Inversion Of Electrical Resistivity Tomography Data Research Articles

Salinity distribution in agricultural land by geophysical, hydrochemical and geostatistical approaches: a pilot area located in Qelabshowah–Belqas, East Nile Delta region, Egypt

The study area is situated in the Qelabshowah–Belqas region, known for its Quaternary deposits. This research aims to demonstrate the two-dimensional (2D) variation of subsurface layers and salinity distribution using geoelectrical data, hydrochemical analysis, and geostatistical analysis. DC resistivity measurements were taken at fifteen vertical electrical sounding (VES) survey points using a Schlumberger array (AB/2 = 100 m) along three profiles. In addition, an electrical resistivity tomography (ERT) survey was conducted with a dipole–dipole array across one profile. Seven surface water samples were collected in the area. From the 1D and 2D inversion of VES and ERT data sets, three-to-four geoelectric layers were identified, including unconsolidated surface deposits, saturated clayey sand, saturated sand, and a salt-rich layer. The 2D inversion of VES data revealed an ancient salt-rich layer deposited in swampy conditions over a conductive wet sand layer along profile one due to salt mineral infiltration and dissolution. The 2D inversion of ERT data showed accurate lateral geometric accuracy compared to the 2D inversion of VES data, highlighting geological features, such as caves in the second layer and a buried water canal on the ground surface. Surface water samples showed high salinity levels with sodium hazards, indicating an Na–Cl composition. Geoelectric and hydrochemical data sets were geostatistically analyzed using spherical variogram supported ordinary Kriging interpolation. The analysis indicated weak to moderate spatial dependency for true resistivity parameters, while sodium content (SC) and permeability index (PI) showed strong spatial correlation. The 2D spatial distribution resistivity maps based on the 1D inversion of VES data displayed a general decrease in resistivity with depth, likely due to clay minerals or moist soil in the second layer and saline irrigation water infiltration in the third layer. The 2D spatial distribution of SC and PI showed a high concentration zone, posing a potential risk to agricultural crops regardless of soil permeability. It is recommended to use these maps when cultivating plants that can tolerate high sodium levels during the reclamation process.

Massively parallel modeling and inversion of electrical resistivity tomography data using PFLOTRAN

Abstract. Electrical resistivity tomography (ERT) is a broadly accepted geophysical method for subsurface investigations. Interpretation of field ERT data usually requires the application of computationally intensive forward modeling and inversion algorithms. For large-scale ERT data, the efficiency of these algorithms depends on the robustness, accuracy, and scalability on high-performance computing resources. In this regard, we present a robust and highly scalable implementation of forward modeling and inversion algorithms for ERT data. The implementation is publicly available and developed within the framework of PFLOTRAN, an open-source, state-of-the-art massively parallel subsurface flow and transport simulation code. The forward modeling is based on a finite-volume discretization of the governing differential equations, and the inversion uses a Gauss–Newton optimization scheme. To evaluate the accuracy of the forward modeling, two examples are first presented by considering layered (1D) and 3D earth conductivity models. The computed numerical results show good agreement with the analytical solutions for the layered earth model and results from a well-established code for the 3D model. Inversion of ERT data, simulated for a 3D model, is then performed to demonstrate the inversion capability by recovering the conductivity of the model. To demonstrate the parallel performance of PFLOTRAN's ERT process model and inversion capabilities, large-scale scalability tests are performed by using up to 131 072 processes on a leadership class supercomputer. These tests are performed for the two most computationally intensive steps of the ERT inversion: forward modeling and Jacobian computation. For the forward modeling, we consider models with up to 122 ×106 degrees of freedom (DOFs) in the resulting system of linear equations and demonstrate that the code exhibits almost linear scalability on up to 10 000 DOFs per process. On the other hand, the code shows superlinear scalability for the Jacobian computation, mainly because all computations are fairly evenly distributed over each process with no parallel communication.

