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SUMMARY In general, the inverse problem of electrical resistivity tomography (ERT) is treated using a deterministic algorithm to find a model of subsurface resistivity that can numerically match the apparent resistivity data acquired at the ground surface and has a smooth distribution that has been introduced as prior information. In this paper, we propose a new deep learning algorithm for processing the 3-D reconstruction of ERT. This approach relies on the approximation of the inverse operator considered as a nonlinear function linking the section of apparent resistivity as input and the underground distribution of electrical resistivity as output. This approximation is performed with a large amount of known data to obtain an accurate generalization of the inverse operator by identifying during the learning process a set of parameters assigned to the neural networks. To train the network, the subsurface resistivity models are theoretically generated by a geostatistical anisotropic Gaussian generator, and their corresponding apparent resistivity by solving numerically 3-D Poisson's equation. These data are formed in a way to have the same size and trained on the convolutional neural networks with SegNet architecture containing a three-level encoder and decoder network ending with a regression layer. The encoders including the convolutional, max-pooling and nonlinear activation operations are sequentially performed to extract the main features of input data in lower resolution maps. On the other side, the decoders are dedicated to upsampling operations in concatenating with feature maps transferred from encoders to compensate the loss of resolution. The tool has been successfully validated on different synthetic cases and with particular attention to how data quality in terms of resolution and noise affects the effectiveness of the approach.

Imaging characterization of a heterogeneous alluvial aquifer at a decametric scale is presented. The characterization relies on responses to oscillatory pumping tests led in two different wells and at two different periods of oscillation (5 and 10 min). These specific oscillatory responses are extracted from the hydraulic pressure values, measured in 13 boreholes during the pumping tests, through a data processing procedure. Then, a deterministic inversion process, led with a two-dimensional hydraulic properties model, aims to reproduce this set of oscillatory responses, in a frequency domain, by optimizing the distribution of the property values in the model. Two inversion processes are led separately with each set of responses corresponding to the two periods of oscillation used, and one joint inversion is led with the set of all responses together. The inversion results image the heterogeneities in the distribution of the field properties. The results suggest that longer periods of oscillation (in this case 10 min) permit characterization of larger areas around the pumping wells. In contrast, shorter periods (in this case 5 min) propagate more readily in the conductive zones near the pump and provide less information for the less conductive areas. Therefore, it appeared that performing a joint inversion, combining the information carried by the responses to both periods, provided more information on the heterogeneous distribution of the field properties and resulted in better constrained property maps than the ones obtained from separate inversions.

The hydraulic characterization of a highly anthropized coastal aquifer in France is presented. The current industrial operations of the study site prevent the use of standard ‘active’ hydrogeological investigation methods (pumping, slug tests). However, the studied field is bordered on its north-western side by a channel directly connected to the sea, which allows for characterization of the hydraulic properties of the aquifer from its natural responses to the channel’s tidal signal. Piezometers (37) were monitored, from which oscillatory water-level responses (amplitude and phase-offset) to the tidal signal were extracted through linear regression and fast Fourier transform. A two-dimensional (2D) numerical model in the frequency domain was built to simulate the oscillations. The anthropic buried walls and barriers existing at the site are represented as 1D elements in a 2D model representing the properties of the aquifer. A deterministic inversion process optimizes the spatial distribution of aquifer properties and anthropic-structure properties in the model, in order to minimize the differences between the responses simulated with the model and those measured in the field. The results of the characterization on this complex study case (flows highly constrained by hydraulic barriers or buildings, and the impossibility to perform pumping tests) generate simulations able to reproduce the observed responses. The property and simulation maps generated make it possible to take into account the impact of the anthropic structures on the groundwater flows and to localize the parts of the hydraulic barriers where most exchanges between the channel and the aquifer occur.

SUMMARY We present an inversion algorithm to reconstruct the spatial distribution of the electrical conductivity from the analysis of magnetometric resistivity (MMR) data acquired at the ground surface. We first review the theoretical background of MMR connecting the generation of a magnetic field in response to the injection of a low-frequency current source and sink in the ground given a known distribution of electrical conductivity in the subsurface of the Earth. The forward modelling is based on sequentially solving the Poisson equation for the electrical potential distribution and the magnetostatic (Biot and Savart) equation for the magnetic field. Then, we introduce a Gauss–Newton inversion algorithm in which the logarithm of the electrical conductivity field is parametrized by using the chaos polynomial expansion in order to reduce the number of model parameters. To illustrate how the method works, the algorithm is successfully applied on four synthetic models with 3-D heterogeneous distribution of the electrical conductivity. Finally, we apply our algorithm to a field case study in which seepage was known to be occurring along an embankment of a headrace channel to a power station.

We present a synthetic hydraulic analysis of the propagation of oscillatory perturbations in a two-dimensional saturated zone bounded above by a capillary fringe. Unsaturated flows are simulated in a physical model using a hysteretic form of Richards' equation parameterized using the van Genuchten water retention curve and the Mualem hydraulic conductivity equation for a sand, loam, and intermediate soil. Soil type affects periodic responses as a function of their hydrodynamic and van Genuchten properties. We first analyze the effect of various hydraulic or signal properties on the oscillatory responses simulated at different locations and depths. We then test the imaging potential of oscillatory responses recorded in the saturated zone to spatially charaterize homogeneous or heterogeneous soils, also considering the effect of period of oscillation. We find that a separation of these responses into amplitude/phase couples permits to dissociate the characterization of different hydraulic properties. Periodic amplitudes decay with distance mainly as a function of hydraulic conductivity and phase lags decrease with frequency due to storage in the capillary fringe. Thus, responses amplitude appears to be especially sensitive to conductivity K , which allows to isolate this property from the others. Phases can then be used to better characterize the vertical flows effect, through the Van Genuchten parameters α and n . Higher periods will tend to accentuate the unsaturated flows effect on the responses and can therefore be adopted for a better characterization of α and n . However, using low-period responses can also be useful, as they provide better estimates of conductivity values in media with low heterogeneities. We consider this work as a useful preliminary analysis for future sandbox or field real cases applications and provide advices for such applications in the discussion.

International audience; Monitoring groundwater level (GWL) over long time periods is critical in understanding the variability of groundwater resources in the present context of global changes. However, in Normandy (France) for example, GWLs have only been systematically monitored for ~20 to 50 years. This study evaluates Long Short-Term Memory (LSTM) neural network modeling to reconstruct GWLs, fill gaps and extend existing time-series. The approach is illustrated by using available monitoring fluctuations in piezometers implanted in the chalk aquifer in the Normandy region, Northern France. Here GWL data recorded over 50 years at 31 piezometers in northwestern Normandy is employed to perform GWL prediction. To optimize the network performance, the most influential factors that impact the accuracy of prediction are first determined, such as the network architecture, data quantity and quality. The resulting network is adopted to reconstruct measurements in the piezometers step by step with an increment of missing observation time. The approach requires no calibration for the time-lag in data processing and the implementation relies only on the groundwater level fluctuations to retrieve missing data in the targeted piezometers.

