERT results: ERT range appears less resistive than KERT for instance on the first part of the tomography of reference which present value lower than 500 Ω.m at 1 m in depth, or else on the second transect part with some resistivities as lower as 70 Ω.m at the surface. Even though the KERT is compared here with the ERT used for its calibration, it shows that the FFT allows the data to be cleaned by conserving the relative variation which is of interest for interpretation. Then, through a calibration phase done on a single average value by level, the treatment gives a good range for the resistivity values, even if the correspondence is not exact. This is a basis for a more advanced procedure where the ERT for calibration is performed only on a part of the prospected transect, and the Xc factors (assessed on this ERT) will be generalized along the entire KERT transect. In terms of the analysis of true resistivity (inverted with RES2DInv), we can observe in this case

Fig. 6. Relations between the apparent resistivity of the KERT and the ERT, effects of the treatments (smoothing process and calibration) on the distribution of apparent resistivity.

O. Guerrero et al. / Geoderma 284 (2016) 22–33 Table 2 Determination of factors Xc according to levels of investigation. Calibration factors Xc Levels

Average

C.V. (%)

Nb

Level 1 Level 2 Level 3 Level 4 Level 5

1.29 1.63 1.95 2.65 3.14

11 11 12 11 12

45 45 45 45 45

study that the low resistivities are undervalued by KERT. At this stage, no explanation is given. Nevertheless it is clear that from a qualitative point of view, the zonation of the transect could be performed sharply along the transect as well as in depth, in a satisfactory manner. Thus, at present stage of development of the measuring device, the ERT data still need to be assessed in terms of performance to calibrate a KERT. This calibration associates with each KERT level of investigation, a unique factor Xc. For each level considered, the apparent resistivity measured at each point (ρapp) obtained after smoothing of the data by FFT, is treated according to Eq. (2) to obtain a calibrated apparent resistivity (C-FFT) designated by ρ'app.  1 ρ0app ¼ ρapp =Xc

ð4Þ

3.5. Validation on test site number 2 Preliminary electric and electromagnetic geophysical surveys have identified the existence of a zone with low resistivity (attached to an area of rainwater retention). The location of this transition of the geoelectrical structures is chosen to implement two neighboring ERT of 72 electrodes (Dipole-Dipole device 1 m spacing between electrodes). The combination of these two ERT can be used to form a continuous ERT transect of 120 m in length and 3.5 m in depth. As in the first case we note significant differences between the initial KERT results and the reference static ERT on the same portion: large difference in terms of resistivity ranges, and abnormal resistivity ranges for KERT (up to 650,000 Ohm.m in terms of apparent resistivity). The raw KERT data look totally incoherent compared to static reference ERT (Fig. 8a, b & d). All the analyses and treatments on measuring the apparent resistivity previously presented are applied in this case (Fig. 8c). The first step is the FFT filtering with the threshold low pass filters fixed to 0.2 m−1. Then the second step: the calculation for each level of the Xc factor is performed. Table 4 represents the calibration factors Xc that were obtained on this study site, varying between 1 for the top level and 1.35 in depth. Note that as ERT is performed with 1 m spacing, for 0.5 m spacing with KERT, a compromise is achieved by considering only even-numbered levels (2, 4, 6, etc.). As expected from the study in the first part, the variations in factors Xc show that the KERT measuring device is more sensitive to measurement bias in its deepest investigation levels. The Fig. 8d shows the result of the ERT survey which can be qualitatively compared to the KERT perform on the same location after numerical treatment (C-FFT KERT, Fig. 8c). Both figures. Show globally the same electrical structures useful to establish a zoning of the cross-