Characterization of gas‐bearing sediments in the coastal environment using geophysical and geotechnical data

AbstractSeismic investigation in marine gas‐bearing sediments often fails to get information below the acoustic mask created by free gas. To circumvent this problem, we combined collocated multichannel ultra‐high resolution seismic imaging, marine electrical resistivity tomography and core sampling to study the physical properties of gas‐bearing sediments in the Bay of Concarneau (France). We obtained sections of compression (P‐) wave velocity () from the multichannel processing and 2D resistivity models from the marine electrical resistivity tomography data inversion. We observed low resistivity (∼0.5 Ω·m) and low (∼1200 m/s) values where free gas was identified in the seismic data. We tested a joint processing workflow combining the 1D inversion of the marine electrical resistivity tomography data with the 2D P‐wave velocity through a structural coupling between resistivity and velocity. We obtained a series of 2D resistivity models fitting the data whilst in agreement with the data. The resulting models showed the continuity of the geological units below the acoustic gas fronts, which are associated with paleo‐valley sediment infilling. We were able to demonstrate relationships between resistivity and velocity differing from superficial to deeper sediments. We established these relationships at the geophysical scale and then compared the results to data from core sampling ( and porosity). We inferred the porosity distribution from the marine electrical resistivity tomography data. At the core locations, we observed a good agreement between this geophysical scale porosity and the core data both within and outside the gas‐bearing sediments. This agreement demonstrated that resistivity could be used as a proxy for porosity where no was available below gas caps. In these regions, the observed low resistivity showed a high porosity (60%–70%) down to about 10–20 m in depth, in contrast with the surrounding medium that has a porosity of less than 55%. These results support the hypothesis that failures inside the paleo‐valley sediment could control the gas migration.

Monitoring the perturbation zone near a foundation excavation with electrical resistivity tomography: Comparison between time-lapse 3D and 2D inversions in single-profile study

On construction sites, ground loosening can trigger land collapses or sinkholes that compromise safety. Electrical resistivity tomography (ERT) is a very useful non-destructive method to monitor subsurface ground stability during the construction of foundation pits. We used inclined drilling to construct an artificial loosening zone near a test-bed excavation pit and performed time-lapse (TL) ERT surveys along lines lying over the loosening zone. The surveys were performed before and after excavation of the pit, and after construction of the loosening zone. As performing three-dimensional (3D) inversion for the ERT data, independent 3D inversion sequences monitor subsurface changes only when an appropriate initial model is available, which can be obtained via 2D inversion of ERT data. To overcome the limitations of 3D inversion, we subjected all TL ERT data to four-dimensional inversion, with consideration of the pit, to ensure that changes were accurately detected regardless of the initial model chosen. Our inversion strategy aids interpretation of TL ERT data obtained to monitor ground loosening on construction sites.

A comprehensive workflow to analyze ensembles of globally inverted 2D electrical resistivity models

Electrical resistivity tomography (ERT) aims at imaging the subsurface resistivity distribution and provides valuable information for different geological, engineering, and hydrological applications. To obtain a subsurface resistivity model from measured apparent resistivities, stochastic or deterministic inversion procedures may be employed. Typically, the inversion of ERT data results in non-unique solutions; i.e., an ensemble of different models explains the measured data equally well. In this study, we perform inference analysis of model ensembles generated using a well-established global inversion approach to assess uncertainties related to the non-uniqueness of the inverse problem. Our interpretation strategy starts by establishing model selection criteria based on different statistical descriptors calculated from the data residuals. Then, we perform cluster analysis considering the inverted resistivity models and the corresponding data residuals. Finally, we evaluate model uncertainties and residual distributions for each cluster. To illustrate the potential of our approach, we use a particle swarm optimization (PSO) algorithm to obtain an ensemble of 2D layer-based resistivity models from a synthetic data example and a field data set collected in Loon-Plage, France. Our strategy performs well for both synthetic and field data and allows us to extract different plausible model scenarios with their associated uncertainties and data residual distributions. Although we demonstrate our workflow using 2D ERT data and a PSO-based inversion approach, the proposed strategy is general and can be adapted to analyze model ensembles generated from other kinds of geophysical data and using different global inversion approaches.