Hydraulic characterization of a contaminated aquifer is an important step in depollution processes because its hydraulic parameters control the choice and efficiency of the depollution protocol to be adopted. The characterization presented in this article uses a 3D electrical resistivity imagery to identify the spatial heterogeneities of a contaminated aquifer under tidal influence. Indeed, we use a 3D resistivity model as a source of information to parameterize the reconstruction of the hydraulic conductivity in 3D by inverting a set of hydraulic data acquired on the 13 monitored wells in response to two pumping tests. This parameterization relies on the identification of the main electro-facies in the resistivity model in the saturated zone, which will then be exploited in the hydraulic characterization to find their corresponding hydraulic conductivity values. This strategy of parameterization permits to reduce the number of the hydraulic conductivity parameters to be identified to eight hydro-facies, with a stochastic algorithm called the Adaptive Metropolis Algorithm. The hydraulic responses associated with the pumping tests are obtained once the natural effect of the tide is removed. The hydraulic conductivity model has permitted to highlight the main heterogeneities in the aquifer in which the hydraulic conductivity is ranging between [10-4.6, 10-2.8 m/s]. This range of variability reveals the permeable and smooth character of the aquifer in which the presence of coarse sand and flint blocks enhances its transmissivity. These permeable zones are electrically identified by resistive anomalies in the 3D electrical resistivity imaging.

International audience; The flow of the ground water in an aquifer or during pumping test generates an electrical current (called the streaming current), which is of advective nature. The resulting electrical field (streaming potential field, one of the components of the self-potential field) can be remotely measured at the ground surface or in boreholes. We first discuss the underlying physics of this electrokinetic effect and the role of the electrical double layer coating the surface of the grains. We show how the drag of the excess of electrical charge of the pore water by the flow is equivalent to a source current density. Then, we discuss the metrological aspects, the type of voltmeter and electrodes required to carry out good measurements in field conditions. Two applications are discussed in steady-state conditions. The first is dedicated to the flow of water in shallow aquifers. In this case, the streaming current and the conduction current are nearly balanced and, inside the aquifer, the electrical equipotentials mimic the hydraulic equipotentials. They have, however, the advantage to extend the shape of these hydraulic equipotentials up to the ground surface. The second case is related to the flow of water in the vadose zone, here again investigated in steady-state conditions. In this situation, the vadose zone is polarized and the ground surface electrical potential map reflects essentially the depth of the vadose zone. A case study is shown for a small watershed in the South of France. The resistivity tomography shows no contrast in resistivity between the vadose zone and the aquifer and the observed self-potential data are observed to be linearly correlated to the depth of the water table.

(IF 3.73; Q1); International audience; We apply a stochastic Newton (SN) approach to solve a high-dimensional hydraulic inverse problem in highly heterogeneous geological media. By recognizing the connection between the cost function of deterministic optimizations and the posterior probability density of stochastic inversions, the Markov chain Monte Carlo (MCMC) sampler of SN is constructed by two parts: a deterministic part, which corresponds to a Newton step of deterministic optimization, and a stochastic part, which is a Gaussian distribution with the inverse of the local Hessian as the covariance matrix. The hybrid inverse method exploits the efficient tools for fast solution of deterministic inversions to improve the efficiency of the MCMC sampler. To address the ill-posedness of the inverse problem, a priori models, generated by a transition-probability geostatistical method, and conditioned to inter-well connection data, are used as regularization constraints.The effectiveness of the stochastic Newton method is first demonstrated by a synthetic test. The transmissivity field of the synthetic model is highly heterogeneous, and includes sharp variations. The inverse approach was then applied to a field hydraulic tomography investigation in a fractured and karstified aquifer to reconstruct its transmissivity field from a collection of real hydraulic head measurements. From the inversions, a series of transmissivity fields that produce good correlations between the inverted and the measured hydraulic heads were obtained. The inverse approach produced slightly different a posteriori transmissivity patterns for different a priori structure models of transmissivity; however, the trend and location of the high-transmissivity channels are consistent among various realizations. In addition, the uncertainty associated with each realization of the inverted transmissivity fields was quantified.

(IF 1.06; Q3); International audience; Hydrocarbon contamination, which can alter the physiochemical and biological properties of the subsurface, can be monitored by using geochemical analyses and integrated geophysical techniques. Electrical resistivity tomography, induced polarization, ground-penetrating radar, and self-potential methods were used in this work to characterise the hydrocarbon contamination and investigate the geoelectrical properties of a site impacted by an aged hydrocarbon plume. Throughout the investigation, geoelectrical measurements supported the conductive plume model and consistently recorded low-resistivity anomalies and high-chargeability values in the contaminated aquifer. Furthermore, the low-resistivity anomalies were found to be coincident with regions of ground-penetrating radar attenuated reflections and significant negative self-potential anomalies associated with oxidation– reduction processes. These findings were supported by the geochemical measurements, which revealed depleted concentrations of terminal electron acceptors (TEAs) and elevated amounts of ions and total dissolved solids, which could be attributed to bacterial biodegradation of hydrocarbons. The study showed that biological alterations of hydrocarbon-induced subtle changes in the pore water biogeochemistry, which consequently modified the geophysical properties of the contaminated sediments. Based on these observations, the extent of groundwater contamination was delineated according to the geophysical contrast between the contaminated and clean zones. The combination of different geophysical methods constrained by geochemical point measurements provided insight on the different processes that might have modified the soil and groundwater biogeochemical properties.

(IF 3.67 [2018]; Q1); International audience; Clogging due to transport and accumulation of the colloids in the pore space has been recognized as one of the most significant challenges in water management research and environmental engineering. This paper proposes an inversion algorithm in time-lapse mode to track that complex process through the assessment of alteration in the transmissivity field produced by the injection of colloids. The concept is based on a joint inversion of hydraulic head and colloidal particles concentration data acquired during the injection of colloids in the porous aquifer to reconstruct the spatial variability of the transmissivity field at different times. The inversion code is deterministic and was implemented in the time-lapse scheme by adding in the objective function a temporal geostatistical constraint to control changes of the hydraulic transmissivity. This algorithm is linked to a forward problem that consists of the groundwater flow and transport equations, which were solved numerically and jointly by considering the effect of particles deposition on the decrease of hydraulic properties. As the inverse problem is deterministic and underdetermined, we have opted to use the efficient adjoint state technique to derive the sensitivity matrices. The approach has been successfully applied to a theoretical case in which the hydraulic head responses have been used alone and jointly to assess the evolution of the clogging impact on hydraulic transmissivity.

(IF 3.19 [2018]; Q1); International audience; The study on the hydraulic properties of coastal aquifers has significant implications both in hydrological sciences and environmental engineering. Although many analytical solutions are available, most of them are based on the same basic assumption that assumes aquifers extend landward semi‐infinitely, which does not necessarily reflect the reality. In this study, the general solutions for a leaky confined coastal aquifer have been developed that consider both finitely landward constant‐head and no‐flow boundaries. The newly developed solutions were then used to examine theoretically the joint effects of leakage and aquifer length on hydraulic head fluctuations within the leaky confined aquifer, and the validity of using the simplified solution, which assumes the aquifer is semi‐infinite. The results illustrated that the use of the simplified solution may cause significant errors, depending on joint effects of leakage and aquifer length. A dimensionless characteristic parameter was then proposed as an index for judging the applicability of the simplified solution. In addition, practical application of the general solution for the constant‐head inland boundary was used to characterize the hydraulic properties of a leaky confined aquifer using the data collected from a field site at the Seine River estuary, France, and the versatility of the general solution was further justified.