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section. We can firstly note on both figures a decrease in resistivity values as a function of the depth, except for the sides of the low part of the ERT figure which show high values of resistivity which are not visible on KERT. For others depths, the evolution of resistivity with depth is very similar on both figures. Secondly, we can clearly observe on both figures at about 170 m, a “column” of lower resistivity represented in yellow-green. Such a structure is typically the kind of information that we search in a zoning aim. Finally, at a middle depth, we can observe on both figures an alternation of red/orange zones. A quantifiable comparison is more difficult because the variability in resistivity values is different between ERT and KERT. Nevertheless, for the aim that has been announced (establishment of an electrical zoning of a cross-section), this qualitative analysis shows that the same structures are well identified with both methods. The KERT prospection, coupled with data treatment by an FFT analysis, reveals the main geoelectrical structures of the soil, and through an appropriate choice of the low-pass frequency, it allows us to focus on the analysis of the major true resistivity contrasts within the transect. The comparison between the resistivity of ERT and treated resistivity KERT can highlight the relative agreement between measurements. This correspondence is marked even if some differences can be noted at the limits of higher or lower resistivities, by comparison of reference ERT and final KERT. By studying the different geoelectrical structures, identified by this transect and the in-situ observations, we note different zones of low resistivity (interpreted as preferential infiltration areas) on the KERT transect for x = 64 m; 160 m; 290 m and 350 m. This test on a real site, based on the application of experimental site experimentation, proves that on the one hand the device can perform a large-scale transect (420 m), and on the other hand that the methodology based on the FFT filtering with a low pass filters taken about 0.2 m−1 is well adapted to our site. The comparison between the KERT and an ERT transect performed on a limited part of this KERT transect allowed us to determine each Xc factor of calibration for all the levels of investigation. This local Xc factor can be generalized to the entire KERT transect to calibrate the apparent resistivity. Furthermore, resistivity can be inverted, and a 420 m long transect with a sampling of 1 m and ten levels of investigation can be studied via its true resistivity with true depths. For an investigation aiming at the zoning of soil structures in depth along transect this methodology is now possible. 4. Discussion For both sites, located in the Bordeaux area, we note similar initial results for the KERT with resistivity ranges which first look doubtful. After data processing, for both sites the resistivity ranges appear to be closer to what is expected in their respective areas: between 50 and 1500 Ω.m for the first and 50 to 10,000 for the second. Relatively to other works in the same area, the ranges are in agreement with the high level of heterogeneity of this part of the Bordeaux area (Chretien et al., 2014; Marache et al., 2009) or in a larger region (André et al., 2012). The methodology has been successfully tested on two significantly different sites, proving its operability. Considering accuracy defined by Adamchuck et al. (2004) as “how well the sensor measurements correlate an actual soil property that is determined using a conventional (reference) measurement technique”, one can consider that these developments lead to an accurate method in terms

Table 3 Evolution of the noise of measurement based on the treatment provided to the KERT data. Comparaisons

Between two ERT Between ERT and raw KERT Between ERT and smoothed (0,2 m−1) KERT Between ERT and smoothed calibrated KERT (C-FFT)

RMSE (Ω.m) Average Resistivity(Ω.m) CoV(%)

0.02 478

10.7.105 1.48.1012

8.1.104 4.4.105

33 512

1.59

5.8

2.61

1.55

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O. Guerrero et al. / Geoderma 284 (2016) 22–33

Fig. 7. Results, in true resistivity, of KERT treatment after smoothing, calibration and inversion of apparent resistivity.

of measurement. At all events, the question could be seen as being more complex since the electrical properties of soils are linked to a number of physical characteristics: moisture, salinity, clay content, as well as

temperature, etc. Some of these parameters are given for a soil, others could evolve over time. Generally, simplification of these parameters is performed according to the hypothesis of achieving digital

Fig. 8. Results of a KERT prospection with true resistivity over a great length, a) raw KERT transect represented with a “free” scale of resistivity, b) raw KERT transect represented with the reference ERT resistivity scale, c) C-FFT KERT transect represented with the reference ERT resistivity scale, d) reference ERT with its resistivity scale.