Enhancing the resolving ability of electrical resistivity tomography for imaging saltwater intrusion through improvements in inversion methods: A laboratory and numerical study

Mapping and monitoring saltwater intrusion are critical for the sustainable management of groundwater in coastal aquifers around the world. Increasingly, geophysical methods, such as electrical resistivity tomography (ERT), have been used to address these needs. We identify methods for the inversion of ERT data that would most accurately map the location and geometry of an intrusion wedge. This is accomplished using laboratory and synthetic experiments, with the classic representation of an intrusion wedge perpendicular to the coast. The laboratory experiments allow us to collect ERT data on a saltwater intrusion wedge in an environment in which we have supporting data that provided (1) the distribution of salinity within the tank with which to verify our inversion results, (2) the resistivity, porosity, and permeability of the porous medium, and (3) the transform between resistivity and salinity. The synthetic experiments allow exploration of issues of specific interest related to the presence of lithologic heterogeneity at a field site: the role of lithologic heterogeneity in introducing complexity into the resistivity-salinity relationship and the geometry of the saltwater intrusion wedge. We find that using a reference model with a good approximation of the wedge to inform the inversion greatly improves the ability of the resulting resistivity profile to map the wedge. Where there is no, or limited, lithologic heterogeneity, a parametric approach, which constrains the range of possible solutions by solving for a sharp interface between the saltwater and freshwater regions, is very effective at capturing the wedge location and geometry. Where there is lithologic heterogeneity, a hybrid between the parametric and informed inversion approaches is most effective, resolving the wedge with a high level of accuracy with little a priori information.

Soil electrical resistivity monitoring as a practical tool for evaluating irrigation systems efficiency at the orchard scale: a case study in a vineyard in Central Chile

In many orchards, irrigation scheduling is designed based on data from meteorological networks and considering homogeneous soil properties. Such assumptions may result in inefficient irrigation, which is difficult to constrain without expensive or invasive techniques. Here we have evaluated the ability of the electrical resistivity tomography (ERT) for detecting meter-scale irrigation uniformity and deep percolation during irrigation. The spatiotemporal variability of soil volumetric water content (VWC) in a vineyard located near Santiago (Chile) was inferred using ERT monitoring of two irrigation cycles. The electrical resistivity structure up to 4 m depth was estimated using two-dimensional inversion of ERT data. ERT results were verified by comparing resistivity models with VWC measured with soil moisture sensors, soil properties mapped in a 2 m-depth soil pit, and the spatiotemporal evolution of VWC obtained by solving numerically Richards equation. Largest temporal variations of resistivity were observed within the root depth (1 m) and are consistent with expected relative changes in VWC during irrigation. ERT images exhibit lateral changes in resistivity at these depths, likely indicating non-uniform infiltration of water controlled by observed soil texture variations. Resistivity changes were also observed below the root zone, suggesting that a fraction of the irrigation water percolates downward. These findings can be explained by an excess of irrigation water applied during the monitoring, which was planned considering regional evapotranspiration (ET) data that overestimated the actual ET measured at the vineyard. Altogether, our results suggest that ERT monitoring during irrigation is a cost-effective tool to constrain the performance of irrigation systems.

An assessment of ERT as a method to monitor water content regime in flood embankments: The case study of the Adige River embankment

Stability of flood embankments is strongly affected by the water flow taking place in the saturated and unsaturated soil. Monitoring of the water flow in flood embankments is therefore essential in the context of flood risk management to predict and prevent failures of embankments. Electrical Resistivity Tomography (ERT) is gaining popularity for its ability to monitor water regime in the subsoil more quickly, cost-effectively and on a larger scale compared to traditional geotechnical monitoring systems that rely on local sensors. This paper presents the application of ERT to the monitoring of water content in a flood embankment on the Adige River in Italy. The resistivity profiles obtained from the ERT measurements were converted into water content profiles via a laboratory-derived relationship between resistivity and water content. At the same time, local sensors to monitor pore water pressure were installed in the saturated and unsaturated zone of the embankment and this allowed reconstructing the water content regime in the embankment via inverse analysis of water flow. This offered the chance to benchmark ERT-derived water content against independent indirect measurements of water content in the field.ERT-inferred water content profiles based on laboratory calibration could capture the water content profiles derived from water flow analysis only qualitatively. This was attributed to artefacts in the ERT data inversion arising from the high contrasts in resistivity between different embankment layers. On the other hand, ERT proved to be a valuable tool to quantify the water content in the soil if field-specific relationship between water content and ERT-measured resistivity is developed.