(IF 3.91 [2018]; Q1); International audience; The self-potential method can be used to detect and monitor anomalous seepages in dams and embankments. In such a case, an electrical field of electrokinetic nature (i.e., associated with pore water flow) can be measured using a set of non-polarizable electrodes typically located at the ground surface or in some wells. This field can be in turn related to the pattern of groundwater flow. We built an experimental dam to investigate to which extent the self-potential method can help characterizing seepages in dams. We first use the finite element method to simulate the ground water flow in a heterogeneous porous and permeable material by solving the groundwater flow equation. The resulting groundwater flow solution is then used to compute the electrical potential distribution by solving the corresponding elliptic partial differential equation. In a preliminary experiment, we could not measure any self-potential anomaly associated with the infiltration of water in the dam. Our numerical simulations showed that the magnitudes of the self-potential anomalies were controlled by (1) the nature of the flow regime (viscous laminar versus inertial laminar flow regimes) and (2) the presence of insulating Polyvinyl Chloride (PVC) tubes located at the end of the preferential flow channels in the structure of the dam. Thanks to these numerical simulations, we added sand at the entrance of the infiltration area in order to reduce the effects of the PVC tubes and to restrain the flow regime to the viscous laminar flow regime. New experiments allowed for detecting a self-potential anomaly with an amplitude of around −9 mV consistent with that obtained through numerical modelling with a finite element simulator. This comparison was used to test the accuracy of the modelling approach and define the strengths and weaknesses of the self-potential method to determine preferential seepages in earth dam structures.

International audience; Transient hydraulic tomography is used to image the heterogeneous hydraulic conductivity and specific storage fields of shallow aquifers using time series of hydraulic head data. Such ill-posed and non-unique inverse problem can be regularized using some spatial geostatistical characteristic of the two fields. In addition to hydraulic heads changes, the flow of water, during pumping tests, generates an electrical field of electrokinetic nature. These electrical field fluctuations can be passively recorded at the ground surface using a network of non-polarizing electrodes connected to a high impedance (> 10 MOhm) and sensitive (0.1 mV) voltmeter, a method known in geophysics as the self-potential method. We perform a joint inversion of the self-potential and hydraulic head data to image the hydraulic conductivity and specific storage fields. We work on a 3D synthetic confined aquifer and we use the adjoint state method to compute the sensitivities of the hydraulic parameters to the hydraulic head and self-potential data in both steady-state and transient conditions. The inverse problem is solved using the geostatistical quasi-linear algorithm framework of Kitanidis. When the number of piezometers is small, the record of the transient self-potential signals provides useful information to characterize the hydraulic conductivity and specific storage fields. These results show that the self-potential method reveals the heterogeneities of some areas of the aquifer, which could not been captured by the tomography based on the hydraulic heads alone. In our analysis, the improvement on the hydraulic conductivity and specific storage estimations were based on perfect knowledge of electrical resistivity field. This implies that electrical resistivity will need to be jointly inverted with the hydraulic parameters in future studies and the impact of its uncertainty assessed with respect to the final tomograms of the hydraulic parameters.

International audience; Hydraulic tomography is a technique used to characterize the spatial heterogeneities of storativity and transmissivity fields. The responses of an aquifer to a source of hydraulic stimulations are used to recover the features of the estimated fields using inverse techniques. We developed a 2D free source Matlab package for performing hydraulic tomography analysis in steady state and transient regimes. The package uses the finite elements method to solve the ground water flow equation for simple or complex geometries accounting for the anisotropy of the material properties. The inverse problem is based on implementing the geostatistical quasi-linear approach of Kitanidis combined with the adjoint-state method to compute the required sensitivity matrices. For undetermined inverse problems, the adjoint-state method provides a faster and more accurate approach for the evaluation of sensitivity matrices compared with the finite differences method. Our methodology is organized in a way that permits the end-user to activate parallel computing in order to reduce the computational burden. Three case studies are investigated demonstrating the robustness and efficiency of our approach for inverting hydraulic parameters.

(IF 2.78; Q1); International audience; The injection of a low frequency electrical current in the ground between two electrodes A and B generates a magnetic field that can be measured at the ground surface with sensitive magnetic sensors. The map of the magnetic field, measured at the frequency of the injected current, can be used to determine the paths of the current through the ground. When the current is channelled along preferential conductive paths, the MagnetoMetric Resistivity (MMR) method can be used to detect these paths. Conductive current paths can be associated with preferential flow paths of groundwater when the two electrodes A and B are in the direction of the flow and when the flow path is highly electrically conductive with respect to the background. We first review the background equations for the magnetic field in MMR. Then, we provide the kernel of the problem using Biot and Savart law to connect the components of the observed magnetic field to the current density distribution. We also develop a simple approach to invert the magnetic field in terms of electrical current paths. To illustrate how the method works, we develop five synthetic models to test the sensitivity of the method to the properties of the conductive targets channelling the electrical current. The targets are characterized by different shapes, sizes, depths, and conductivity contrasts with the background. Then, we proceed with a case study for which the MMR method is used to identify and map preferential groundwater flow paths bypassing a mine waste rock dump drainage collection trench into the tailings pond. In this case, the conductivity of the flow paths is much stronger than the background conductivity due to the high mineralization of the ground water along these paths. The method underlines the 3-D architecture of these flow paths.

International audience; In steady-state hydraulic tomography, the head data recorded during a series of pumping or/and injection tests can be inverted to determine the transmissivity distributions of an aquifer. This inverse problem is usually under-determined and ill-posed. We propose to use structural information inferred from a guiding image to constrain the inversion process. The guiding image can be drawn from soft data sets such as seismic and ground penetrating radar sections or from geological cross-sections inferred from the wells and some geological expertise. The structural information is extracted from the guiding image through some digital image analysis techniques. Then, it is introduced into the inversion process of the head data as a weighted four direction smoothing matrix used in the regularizer. Such smoothing matrix allows applying the smoothing along the structural features. This helps preserving eventual drops in the hydraulic properties. In addition, we apply a procedure called image-guided interpolation. This technique starts with the tomogram obtained from the image-guided inversion and focus this tomogram. These new approaches are applied on four synthetic toy problems. The hydraulic distributions estimated from the image-guided inversion are closer to the true transmissivity model and have higher resolution than those computed from a classical Gauss–Newton method with uniform isotropic smoothing.

Mapping the redox potential of shallow aquifers impacted by hydrocarbon contaminant plumes is important for the characterization and remediation of such contaminated sites. The redox potential of groundwater is indicative of the biodegradation of hydrocarbons and is important in delineating the shapes of contaminant plumes. The self-potential method was used to reconstruct the redox potential of groundwater associated with an organic-rich contaminant plume in northern France. The self-potential technique is a passive technique consisting in recording the electrical potential distribution at the surface of the Earth. A self-potential map is essentially the sum of two contributions, one associated with groundwater flow referred to as the electrokinetic component, and one associated with redox potential anomalies referred to as the electroredox component (thermoelectric and diffusion potentials are generally negligible). A groundwater flow model was first used to remove the electrokinetic component from the observed self-potential data. Then, a residual self-potential map was obtained. The source current density generating the residual self-potential signals is assumed to be associated with the position of the water table, an interface characterized by a change in both the electrical conductivity and the redox potential. The source current density was obtained through an inverse problem by minimizing a cost function including a data misfit contribution and a regularizer. This inversion algorithm allows the determination of the vertical and horizontal components of the source current density taking into account the electrical conductivity distribution of the saturated and non-saturated zones obtained independently by electrical resistivity tomography. The redox potential distribution was finally determined from the inverted residual source current density. A redox map was successfully built and the estimated redox potential values correlated well with in-situ measurements.