O. Guerrero et al. / Geoderma 284 (2016) 22–33 Table 4 Variations of the calibration factors Xc, according to levels of investigation. KERT levels of investigation

Xc average Variation Coefficient (%)

Lvl 2

Lvl 4

Lvl 6

Lvl 8

Lvl 10

1.00 5

0.98 9

1.06 12

1.34 9

1.35 10

representation of soils (Séger et al., 2014; Chaplot et al., 2010). So the discussion in this chapter is limited to the question of the data treatment, leaving considerations on methodology interpretation for further developments. The question addressed is the ability to record data which could be processed to propose a resistivity transect in depth for inverse analysis with classical tools, leading to an inverted resistivity tomography, which is not performed by the other techniques mentioned in the introductory paragraph. The main question is about data noise, and the dynamic range needed for accurate soil characterization. Compared to classical static devices, the main difference is the use of on-the-go sensors. The high noise level observed is then logically attributed to them, according to two main effects: (1) the quality of electrical coupling between sensor and top soil; (2) the velocity of device influencing the electrical coupling. Primarily, the contact resistance of the on-the-go sensors' electrode is less likely to be linked to top-soil than classical electrodes for ERT. In this study, consideration of a distance lower than 500 m is used for convenience in terms of the speed of the moving device. The latter also factors in to the quality of the electrical contact between probes and soil. All these factors contribute largely to the noise field data measured. According to Lueck and Ruehlmann (2013), with good galvanic coupling between electrode and soil, the influence of driving velocity is negligible. Nevertheless they mention the influence of coulter depth variations which could lead to noise if the velocity is higher than 8 km/h. Indeed, the quality of contact between topsoil and electrode-coulter is one of the main sources of noise. We observed with a test on moistened grass (with morning dew for instance) that electrical coupling is improved and leads to a significant decrease in noise. On the contrary, in measurements on gravelly dry soil, bad electrical coupling can limit the investigation. These results are in accordance with those of Mueller et al. (2003) or Lück et al. (2009) on the influence of measurement conditions in terms of moisture and type of top soils. The electrode's movement could also influence the characteristics of output current, and hence the input voltage which could decrease to a few millivolts (Lueck and Ruehlmann, 2013; Shima et al., 1996). This effect is notably important in the case of deeper investigation channels (with measurement electrodes far from the injection electrodes), where the measured voltages are already weak. In this case output voltages could have a low signal-to-noise. The weaker voltage could even be comparable to the natural spontaneous potential of the soil, thus enhancing noise. Various tests led us to prefer to put in the injection probes first followed by the measurement potential sensors. In this configuration, due to the effect of traction of the latter sensors on the former, we note that the electrical coupling is better for the first sensors. This arrangement is to privilege for the injection probes. Velocity mainly influences the resolution of the investigations. Lueck and Ruehlmann (2013) suggest a velocity in the range of 5 to 15 km/h, in order to get about one point per 5 m (with their device). According to our device and after data treatment (considering 0.2 m−1 for low pass frequency) we reach this resolution with de-noised data. This resolution does not appear to be suitable for very fine detection of soil structures shorter than 5 m, but this approach does allow a quick delineation of the main soil units on a large area for accurate zoning. If this first investigation is not sufficient it could be completed by either another technique (classical ERT for instance) or a new transect, performed more slowly and hence in shorter investigation steps. In this way, combining