A Weighting Function-Based Method for Resistivity Inversion in Subsurface Investigations

There is a high demand for high detection accuracy and resolution with respect to anomalous bodies due to the increased development of underground spaces. This study focused on the weighted inversion of observed data from individual array type electrical resistivity tomography (ERT), and developed an improved method of applying a data weighing function to the geoelectrical inversion procedure. In this method, the weighting factor as an observed data weighting term was introduced into the objective function. For individual arrays, the sensitivity decreases with increasing electrode interval. Therefore, the Jacobian matrices were computed for the observed data of individual arrays to determine the value of the weighting factor, and the weighting factor was calculated automatically during inversion. In this work, 2D combined inversion of ERT data from four-electrode Alfa-type arrays is examined. The effectiveness of the weighted inversion method was demonstrated using various synthetic and real data examples. The results indicated that the inversion method based on observed data weighted function could improve the contribution of observed data with depth information to the objective function. It has been proven that the combined weighted inversion method could be a feasible tool for improving the accuracies of positioning and resolution while imaging deep anomalous bodies in the subsurface.

Using Electrical Resistivity Tomography (ERT) to Delineate Subsurface Structures at Siloam Hot Spring in the Soutpansberg Basin, South Africa

Electrical resistivity tomography (ERT) was used to delineate subsurface structures at Siloam hot spring in the Soutpansberg Basin of South Africa. The spring water was reported to be hottest in South Africa. Groundwater with temperature ranging between 63.3 °C and 67.5°C was observed flowing from the spring. Relatively wet areas were noted to the south and north of the spring. Electrical resistivity arrays with Dipole-dipole and Wenner-Schlumberger configurations were used. Current injection and potential dipole separations of 5 m and 10 m were applied across the spring. Inversion results for arrays with the shorter dipole separation of 5 m had better resolution. Resistivity sections were generated from inversion of ERT data. The resistivity values for the low and high resistive zones were ρa < 10 and ρa > 70 Ωm respectively. Sub-horizontal resistivity zones were obtained from the inversion of Wenner-Schlumberger array survey data. High resistivity zones associated with dykes or sills were delineated on Dipole-dipole derived depth sections. Near vertical structures associated with water bearing faults or fractures were delineated at the Siloam hot spring.

Construction of structural reference model for ERT data inversion in heavy metal contaminated sites surveys

Electrical resistivity tomography (ERT) surveys can provide useful information on heavy metal contaminated sites assessment. Structural reference model is introduced as a constraint to guide ERT data inversion in ERT survey. In this paper, we propose a novel method, which integrate soil physical and chemical information into structural reference model construction for ERT data inversion to improve the accuracy of inversion results. The reference model consists of two parts: contaminated area and uncontaminated area. The scope of contaminated areas is recognised using soil physical and chemical properties and the apparent resistivity data extracted from the ERT profile at the borehole location, and then the resistivity distribution of reference model is set according to the average resistivity of soil samples. The accuracy of the proposed method is evaluated with two numerical experiments. The experiment results of synthetic models show that the structural reference model constructed by the proposed method is close to the synthetic model and effectively improves the inversion results.

Forward modeling to investigate inversion artifacts resulting from time-lapse electrical resistivity tomography during rainfall simulations

Time-lapse electrical resistivity tomography (ERT) is commonly used as a minimally invasive tool to study infiltration processes. In 2014, we conducted field studies coupling variable intensity rainfall simulation with high-resolution ERT to study the real-time partitioning of rainfall into surface and subsurface response. The significant contrast in resistivity in the subsurface from large changes in subsurface moisture resulted in artifacts during the inversion process of the time-lapse ERT data collected using a dipole-dipole electrode array. These artifacts, which are not representative of real subsurface moisture dynamics, have been shown to arise during time-lapse inversion of ERT data and may be subject to misinterpretation. Forward modeling of the infiltration process post field experiments using a two-layer system (saprolite overlain by a soil layer) was used to generate synthetic datasets. The synthetic data were used to investigate the influence of both changes in volumetric moisture content and electrode configuration on the development of the artifacts identified in the field datasets. For the dipole-dipole array, we found that a decrease in the resistivity of the bottom layer by 67% resulted in a 50% reduction in artifact development. Artifacts for the seven additional array configurations tested, ranged from a 19% increase in artifact development (using an extended dipole-dipole array) to as much as a 96% decrease in artifact development (using a wenner-alpha array), compared to that of the dipole-dipole array. Moreover, these arrays varied in their ability to accurately delineate the infiltration front. Model results showed that the modified pole-dipole array was able to accurately image the infiltration zone and presented fewer artifacts for our experiments. In this study, we identify an optimal array type for imaging rainfall-infiltration dynamics that reduces artifacts. The influence of moisture contrast between the infiltrating water and the bulk subsurface material was characterized and shown to be a major factor in contributing to artifact development. Through forward modeling, this study highlights the importance of considering array type and subsurface moisture conditions when using time-lapse resistivity to obtain reliable estimates of vadose zone flow processes during rainfall-infiltration events.