Inverse modeling of geophysical data involves the recovery of a subsurface structural model and the distribution of petrophysical properties. Independent information regarding the subsurface structure is usually available, with some uncertainty, from the expertise of a geologist and possibly accounting for sedimentary and tectonic processes. We have used the available structural information to construct a model covariance matrix and to perform a structure-constrained inversion of the geophysical data to obtain a geophysical tomogram [Formula: see text]. We have considered that the geologic models [Formula: see text] were built from random variables and were described with a priori probability density function in the Bayesian framework. We have explored for the a posteriori probability density of the geologic models (i.e., the structure of the guiding image) with the Markov-chain Monte Carlo method, and we inverted at the same time, in a deterministic framework, the geophysical data. The sampling of the geologic models was performed in a stochastic framework, and each geologic model [Formula: see text] was used to invert the geophysical model [Formula: see text] using image-guided inversion. The adaptive metropolis algorithm was used to find the proposal distributions of [Formula: see text] reproducing the geophysical data and the geophysical information. In other words, we have tried to find a compromise between the a priori geologic information and the geophysical data to get, as end products, an updated geologic model and a geophysical tomogram. To demonstrate our approach, we used here electrical resistivity tomography as a technique to identify a correct geologic model and its a posteriori probability density. The approach was tested using one synthetic example (with three horizontal layers displaced by a normal fault) and one field case corresponding to a sinkhole in a three-layer structure. In both cases, we were able to select the most plausible geologic models that agreed with a priori information and the geophysical data.

We propose a cross-hole imaging approach based on seismoelectric conversions (SC) associated with the transmission of seismic waves from seismic sources located in a borehole to receivers (electrodes) located in a second borehole. The seismoelectric (seismic-to-electric) problem is solved using Biot theory coupled with a generalized Ohm's law with an electrokinetic streaming current contribution. The components of the displacement of the solid phase, the fluid pressure, and the electrical potential are solved using a finite element approach with Perfect Match Layer (PML) boundary conditions for the seismic waves and boundary conditions mimicking an infinite material for th electrostatic problem. We develop an inversion algorithm using the electrical disturbances recorded in the second borehole to localize the position of the heterogeneities responsible for the SC. Because of the ill-posed nature of the inverse problem (inherent to all potential-field problems), regularization is used to constrain the solution at each time in the SC-time window comprised between the time of the seismic shot and the time of the first arrival of the seismic waves in the second borehole. All the inverted volumetric current source densities are aggregated together to produce an image of the position of the heterogeneities between the two boreholes. Two simple synthetic case studies are presented to test this concept. The first case study corresponds to a vertical discontinuity between two homogeneous sub-domains. The second case study corresponds to a poroelastic inclusion (partially saturated by oil) embedded into an homogenous poroelastic formation. In both cases, the position of the heterogeneity is recovered using only the electrical disturbances associated with the SC. That said, a joint inversion of the seismic and seismoelectric data could improve these results.

International audience; Pumping tests can be used to estimate the hydraulic conductivity field from the inversion of hydraulic head data taken intrusively in a set of piezometers. Nevertheless, the inverse problem is strongly underdetermined. We propose to add more information by adding self‐potential data taken at the ground surface during pumping tests. These self‐potential data correspond to perturbations of the electrical field caused directly by the flow of the groundwater. The coupling is electrokinetic in nature that is due to the drag of the excess of electrical charges existing in the pore water. These self‐potential signals can be easily measured in field conditions with a set of the nonpolarizing electrodes installed at the ground surface. We used the adjoint‐state method for the estimation of the hydraulic conductivity field from measurements of both hydraulic heads and self potential during pumping tests. In addition, we use a recently developed petrophysical formulation of the streaming potential problem using an effective charge density of the pore water derived directly from the hydraulic conductivity. The geostatistical inverse framework is applied to five synthetic case studies with different number of wells and electrodes and thickness of the confining unit. To evaluate the benefits of incorporating the self‐potential data in the inverse problem, we compare the cases in which the data are combined or not. Incorporating the self‐potential information improves the estimate of hydraulic conductivity field in the case where the number of piezometers is limited. However, the uncertainty of the characterization of the hydraulic conductivity from the inversion of the self‐potential data is dependent on the quality of the distribution of the electrical conductivity used to solve the Poisson equation. Consequently, the approach discussed in this paper requires a precise estimate of the electrical conductivity distribution of the subsurface and requires therefore new strategies to be developed for the joint inversion of the hydraulic and electrical conductivity distributions.

International audience

International audience; The seismoelectric method is based on the interpretation of the electrical field associated with the conversion of mechanical to electromagnetic energy during the propagation of seismic waves in heterogeneous porous media. We propose an extension of a poroacoustic model that takes into account fluid flow and the effect of saturation. This model is coupled with an electrokinetic model accounting for the effect of saturation and in agreement with available experimental data in sands and carbonate rocks. We also developed new scaling laws for the permeability, the streaming potential coupling coefficient and the capillary entry pressure of porous media. The theory is developed for frequencies much below the critical frequency at which inertial effects starts to dominate in the Navier–Stokes equation (>10 kHz). The equations used to compute the propagation of the P waves and the seismoelectric effect in unsaturated condition are solved with finite elements using triangular meshing. We demonstrate the usefulness of a recently developed technique, seismoelectric beamforming, to localize saturation fronts by focusing seismic waves and looking at the resulting seismoelectric conversions. This method is applied to a cross-hole problem showing how a saturation front characterized by a drop in the electrical conductivity and compressibility is responsible for seismoelectric conversions. These conversions can be used, in turn, to determine the position of the front over time.

The self-potential method enables non-intrusive assessment and imaging of disturbances in electrical currents of conductive subsurface materials. It has an increasing number of applications, from mapping fluid flow in the subsurface of the Earth to detecting preferential flow paths in earth dams and embankments. This book provides the first full overview of the fundamental concepts of this method and its applications in the field. It discusses a historical perspective, laboratory investigations undertaken, the inverse problem and seismoelectric coupling, and concludes with the application of the self-potential method to geohazards, water resources and hydrothermal systems. Chapter exercises, online datasets and analytical software enable the reader to put the theory into practice. This book is a key reference for academic researchers and professionals working in the areas of geophysics, environmental science, hydrology and geotechnical engineering. It will also be valuable reading for related graduate courses.