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fast and slower investigation of the zone under consideration, we can speak about prospecting optimization. The issue of the speed of investigation and the quality of contact must be addressed by its influence on measurement sensitivity. Indeed the current injection during 0.25 s combine with the on the go process at about 6 km/h (1.66 m/s) results to an injection on a 40 cm interval in length. The quality of contact as well as the distribution of current density is then continuously changing for each resistivity measure. As current density is more influenced by lower resistivity than by higher, it leads to overestimate the influence of conductive bodies. This effect is more important when the resistivity is low. This can be seen on Figs. 7 and 8 when one compares the resistivity distribution resistivity distribution. Concerning the number of channels, we note the range for the various Xc on the respective levels on the two sites. They are in the same range, evolving between 1 and 3.14. This mainly traduces the diverse conditions on the two sites. The increase with depth observed on the two sites reflects the decrease in reliability with depth. For upper levels the measurement looks more representative of soil resistivity variation, and for the latter channel the link between measurement and soil properties looks thinner. Of course, the work with apparent resistivity which includes all the depths from the surface partly explains this point; indeed, the depth of investigation corresponds to the thickness of the soil taken into account by measurement from the surface to the nominal depth of investigation. For greater depths of investigation, the contribution of deeper layers is then averaged with the upper layers. At all events, for greater depths of investigation, the use of a more distant sensor is also a cause of this. The further the sensor is from the injection dipole, the weaker the potential measured. This leads to an increase in the noise part (as explained above). The array used for this application is the dipole-dipole. This array presents the lesser quality of signal measured due to its high sensitivity to measurement noises (Dahlin and Zhou, 2004). Nevertheless this solution presents several advantages, essentially practical: it allows the use of the optimized mode for acquisition on SyscalPro, leading to high rate sampling for on-the-go prospecting. Additionally, this array avoids the need for any remote electrodes (which would limit the interest of high sampling rate measurement prospect). This array, imposed by technological constraints, presents a good sensitivity to the variations in horizontal and vertical physical properties (Dahlin and Zhou, 2004). Finally, the ability to consider the limited entries for electrodes (11 channels of measurement), leading to recording of the pseudo-section, is also a positive factor. Still today, with this approach, after data processing, we can have a pseudo-section of apparent resistivity which can be studied with classical tools for inversion. Thanks to this point the KERT is the right approach for assessing variations in true resistivity as performed with classical tomography, combined with high rate investigation. Even if this technique can operate for high rate sampling investigation on sub-soil along transect, two main questions can be addressed for improvement. The first is that, the methodology need to perform an ERT of reference on a limited part of transect. It is used for the assessment of the fx low pass cutoff frequency for FFT processing, and for the evaluation of the Xc factors for the calibration of data. This step limits the speed of investigation, and it needs to be studied on the location and the minimum length of ERT of reference for the better reliability of results. The second is the question of the resistivity range's shift between processed KERT and reference ERT, partly explained to the injection length with KERT which promotes conductive body's influence. The quality of accuracy for the higher and lower resistivity has shown some weaknesses concerning the values, limiting the analysis of correlation on resistivity values. However the qualitative variations are reliable. 5. Conclusions We developed a new device and data treatment for qualifying the spatial variability of resistivity in subsurface soil. Our device works

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O. Guerrero et al. / Geoderma 284 (2016) 22–33

with on-the-go sensors. The phases of each study and the performance of tests helped in developing a prototype consisting of 13 on-the-go sensors with 0.5 m spacing (2 electrodes for the injection of current and 10 couples of electrodes for measuring the potential difference). This prototype performs measurements of apparent resistivity simultaneously on 10 levels of investigation during the movement of the device. With this configuration, the minimum step of measure can be of 0.1 m and the depth of investigation can be of 1.4 m. This depth of investigation can be increased in parallel to the interelectrode spacing. All the elements developed in this paper are also applicable for a wider interelectrode spacing. The device not only yielded information about lateral heterogeneity within a large-scale site, but also about the vertical variability of resistivity. All the analyses carried out to study the potentials of this prototype permitted us to identify the different biases in the KERT data, such as random variations in the measurement of ρapp. To filter these sources of bias, a method to treat the KERT data was developed. This process consists of a phase of smoothing using Fourier Analysis (FFT). The determination of the inverse Fourier Transform low pass-filter frequency (fx) is based on the minimum loss of information within the KERT data prospection. Next comes a recalibration of the ρapp by a Xc factor to ranges of comparable values to those measured by an ERT of reference which remains necessary. We notice that in some cases (when the contact between the ground and the on-the-go sensors appears to be of good quality), the value of Xc is close to the unit for the 10 levels of a KERT. If not, the assessment of Xc appears to be a satisfactory approach, allowing us to translate the correct resistivity ranges. Calibrating the KERT data is intended to make the data usable for performing measurement inversion. This gives a tomography with true resistivity and true depths, which makes for more original results in terms of technical developments. The device and the protocol of analysis developed offer less painstaking (reduced time) prospection as compared to a conventional ERT, placing geoelectrical prospection among the high-yield prospections. This type of electrical device opens up new possibilities for visualizing soil heterogeneities within large-scale prospection.