PFLOTRAN-E4D: A parallel open source PFLOTRAN module for simulating time-lapse electrical resistivity data

Time-lapse electrical resistivity tomography (ERT) is finding increased application for remotely monitoring processes occurring in the near subsurface in three-dimensions (i.e. 4D monitoring). However, there are few codes capable of simulating the evolution of subsurface resistivity and corresponding tomographic measurements arising from a particular process, particularly in parallel and with an open source license. Herein we describe and demonstrate an electrical resistivity tomography module for the PFLOTRAN subsurface flow and reactive transport simulation code, named PFLOTRAN-E4D. The PFLOTRAN-E4D module operates in parallel using a dedicated set of compute cores in a master-slave configuration. At each time step, the master processes receives subsurface states from PFLOTRAN, converts those states to bulk electrical conductivity, and instructs the slave processes to simulate a tomographic data set. The resulting multi-physics simulation capability enables accurate feasibility studies for ERT imaging, the identification of the ERT signatures that are unique to a given process, and facilitates the joint inversion of ERT data with hydrogeological data for subsurface characterization. PFLOTRAN-E4D is demonstrated herein using a field study of stage-driven groundwater/river water interaction ERT monitoring along the Columbia River, Washington, USA. Results demonstrate the complex nature of subsurface electrical conductivity changes, in both the saturated and unsaturated zones, arising from river stage fluctuations and associated river water intrusion into the aquifer. The results also demonstrate the sensitivity of surface based ERT measurements to those changes over time. PFLOTRAN-E4D is available with the PFLOTRAN development version with an open-source license at https://bitbucket.org/pflotran/pflotran-dev.

3D inversion of ERT data on an archaeological site using GPR reflection and 3D inverted magnetic data as a priori information

Non‐destructive geophysical prospecting methods are increasingly used for the investigation of archaeological sites, where a detailed physical and geometrical reconstruction of structures is required prior to any excavation work. In 1996, at the Archaeological Test Site of the Sabine Necropolis at Research Area of National Research Council of Rome (Montelibretti, Italy), a small area had been selected to test the integration of magnetic, ground‐penetrating radar, and electrical resistivity tomography techniques.The magnetic data were acquired as the vertical gradient of the total magnetic field and were inverted by minimizing an L‐2 norm. The ground‐penetrating radar data were acquired as single‐offset measurements on a regular grid and processed to obtain time slices of reflection amplitude. The electrical resistivity tomography data were acquired with dipole–dipole array along parallel profiles in both east–west and north–south directions.In this work, we reprocessed the data collected in 1996 performing a three‐dimensional inversion of electrical resistivity tomography data using ground‐penetrating radar data and three‐dimensional inversion results of the magnetic data. We inverted electrical resistivity tomography data according to L2 and L1 norm minimization. Both the mean apparent resistivity and different resistivity distributions derived from processed ground‐penetrating radar and three‐dimensional inversion of the vertical gradient of the total magnetic field data were used as a starting model.The results were then compared in the volume under the surveyed area: merits and shortcomings of the different techniques are pointed out and analyzed.From the results of the different applied techniques, it comes that both electrical resistivity tomography and vertical gradient of the total magnetic field locate the searched tomb as a volume, whereas ground‐penetrating radar mainly identified the ceiling of the tomb. Vertical gradient of the total magnetic field data inversion obtained from minimization of the L2 norm properly locates both the chamber and the corridor but produces smeared overestimated volumes. Three‐dimensional inversions of electrical resistivity tomography data with a priori information give an accurate picture of the chamber and delineates the corridor, even if the resistivity values are underestimated if compared with the expected resistivity of void. Results are compared with the archaeological findings as the area was unearthed and verified in 2001.