International audience; The assessment of hydraulic conductivity of heterogeneous aquifers is a difficult task using traditional hydrogeological methods (e.g., steady state or transient pumping tests) due to their low spatial resolution. Geophysical measurements performed at the ground surface and in boreholes provide additional information for increasing the resolution and accuracy of the inverted hydraulic conductivity field. We used a stochastic joint inversion of Direct Current (DC) resistivity and self-potential (SP) data plus in situ measurement of the salinity in a downstream well during a synthetic salt tracer experiment to reconstruct the hydraulic conductivity field between two wells. The pilot point parameterization was used to avoid over-parameterization of the inverse problem. Bounds on the model parameters were used to promote a consistent Markov chain Monte Carlo sampling of the model parameters. To evaluate the effectiveness of the joint inversion process, we compared eight cases in which the geophysical data are coupled or not to the in situ sampling of the salinity to map the hydraulic conductivity. We first tested the effectiveness of the inversion of each type of data alone (concentration sampling, self-potential, and DC resistivity), and then we combined the data two by two. We finally combined all the data together to show the value of each type of geophysical data in the joint inversion process because of their different sensitivity map. We also investigated a case in which the data were contaminated with noise and the variogram unknown and inverted stochastically. The results of the inversion revealed that incorporating the self-potential data improves the estimate of hydraulic conductivity field especially when the selfpotential data were combined to the salt concentration measurement in the second well or to the time-lapse cross-well electrical resistivity data. Various tests were also performed to quantify the uncertainty in the inverted hydraulic conductivity field.

The self-potential method corresponds to the passive measurement of the electrical field in response to the occurrence of natural sources of current in the ground. One of these sources corresponds to the streaming current associated with the flow of the ground water. We can therefore apply the self-potential method to recover non-intrusively some information regarding the ground water flow. We first solve the forward problem starting with the solution of the ground water flow problem, then computing the source current density, and finally solving a Poisson equation for the electrical potential. We use the finite-element method to solve the relevant partial differential equations. In order to reduce the number of (petrophysical) model parameters required to solve the forward problem, we introduced an effective charge density tensor of the pore water, which can be determined directly from the permeability tensor for neutral pore waters. The second aspect of our work concerns the inversion of the self-potential data using Tikhonov regularization with smoothness and weighting depth constraints. This approach accounts for the distribution of the electrical resistivity, which can be independently and approximately determined from electrical resistivity tomography. A numerical code, SP2DINV, has been implemented in Matlab to perform both the forward and inverse modeling. Three synthetic case studies are discussed.

[1] A method is proposed to localize preferential fluid flow pathways in porous media on the basis of time-lapse self-potential measurements associated with salt tracer injection upstream. This method is first tested using laboratory data. A network of nonpolarizing electrodes located is connected to a highly sensitive voltmeter used to record the resulting electrical field fluctuations occurring over time at the surface of the tank. The transport of the conductive salt plume through the permeable porous materials changes the localized streaming potential coupling coefficient associated with the advective drag of the excess charge of the pore water and is also responsible for a diffusion current associated with the salinity gradient. Monitoring of the electrical potential distribution at the ground surface can be used to localize the pulse of saline water over time and to determine its velocity. This method applies in real time and can be used to track highly localized flow pathways characterized by high permeability. Our sandbox experiment demonstrates the applicability of this new method under well-controlled conditions with a coarse-sand channel embedded between fine-sand banks. A finite element model allows us to reproduce the time-lapse electrical potential distribution over the channel, but some discrepancies were observed on the banks. Finally, we performed a numerical simulation for a synthetic case study inspired by a recently published field case study. A Markov chain Monte Carlo sampler is used to determine the permeability and the porosity of the preferential fluid flow pathway of this synthetic case study.

International audience

Summary The record of the head fluctuations of an alluvial aquifer connected to the estuary of a river submitted to tidal influence can be used to reconstruct the transmissivity field of the aquifer. A Markov chain Monte Carlo (McMC) sampler is used to invert the transmissivity field at a set of pilot points. Our approach is first successfully benchmarked on a synthetic case study. Then, we present a real case study in which both a semi-confined aquifer and a shallow unconfined aquifer are connected to the estuary of the Seine River in the western-north of France. These aquifers experience strong tidal variations up to 8.4 m. This test site is equipped with a series of seventeen wells in which the temporal fluctuations of water heads associated with megatidal forcing were recorded during several years. In addition to the use of the pilot points method, a zoning parameterization with 45 zones is used to determine the vertical leakage coefficient from the semi-confined aquifer into the shallow unconfined aquifer. The distribution of the vertical leakage coefficient is determined by inverting the hydraulic head at a set of wells localized in the semi-confined aquifer. We determine jointly the distribution of the hydraulic transmissivity and the vertical leakage from the semi-confined into the unconfined aquifer using 72 pilot points. The storage coefficient is assumed to be constant over the whole domain. Its value is determined from three pumping tests that show a consistent value for this parameter (log10S = −5 and 0.11 as a variance). In our approach, there are 119 model parameters (72 transmissivity values at the pilot points, 45 values of the vertical leakage coefficient, and two parameters (sill and range) for the isotropic variogram). The spatial distribution of the hydraulic transmissivity agrees qualitatively with the soil texture variations observed in the semi-confined aquifer and core samples analysis.

International audience; Electromagnetic signals have been observed in association with fracking experiments in the laboratory, and in the field. We have developed a seismoelectric forward modeling approach to produce synthetic seismograms and electrograms generated by fracking events using the finite-element method with perfect matched-layer boundary conditions. The poroelastodynamic equations are solved in the frequency domain using a formulation based on the solid phase displacement and the pore pressure. These results are used to compute the electrical field disturbances of electrokinetic nature. Three types of electrical signals are generated: Type I disturbance is associated with the seismic source itself, Type II disturbance corresponds to seismoelectric conversions, and Type III corresponds to coseismic signals. This model is applied to simulate the seismic and electrical signals corresponding to the occurrence of a fracking event in a two-layers system. We perform a stochastic joint inversion of the seismograms and electrograms using the adaptive Metropolis algorithm (AMA) to obtain the posterior probability density functions of the parameters characterizing the seismic source assuming that the velocity model is perfectly known. The joint waveform inversion is performed on synthetic noise-free data and the AMA algorithm is successful in retrieving the true values of the unknown parameters. The proposed approach is then tested on the same synthetic data after being contaminated with 15% random noise with respect to the maximum amplitude of the signals. The model parameters are better determined for the joint inversion of seismic and electrical data by comparison with the inversion of the seismic time-series alone. We also propose a deterministic tomographic algorithm that is successful in locating the in situ source current density distribution for Types I and II anomalies from the electrical data alone.

International audience; The complex conductivity of porous materials and colloidal suspensions comprises two components: an in‐phase conductivity associated with electromigration of the charge carriers and a quadrature conductivity associated with the reversible storage of the charges at some polarization length scales. We developed a quantitative model to investigate the frequency domain induced polarization response of suspensions of bacteria and bacteria growth in porous media. Induced polarization of bacteria (α polarization) is related to the properties of the electrical double layer of the bacteria. Surface conductivity and α polarization are due to the Stern layer of counterions occurring in a brush of polymers coating the surface of the bacteria. These phenomena can be related to their cation exchange capacity. The mobility of the counterions in this Stern layer is found to be very small (4.7 × 10−10 m2 s−1 V−1 at 25°C). This implies a very low relaxation frequency for the αpolarization of the bacteria cells (typically around 0.1–5 Hz), in agreement with experimental observations. This new model can be coupled to reactive transport modeling codes in which the evolution of bacterial populations are usually described by Monod kinetics. We show that the growth rate and endogenous decay coefficients of bacteria in a porous sand can be inferred nonintrusively from time‐lapse frequency domain induced polarization data.