Acknowledgments This work was done within the framework of the program D2SOU (Développement Durable et SOls Urbains). It is co-financed by the French National Agency (ANR) (ANR-09-VILL-0005-02), and started in 2009 and finished in 2015, in collaboration with BRGM, GEOCARTA, SEP Poitoux, REEDS and I2M. The authors would like to thank F. Naessens for his hard work and his help in constructing and mounting the on-the-go sensors and the device system. We would like to thank the anonymous reviewers for their constructive comments which significantly improved the quality of the manuscript.

References Adamchuck, V.I., Hummel, J.W., Morgan, M.T., Upadhyaya, S.K., 2004. On-the-go soil sensors for precision agriculture. Comput. Electron. Agric. 44, 71–91. Amato, U., De Feis, I., 2000. Smoothing data with correlated noise via Fourier transform. Math. Comput. Simul. 52, 175–196. André, F., Van Leeuwen, C., Saussez, S., Van Durmen, R., Bogaert, P., Moghadas, D., de Rességuier, L., Delvaux, B., Vereecken, H., Lambot, S., 2012. High-resolution imaging of a vineyard in south of France using ground-penetrating radar, electromagnetic induction and electrical resistivity tomography. J. Appl. Geophys. 78, 113–122. Angelini, C., De Canditiis, D., 2000. Fourier frequency adaptive regularization for smoothing data. J. Comput. Appl. Math. 115, 35–50. Barker, R.D., 1989. Depth of investigation of collinear symmetrical four-electrode arrays. Geophysics 54, 1031–1037. Bellanger, M., Aigrain, P., 2006. Traitement numérique du signal – Théorie et pratique. 8ème édition. Dunod éd 465 pp. Besson, A., Cousin, I., Samouelian, A., Boizard, H., Richard, G., 2004. Structural heterogeneity of the soil tilled layer as characterized by 2D electrical resistivity surveying. Soil Tillage Res. 79, 239–249.