Challenges and opportunities for fractured rock imaging using 3D cross-borehole electrical resistivity

There is an increasing need to characterize discrete fractures away from boreholes to better define fracture distributions and monitor solute transport. We performed a 3D evaluation of static and time-lapse cross-borehole electrical resistivity tomography (ERT) data sets from a limestone quarry in which flow and transport are controlled by a bedding-plane feature. Ten boreholes were discretized using an unstructured tetrahedral mesh, and 2D panel measurements were inverted for a 3D distribution of conductivity. We evaluated the benefits of 3D versus 2.5D inversion of ERT data in fractured rock while including the use of borehole regularization disconnects (BRDs) and borehole conductivity constraints. High-conductivity halos (inversion artifacts) surrounding boreholes were removed in static images when BRDs and borehole conductivity constraints were implemented. Furthermore, applying these constraints focused transient changes in conductivity resulting from solute transport on the bedding plane, providing a more physically reasonable model for conductivity changes associated with solute transport at this fractured rock site. Assuming bedding-plane continuity between fractures identified in borehole televiewer data, we discretized a planar region between six boreholes and applied a fracture regularization disconnect (FRD). Although the FRD appropriately focused conductivity changes on the bedding plane, the conductivity distribution within the discretized fracture was nonunique and dependent on the starting homogeneous model conductivity. Synthetic studies performed to better explain field observations showed that inaccurate electrode locations in boreholes resulted in low-conductivity halos surrounding borehole locations. These synthetic studies also showed that the recovery of the true conductivity within an FRD depended on the conductivity contrast between the host rock and fractures. Our findings revealed that the potential exists to improve imaging of fractured rock through 3D inversion and accurate modeling of boreholes. However, deregularization of localized features can result in significant electrical conductivity artifacts, especially when representing features with a high degree of spatial uncertainty.

Seismic and geoelectric modeling studies of parameters controlling CO2 geostorage in saline formations

A possible CO2 geostorage in deep saline formation demands the development of a monitoring strategy using techniques of surface seismic reflection and electrical resistivity tomography (ERT) in boreholes. For this purpose, the resolution and sensitivity of both techniques are studied numerically regarding changes induced by CO2 sequestration.We calculated the effect of partially replacing brine with supercritical CO2 on seismic velocities and densities by using the Gassmann equation. Resulting seismic responses and reflection amplitude changes are quite strong in some cases. For thin CO2 layer (thickness<wavelength) the CO2 anomaly can be delimited laterally quite easier than vertically due to possible reflection overlap from the upper and lower CO2 boundaries.To maximize the ERT resolution, we applied the optimized and tripotential electrode configurations with current flows and potential measurements in different spatial orientations. We performed several comparative 2.5D modelling studies assuming different CO2 saturations, plume scenarios, burial depths, electrode configurations and aspect ratios. The results generally reveal the capability of the techniques to map the storage targets (CO2 plumes, saline host formation and impermeable caprock) with different degrees of resolution, smearing and artefacts. The results show the resolution superiority of the optimized arrays over the other arrays.The highest sensitivity to CO2 saturation changes is found for low saturation case in the seismic and for intermediate and high saturation in the geoelectric case. Therefore, a combination of both methods may be necessary for sn accurate determination of CO2 saturation in situ.A supercritical CO2 plume can be resolved as long as its dimensions are larger than the applied electrode spacing and seismic wavelength, respectively. Thinner layers are problematic, particularly in the ERT technique due to its smearing nature. In the North German Basin strongly the salinity increases strongly with depth, and thus causes a dramatical decrease in the resistivity contrasts and anomalies. The depth effect on the seismic resolution is two-fold: on one hand, the contrast in velocity and density between brine and CO2 increases with depth and enhances the reflection strength accordingly; on the other hand attenuation leads to an increase of wavelength causing a resolution decline.The consideration of seismic results in the inversion of ERT data strongly improves the resolution of the resulting tomograms and the CO2 estimation. It also enables reasonable monitoring (even at aspect ratio<1) of CO2 migrations in large areas and thus reduces the costs of the expensive monitoring wells.