International audience; The hydrogeologic influence of the Elkhorn fault in South Park, Colorado, USA, is examined through hydrologic data supplemented by electrical resistivity tomography and self-potential measurements. Water-level data indicate that groundwater flow is impeded by the fault on the spatial scale of tens of meters, but the lack of outcrop prevents interpretation of why the fault creates this hydrologic heterogeneity. By supplementing hydrologic and geologic data with geoelectrical measurements, further hydrogeologic interpretation is possible. Resistivity profiles and self-potential data are consistent with the interpretation of increased fracturing within 70 m of the fault. Further interpretation of the fault zone includes the possibility of a vertical groundwater flow component in a fractured and relatively high permeability damage zone and one or more relatively low permeability fault cores resulting in a conduit-barrier behavior of the fault zone at the meter to tens-of-meters scale. Calculated hydraulic heads from the self-potential data reveal additional complexity in permeability structure, including a steeper hydraulic gradient immediately west of the interpreted fault trace than suggested by the well data alone.

[1] We test the ability of the self-potential method to provide information that can be used to invert the permeability and the dispersivities of a porous material. We first formulate the semi-coupled system of equations describing the occurrence of self-potential signals associated with the transport of salt in a porous material like sand. Two contributions in the source current density arise from the electrokinetic coupling associated with the flow of the pore water and the diffusion potential due to the gradient in the activity of the salt. A controlled laboratory sandbox experiment is performed to show that time-lapse self-potential measurements can be used to invert, in a Bayesian framework, the permeability and dispersivities.

International audience; Nonintrusively monitoring the spread of contaminants in real time with a geophysical method is an important task in hydrogeophysics. We have developed a sandbox experiment showing that the self-potential method can locate both the source of leakage and the front of a contaminant plume. We monitored the leakage of a plume of salty water from a hole at the bottom of a small tank located at the top of a main sandbox. Initially, the sand was saturated by tap water. At a given time, a hole was opened at the bottom of the tank, allowing the salty water to migrate by diffusion and buoyancy-driven flow in the main sandbox. The bottom of the sandbox contained a network of 32 nonpolarizing silver-silver chloride electrodes with amplifiers, connected to a multichannel voltmeter. The self-potential response associated withthe migration of the salt plume in the sandbox was recorded over time. A self-potential anomaly was observed with amplitude varying from a few millivolts at the start of the leak to a few tens of millivolts after a few minutes. The self-potential data were inverted using a time-lapse tomographic algorithm to reconstruct the position of the volumetric source current density over time. A positive volumetric source current density was associated with the position of the leak at the bottom of the leaking tank, whereas a negative volumetric source current density was associated with the salinity front moving down inside the sandbox. These poles were well reproduced by performing a finite-element simulation of the problem. Using this information, we estimated the speed of the salt plume sinking inside the sandbox. Therefore, the self-potential method can be used to track, in real time, the position of the front of a contaminant plume in a porous material.

International audience; We consider a linear poroelastic material filled with a linear viscoelastic solvent like wet heavy oils (oil as opposed to water or brines is wetting the surfaces of the pores). We extend the electrokinetic theory in the frequency domain accounting for the relaxation effects associated with resonance of the viscoelastic fluid. The fluid is described by a generalized Maxwell rheology with a distribution of relaxation times given by a Cole–Cole distribution. We use the assumption that the charges of the diffuse layer are uniformly distributed in the pore space (Donnan model). The macroscopic constitutive equations of transport for the seepage velocity and the current density have the form of coupled Darcy and Ohm equations with frequency-dependent material properties. These equations are combined with an extended Frenkel–Biot model describing the deformation of the poroelastic material filled with the viscoelastic fluid. In the mechanical constitutive equations, the effective shear modulus is frequency dependent. An amplification of the seismoelectric conversion is expected in the frequency band where resonance of the generalized Maxwell fluid occurs. The seismic and seismoelectric equations are modelled using a finite element code with PML boundary conditions. We found that the DC-value of the streaming potential coupling coefficient is also very high. These results have applications regarding the development of new non-intrusive methods to characterize shallow heavy oil reservoirs in tar sands and DNAPL contaminant plumes in shallow aquifers.

International audience; The interpretation of seismoelectrical signals is a difficult task because coseismic and seismoelectric converted signals are recorded simultaneously and the seismoelectric conversions are typically several orders of magnitude smaller than the coseismic electrical signals. The seismic and seismoelectric signals are modeled using a finite-element code with perfectly matched layer boundary conditions assuming a linear poroelastic body. We present a stochastic joint inversion of the seismic and seismoelectrical data based on the adaptive Metropolis algorithm, to obtain the posterior probability density functions of the material properties of each geologic unit. This includes the permeability, porosity, electrical conductivity, bulk modulus of the dry porous frame, bulk modulus of the fluid, bulk modulus of the solid phase, and shear modulus of the formations. A test of this approach is performed with a synthetic model comprising two horizontal layers and a reservoir partially saturated with oil, which is embedded in the second layer. The result of the joint inversion shows that we can invert the permeability of the reservoir and its mechanical properties. ©2010 Society of Exploration Geophysicists

In geothermal fields, open faults and fractures often act as high permeability pathways bringing hydrothermal fluids to the surface from deep reservoirs. The Mount Princeton area, in south-central Colorado, is an area that has an active geothermal system related to faulting and is therefore a suitable natural laboratory to test geophysical methods. The Sawatch range-front normal fault bordering the half-graben of the Upper Arkansas valley is characterized by a right-lateral offset at Mount Princeton Hot springs. This offset is associated with the Chalk Cliffs of hydrothermally altered quartz monzonite. Because fault identification in this area is complicated by quaternary deposits (including glacial and fluvial deposits), we use DC electrical resistivity tomography and self-potential mapping to identify preferential fluid flow pathways. The geophysical data (over 5600 resistivity and 2700 self-potential measurements) provide evidence of the existence of a dextral strike slip fault zone (Fault B) responsible for the offset of the Sawatch fault. A segment of this dextral strike slip fault (termed U1) is acting as the dominant vertical flow path bringing thermal waters to a shallow unconfined aquifer. Upwelling of the thermal waters is also observed at two zones (U2 and U3) of an open fracture called Fault A. This fault is located at the tip of the Sawatch fault and is likely associated with an extensional strain regime in this area. Self-potential measurements are used to estimate the flux of upwelling thermal water. The upflow estimate (4 ± 1 × 10 3 m 3 /day for the open segment of the Fault B and 2 ± 1 × 10 3 m 3 /day for Fault A) from the geophysical data is remarkably consistent with the downstream Mt. Princeton hot water production (4.3–4.9) × 10 3 m 3 /day at approximately 60–86 °C). A temperature map indicates that a third upwelling zone termed U4 may exist at the southern tip of the Sawatch fault.