Blais, J.P., 2004. Méthodologie mise en œuvre par EDF pour la détection de fuites dans les ouvrages en remblais par méthodes non destructives, EDF-SGG. Symposcience communication 18 pp. Buvat, S., Thiesson, J., Michelin, J., Nicoullaud, B., Bourennane, H., Coquet, Y., Tabbagh, A., 2014. Multi-depth electrical resistivity survey for mapping soil units within two 3 ha plots. Geoderma 232-234, 317–327. Chaplot, V., Lorentz, S., Podwojewski, P., Jewitt, G., 2010. Digital mapping of A-horizon thickness using the correlation between various soil properties and soil apparent electrical resistivity. Geoderma 157, 154–164. Chretien, M., Lataste, J.F., Fabre, R., Denis, A., 2014. Electrical resistivity tomography to understand clay behavior during seasonal water content variations. Eng. Geol. 169, 112–123. Christensen, N.B., Sorensen, K., 2001. Pulled array continuous electrical sounding with an additional inductive source: an experimental design stydy. Geophys. Prospect. 49, 241–254 in Besson, 2007. Clomont, G., 2008. Michel Martinaud (1946-2008). ArchéoSciences 32. Coulouma, G., Samyn, K., Gradnjean, G., Follain, S., Lagacherie, P., 2012. Combining seismic and electric methods for predicting bedrock depth along a Mediterranean soil toposequence. Geoderma 170, 39–47. Dabas, M., 2009. Theory and practice of the new fast electrical imaging system ARP. Geophys. Landsc. Archeol. 105–126. Dabas, M., Hesse, A., Tabbagh, J., 2000. Experimental resistivity survey Wroxeter archeological site with a fast and light recording device. Archeolog. Prospect. 7, 107–118. Dahlin, T., Zhou, B., 2004. A numerical comparison of 2D resistivity imaging with 10 electrode arrays. Geophys. Prospect. 52, 379–398. De Benedetto, D., Castrignano, A., Sollitto, D., Modugno, F., Buttafuoco, G., Lo Papa, G., 2011. Integrating geophysical and geostatistical techniques to map the spatial variation of clay. Geoderma 171-172, 53–63. De Canditiis, D., De Feis, I., 2006. Pointwise convergence of Fourier regularisation for smoothing data. J. Comput. Appl. Math. 196, 540–552. Doucet, A., Johansen, A.M., 2010. A Tutorial on Particle Filtering and Smoothing: Fifteen Years later. In: Crisan, D., Rozovsky, B. (Eds.), Handbook of Nonlinear Filtering. Cambridge University Press 39 pp. Ferahtia, J., Djarfour, N., Baddari, K., Kheldoun, A., 2012. A fuzzy logic-based filter for the removal of spike noise from 2D electrical resistivity data. J. Appl. Geophys. 87, 19–27. Friedel, S., Thielen, A., Springman, S.M., 2006. Investigation of a slope endangered by rainfall-induced landslides using 3D resistivity tomography and geotechnical testing. J. Appl. Geophys. 60, 100–114. Fullana, J.M., 2002. Une technique de lissage de données basée sur la théorie de la régularisation. C. R. Mécanique 330, 647–652. Guerrero, O., 2014. Comparaison et couplage de méthodes géophysiques pour une reconnaissance optimisée des sols en milieu périurbain Mémoire de Thèse Université de Bordeaux 274 pp. Guerrero, O., Lataste, J.F., Marache, A., Breysse, D., 2013. High Yield Electrical Propsection for Characterization of Soil. Fourth International Conference on Geotechnical and Geophysical Site Characterization, Porto de Galinhas, Pernambuco, Brésil Vol. 1, pp. 587–595 18–21 septembre 2012. Hesse, A., Jolivet, A., Tabbagh, A., 1986. New prospects in shallow depth electrical surveying for archeological and pedological applications. Geophysics 51, 585–594. Jakosky, J.J., 1938. Method and apparatus for electrical exploration of the subsurface, United States Patent Office, 2.105.247 Köhler, T., Lorenz, D., 2005. A Comparison of Denoising Methods for one Directional Time Series. Technical Report, Deutsche Forschungsgemeinschaft, DGF SSP Priority Programme Vol. 1114 15 pp. Lew, J.J., 1997. Subsurface utility engineering: an initial step in project Developpement. J. Constr. Educ. 2, 109–118. Loke, M.H., Barker, R.D., 1996. Rapid least-squares inversion of apparent resistivity pseudosections by a quasi-Newton method. Geophys. Prospect. 44 (1), 131–152. Loke, M.H., Chambers, J.E., Rucker, D.F., Kunas, O., Wilkinson, P.B., 2013. Recent developments in the direct-current geoelectrical imaging method. J. Appl. Geophys. 95, 135–156. Lück, E., Gebbers, R., Ruehlmann, J., Spangenberg, U., 2009. Electrical conductivity mapping for precision farming. Near Surf. Geophys. 7, 15–25. Lueck, E., Ruehlmann, J., 2013. Resistivity mapping with GEOPHILUS ELECTRICUS – information about lateral and vertical soil heterogeneity. Geoderma 199, 2–11. Lund, E.D., Christy, C.D., Drummond, P.E., 1999. Practical Applications of Soil Electrical Conductivity Mapping, Veris Technologies. Proceeding of the 2nd European Conference on Precision Agriculture 9 pp. Macnae, J.C., Lamontagne, Y., West, G.F., 1984. Noise processing techniques for time-domain EM systems. Geophysics 49, 934–948. Marache, A., Breysse, D., Piette, C., Thierry, P., 2009. Geotechnical modeling at the city scale using statistical and geostatistical tools: the Pessac case (France). Eng. Géol. 107, 67–76. Meric, O., 2006. Etude de movement de terrain par méthodes géophysiques Mémoire de thèse Université Joseph Fourier, Grenoble 252 pp. Mueller, T.G., Hartsock, N.J., Stombaugh, T.S., Shearer, S.A., Cornelius, P.L., Barnhisel, R.I., 2003. Soil electrical conductivuty map variability in limestone soils overlain by loess. Agron. J. 95, 496–507. Neiderleithinger, E., Abraham, O., Mooney, M., 2015. Geophysical Methods in Civil Engineering: Overview and New Concepts. International Sympotium Non-Destructive Testing in Civil Engineering (NDT-CE) September, 6 pp. Panissod, C., Dabas, M., Jolivet, A., Tabbagh, A., 1997. A novel mobile multipole system (MUCEP) for shallow (0-3 m) geoelectrical investigation: the “vol-de-canards” array. Geophys. Prospect. 45, 983–1002.