International audience; A seismo-acoustic and self-potential survey has been performed in the hydrothermal area of the old Waimangu Geyser (New Zealand), which was violently erupting a century ago. Nowadays, no surface activity is visible there. We set-up an array of 16 geophones and recorded a high and steady acoustic ambient noise. We applied the matched field processing (MFP) approach to the acoustic data to locate the sources responsible for the ambient noise. The white noise constraint processor reveals the presence of a unique and well-focused acoustic source at a depth of 1.5 m below the seismic array. For this very shallow source, the application of MFP enabled the determination of both the source location and the dispersion curve of seismic velocity. The study was completed by self-potential (SP) measurements on several profiles around the acoustic noise source, which displayed a large positive anomaly above it. The results of the SP inversion gave an electric streaming current density source very close to the acoustic one. Both sources likely belong to a shallow hydrothermal structure interpreted as a small convective cell of boiling water beneath an impermeable layer. The joint application of these methods is a promising technique to recognize hydrothermal structures and to study their dynamics.

International audience; In contaminant plumes or in the case of ore bodies, a source current density is produced at depth in response to the presence of a gradient of the redox potential. Two charge carriers can exist in such a medium: electrons and ions. Two contributions to the source current density are associated with these charge carriers (i) the gradient of the chemical potential of the ionic species and (ii) the gradient of the chemical potential of the electrons (i.e., the gradient of the redox potential). We ran a set of experiments in which a geobattery is generated using electrolysis reactions of a pore water solution containing iron. A DC power supply is used to impose a difference of electrical potential of 3 V between a working platinum electrode (anode) and an auxiliary platinum electrode (cathode). Both electrodes inserted into a tank filled with a well-calibrated sand infiltrated by a (0.01 mol L−1 KCl+0.0035 mol L−1 FeSO4) solution. After the direct current is turned off, we follow the pH, the redox potential, and the self-potential at several time intervals. The self-potential anomalies amount to a few tens of millivolts after the current is turned off and decreases over time. After several days, all the redox-active compounds produced initially by the electrolysis reactions are consumed through chemical reactions and the self-potential anomalies fall to zero. The resulting self-potential anomalies are shown to be much weaker than the self-potential anomalies observed in the presence of an electronic conductor in the laboratory or in the field. In the presence of a biotic or an abiotic electronic conductor, the self-potential anomalies can amount to a few hundred millivolts. These observations point out indirectly the potential role of bacteria forming biofilms in the transfer of electrons through sharp redox potential gradient in contaminant plumes that are rich in organic matter

International audience; The flow of the ground water is responsible for both thermal and self-potential anomalies. Temperature is usually recorded in boreholes while self-potential is usually recorded at the ground surface of the Earth. This makes the joint inversion of temperature and self-potential data together an attractive approach to invert permeability. We use an Adaptive Metropolis Algorithm to determine the posterior probability densities of the material properties of different geological formations and faults by inverting jointly self-potential and temperature data. The algorithm is tested using a synthetic case corresponding to a series of sedimentary layers overlying a low-permeability granitic substratum. The flow of the ground water (computed in steady-state condition) is mainly localized in two faults acting as preferential fluid flow pathways. The first fault is discharging warmed ground water near the ground surface while the second fault acts as a recharge zone of cold water (a classical scenario in geothermal systems). The joint inversion algorithm yield accurate estimate of the permeability of the different units only if both temperature and self-potential data are jointly inverted. An application using real data is also performed. It concerns the upwelling of a hydrothermal plume through a set of faults and permeable formations at the Cerro Prieto geothermal field in Baja California. The optimized permeabilities are in close agreement with independent hydrogeological estimates.

International audience; Ground water flow associated with pumping and injection tests generates self-potential signals that can be measured at the ground surface and used to estimate the pattern of ground water flow at depth. We propose an inversion of the self-potential signals that accounts for the heterogeneous nature of the aquifer and a relationship between the electrical resistivity and the streaming current coupling coefficient. We recast the inversion of the self-potential data into a Bayesian framework. Synthetic tests are performed showing the advantage in using self-potential signals in addition to in situ measurements of the potentiometric levels to reconstruct the shape of the water table. This methodology is applied to a new data set from a series of coordinated hydraulic tomography, self-potential, and electrical resistivity tomography experiments performed at the Boise Hydrogeophysical Research Site, Idaho. In particular, we examine one of the dipole hydraulic tests and its reciprocal to show the sensitivity of the self-potential signals to variations of the potentiometric levels under steady-state conditions. However, because of the high pumping rate, the response was also influenced by the Reynolds number, especially near the pumping well for a given test. Ground water flow in the inertial laminar flow regime is responsible for nonlinearity that is not yet accounted for in self-potential tomography. Numerical modeling addresses the sensitivity of the self-potential response to this problem.

International audience; We propose an algorithm to invert self-potential signals measured at the ground surface of the Earth to localize hydromechanical disturbances or to the pattern of groundwater flow in geothermal systems. The self-potential signals result from the divergence of the streaming current density. Groundwater flow can be either driven by topography of the water table, free convection, or deformation of the medium. The algorithm includes the electrical resistivity distribution of the medium obtained independently by DC resistance tomography or electromagnetic methods or by coding the assumed geology in terms of distribution of the electrical resistivity accounting for the effect of the temperature and salinity distributions and possibly constraints from borehole measurements. Inversion of the distribution of the source current density from ground surface and borehole self-potential measurements is achieved by solving the inverse problem using Tikhonov regularization solutions that are compatible with the physics of the primary flow problem. By introducing assumptions regarding the smoothness or the compactness of the source and the three-dimensional distribution of the electrical resistivity of the system, the inverse problem can be solved in obtaining the three-dimensional distribution of the current source density in the ground. However, an annihilator can be added to the inverted source geometry without affecting the measured self-potential field. Annihilators can be obtained from boundary conditions. Synthetic models and a sandbox experiment are discussed to demonstrate the validity of the algorithm. An application is presented to the geothermal field of Cerro Prieto, Baja California, Mexico, using literature data. Inversion of the self-potential and resistivity data allows observing a plume of hot groundwater rising to the ground surface in the central part of the investigated area and discharging to the ground surface in the southwest part. The temperature anomaly associated with the existence of this plume is independently observed by interpolating borehole temperature measurements. We found a good agreement between the distribution of the temperature and the inverted source current density. The proposed method appears therefore as a noninvasive method for remote detection and three-dimensional mapping of subsurface groundwater flow.

International audience; Four sandbox experiments were performed to understand the self-potential response to hydro-mechanical disturbances in a water-infiltrated controlled sandbox. In the first two experiments, ∼0.5 mL of water was abruptly injected through a small capillary at a depth of 15 cm using a syringe impacted by a hammer stroke. In the second series of experiments, ∼0.5 mL of pore water was quickly pumped out of the tank, at the same depth, using a syringe. In both type of experiments, the resulting self-potential signals were measured using 32 sintered Ag/AgCl medical electrodes. In two experiments, these electrodes were located 3 cm below the top surface of the tank. In two other experiments, they were placed along a vertical section crossing the position of the capillary. These electrodes were connected to a voltmeter with a sensitivity of 0.1 μV and an acquisition frequency of 1.024 kHz. The injected/pumped volumes of water produced hydro-mechanical disturbances in the sandbox. In turn, these disturbances generated dipolar electrical anomalies of electrokinetic nature with an amplitude of few microvolts. The source function is the product of the dipolar Green's function by a source intensity function that depends solely on the product of the streaming potential coupling coefficient of the sand to the pore fluid overpressure with respect to the hydrostatic pressure. Numerical modeling using a finite element code was performed to solve the coupled hydro-mechanical problem and to determine the distribution of the resulting self-potential during the course of these experiments. We use 2D and 3D algorithms based on the cross-correlation method and wavelet analysis of potential fields to show that the source was a vertical dipole. These methods were also used to localize the position of the source of the hydromechanical disturbance from the self-potential signals recorded at the top surface of the tank. The position of the source agrees with the position of the inlet/outlet of the capillary showing the usefulness of these methods for application to active volcanoes.

International audience; Jardani et al. [2006a] analyzed self-potential signals associated with the shallow groundwater flow in sinkholes. These signals were electrokinetic in nature resulting from the percolation of water in the ground and the drag of the excess of electrical charge that is present in the bulk pore water [e.g., Leroy and Revil, 2004]. Using the formulation of the electrokinetic coupling introduced by Revil and Leroy [2004] (and extended rece tly to unsaturated flow by Revil et al. [2007] and Linde et al. [2007] and to the inertial laminar flow regime by Bole've et al. [2007]), the electrical potential can be obtained from the solution of the Poisson equation. In this equation, the source term is equal to the divergence of the streaming current density, which in turn is equal to the excess of charge per unit pore volume time the seepage velocity. Generalizing the work by Revil et al. [2003b], Jardani et al. [2006a] used a cross-correlation method to reconstruct the possible shapes of the water table and to locate sinkholes at depth. [2] Numerical simulations of self-potential signals associated with the flow of the groundwater shows the dipolar character of the source [e.g., Revil et al., 1999; Bole've et al., 2007]. In a multipole development of the self-potential field, the monopole contribution is equal to zero because of the global electroneutrality condition prevailing in porous materials. Therefore the leading term is the dipolar field. [3] If the support volume of the source is small or if the sources are located along an interface (like the water table), it is possible to use the cross-correlation method to determine the position of the source or to image this interface by optimizing the semblance between the selfpotential anomaly, normalized by its power, and the signal modeled with the appropriate Green function [see Birch, 1993, 1998]. The Green's function can be computed analytically for a homogeneous ground but it can be also computed numerically accounting for the real (or inverted) electrical resistivity distribution and appropriate boundary conditions for the self-potential field. The cross-correlation approach has been used as a source localization method in acoustic [e.g., Omologo and Svaizer, 1994; Thomann, 1996], in seismology [e.g., Saccorotti and Del Pezzo, 2000], in magnetoencephalography [e.g., Cao et al., 2002], and in the localization of contaminant plumes in the atmosphere [e.g., Roussel et al., 2002], just to cite few of them. This is therefore not a new approach. We discuss below the validity of this approach to self-potential data. Note that this approach was also used very successfully by Revil et al. [2001], Iuliano et al. [2002], and Revil et al. [2003a, 2003b] and recently by Jardani et al. [2006b] and Bhattacharyal et al. [2007] to localize the causative source of self-potential anomalies. Finally, we will discuss briefly future exciting trends in the inversion of self-potential signals.

International audience; The percolation of water in the ground is responsible for measurable electric potentials called self-potentials. These potentials are influenced by the distribution of the electrical conductivity of the ground. Because sinkholes are associated both with self-potential and electrical conductivity anomalies, a joint inversion of EM-34 conductivity and self-potential data is proposed as a way of delineating the location of these features. Self-potential and EM conductivity data were obtained at a test site in Normandy (France) where sinkholes and crypto-sinkholes are present over a karstic area in a chalk substratum overlain by clay-with-flint and loess covers. The presence of sinkholes and crypto-sinkholes is associated with negative self-potential anomalies with respect to a reference electrode located outside the area where the sinkholes are clustered. The sinkholes also have a conductivity signature identified by the EM-34 conductivity data. We used the simulated-annealing method, which is a global optimization technique, to invert jointly EM-34 conductivity and self-potential data. Self-potential and electrical conductivity provide clear complementary information to determine the interface between the loess and clay-with-flint formations. The sinkholes and crypto-sinkholes are marked by depressions in this interface, focusing the groundwater flow towards the aquifer contained in the chalk substratum.

International audience; Charge occurrence probability (COP) and dipole occurrence probability (DOP) tomographic imaging of graphite and sulphide orebodies, which were earlier detected by a self-potential (SP) survey, were carried out. Three typical examples, two shallower graphite lenses in Bender and Berni, Orissa State, and one relatively deeper sulphide deposit in Kayar, Rajasthan State, are presented. An exploratory test hole, drilled on the basis of the SP results in Bender and Berni, struck graphite. A mise-à-la-masse survey was also carried out on these two deposits to delineate the orebody. The graphite deposits have subsequently been mined. The shapes of the graphite bodies, especially the upper parts, are now known. The Bender deposit is a single graphite lens, whereas the graphite occurrences in Berni are complex multilens-type deposits. Both the COP and DOP techniques clearly imaged the single lens at Bender, as well as the multilens deposits at Berni. The Kayar sulphide deposit, unlike the graphite deposits, has not yet been mined, and therefore it is not delineated as precisely as the graphite orebodies. However, its outline is known from the drilling data. The imaging results of COP and DOP show good agreement with the drilling results of the sulphide deposits.

The classical formulation of the coupled hydroelectrical flow in porous media is based on a linear formulation of two coupled constitutive equations for the electrical current density and the seepage velocity of the water phase and obeying Onsager's reciprocity. This formulation shows that the streaming current density is controlled by the gradient of the fluid pressure of the water phase and a streaming current coupling coefficient that depends on the so-called zeta potential. Recently a new formulation has been introduced in which the streaming current density is directly connected to the seepage velocity of the water phase and to the excess of electrical charge per unit pore volume in the porous material. The advantages of this formulation are numerous. First this new formulation is more intuitive not only in terms of constitutive equation for the generalized Ohm's law but also in specifying boundary conditions for the influence of the flow field upon the streaming potential. With the new formulation, the streaming potential coupling coefficient shows a decrease of its magnitude with permeability in agreement with published results. The new formulation is also easily extendable to non-viscous laminar flow problems (high Reynolds number ground water flow in cracks for example) and to unsaturated conditions with applications to the vadose zone. We demonstrate here that this formulation is suitable to model self-potential signals in the field. We investigate infiltration of water from an agricultural ditch, vertical infiltration of water into a sinkhole, and preferential horizontal flow of ground water in a paleochannel. For the three cases reported in the present study, a good match is obtained between the finite element simulations performed with the finite element code Comsol Multiphysics 3.3 and field observations. Finally, this formulation seems also very promising for the inversion of the geometry of ground water flow from the monitoring of self-potential signals.

International audience; An algorithm is developed to interpret self-potential (SP) data in terms of distribution of Darcy velocity of the ground water. The model is based on the proportionality existing between the streaming current density and the Darcy velocity. Because the inverse problem of current density determination from SP data is underdetermined, we use Tikhonov regularization with a smoothness constraint based on the differential Laplacian operator and a prior model. The regularization parameter is determined by the L-shape method. The distribution of the Darcy velocity depends on the localization and number of non-polarizing electrodes and information relative to the distribution of the electrical resistivity of the ground. A priori hydraulic information can be introduced in the inverse problem. This approach is tested on two synthetic cases and on real SP data resulting from infiltration of water from a ditch.