O. Guerrero et al. / Geoderma 284 (2016) 22–33 Panissod, C., Dabas, M., Hesse, A., Jolivet, A., Tabbagh, J., Tabbagh, A., 1998. Recent developments in shallow-depth electrical and electrostatic prospecting using mobile arrays. Geophysics 63, 1512–1550. Peyraube, N., Lastenet, R., Lopez, B., Sirieix, C., Naudet, V., Denis, A., 2012. Epikarstic Hydrogeological Reconnaissance Using Geophysical Methods. Case Study of the Lascaux Cave (France), 39 IAH Congresse, Niagara Falls, Canada 16–21 september. Pratviel, L., Duvergé, J., Dubreuilh, J., Wilbert, J., Alvinerie, J., Astié, H., Gayet, J., Duphil, J., 1978. Carte géologique de la France à 1/50 000, Pessac (n°827), Notice d'explication, Ministère de l'industrie du commerce et de l'artisanat. Bureau de Recherches Géologiques et Minières. Service Géologique National, Orléans 37 pp. Reninger, P.A., 2012. Méthodologie d'analyse de levés électromagnétiques aéroportés en domaine temporel pour la caractérisation géologique et hydrologique Mémoire de thèse Université d'Orléans 190 pp. Samouëlian, A., Cousin, I., Tabbagh, A., Bruand, A., Richard, G., 2005. Electrical resistivity survey in soil science: a review. Soil Tillage Res. 83, 173–193. Séger, M., Guérin, R., Frison, A., Bourennane, H., Richard, G., Cousin, I., 2014. A 3D electrical resistivity tomography survey to characterise the structure of a albeluvic tonguing

33

horizon composed of distinct elementary pedological volumes. Geoderma 219-220, 168–176. Shima, H., Sakashita, S., Kobayashi, T., 1996. Developments of non-contact data acquisition techniques in electrical and electromagnetical exploration. J. Appl. Geophys. 35, 167–173. Starck, K.M., Hanstein, T.H., Eilenz, H.N., 1989. LOTEM data processing for areas with high cultural noise levels. Phys. Earth Planet. Inter. 53, 261–269. Tabbagh, A., 1985. The response of a 3-dimensional magnetic and conductive body in shallow depth electromagnetic prospecting. Geophys. J. R. Astron. Soc. 81, 215–230. Tabbagh, A., 1992. Méthodes géophysiques appliqués à la prospection archéologique. Mémoires de la Société Géologique de France, n°161, pp. 9–15. Tabbagh, A., Dabas, M., Hesse, A., Panissod, C., 2000. Soil resistivity: a non-invasive tool to map soil structure horizonation. Geoderma 97, 393–404. Taillet, E., Lataste, J.-F., Rivard, P., Denis, A., 2014. Non-destructive evaluation of cracks in massive concrete using ds resistivity logging. NDT & E Int. 63, 11–20.