Temporal moments in geoelectrical monitoring of salt tracer experiments

Monitoring of salt tracer experiments by electrical resistivity tomography (ERT) has been shown to be a valuable tool for characterizing the hydraulics of an aquifer, but efficient approaches of determining the spatial hydraulic conductivity distribution from ERT data are still missing. Standard inversion of ERT data obtained during salt tracer tests may even lead to estimates of the concentration distribution that are in contradiction to flow and transport of conservative compounds in porous media. In order to avoid nonphysical behavior, we consider the governing equations of groundwater flow, solute transport, and geoelectrics as a coupled system. While the tracer passes through the part of the domain that is sensitive for a particular electrode configuration, the measured electrical potential differences are perturbed. We characterize these perturbations by their temporal moments and relate them to the temporal moments of concentration, which themselves depend on hydraulic conductivity. We present temporal moment‐generating equations leading from the hydraulic conductivity field via heads and velocities to the temporal moments of concentration and electrical potential perturbations. The approach makes use of a linearized version of the Poisson equation. On the basis of this system of coupled steady state equations, we compute the sensitivity of electrical potential perturbations with respect to the log hydraulic conductivity distribution by the continuous adjoint state method for coupled systems. For demonstration, we simulate salt tracer experiments in a virtual quasi‐two‐dimensional sandbox, monitored by ERT. We show that the ratio of the first over the zeroth temporal moment of potential perturbation is less affected by the linearization of the Poisson equation than the zeroth and first moments themselves. Thus, it appears recommendable to use the ratio of first to zeroth moments also as data in inversion. We compare sensitivity patterns resulting from different electrode configurations. The methods of forward simulations and sensitivity calculations presented in this paper can be combined with any inverse kernel to develop a complete inverse model. Altogether, using temporal moments of potential perturbation appears promising for fully coupled hydrogeophysical inversion of ERT surveys during salt tracer tests.

Study of water tension differences in heterogeneous sandy soils using surface ERT

Herbaceous vegetation in the Sahel grows almost exclusively on sandy soils which preferentially retain water through infiltration and storage. The hydrological functioning of these sandy soils during rain cycles is unknown. One way to tackle this issue is to spatialize variations in water content but these are difficult to measure in the vadose zone. We investigated the use of Electrical Resistivity Tomography (ERT) as a technique for spatializing resistivity in a non-destructive manner in order to improve our knowledge of relevant hydrological processes. To achieve this, two approaches were examined. First, we focused on a possible link between water tension (which is much easier to measure in the field by point measurements than water content), and resistivity (spatialized with ERT). Second, because ERT is affected by solution non-uniqueness and reconstruction smoothing, we improved the accuracy of ERT inversion by comparing calculated solutions with in-situ resistivity measurements. We studied a natural microdune during a controlled field experiment with artificial sprinkling which reproduced typical rainfall cycles. We recorded temperature, water tension and resistivity within the microdune and applied surface ERT before and after the 3 rainfall cycles. Soil samples were collected after the experiment to determine soil physical characteristics. An experimental relationship between water tension and water content was also investigated. Our results showed that the raw relationship between calculated ERT resistivity and water tension measurements in sand is highly scattered because of significant spatial variations in porosity. An improved correlation was achieved by using resistivity ratio and water tension differences. The slope of the relationship depends on the soil solution conductivity, as predicted by Archie's law when salted water was used for the rain simulation. We found that determining the variations in electrical resistivity is a sensitive method for spatializing the differences in water tension which are directly linked with infiltration and evaporation/drainage processes in the vadose zone. However, three factors complicate the use of this approach. Firstly, the relation between water tension and water content is generally non-linear and dependent on the water content range. This could limit the use of our site-specific relations for spatializing water content with ERT through tension. Secondly, to achieve the necessary optimization of ERT inversion, we used destructive resistivity measurements in the soil, which renders ERT less attractive. Thirdly, we found that the calculated resistivity is not always accurate because of the smoothing involved in surface ERT data inversion. We conclude that further developments are needed into ERT image reconstruction before water tension (and water content) can be spatialized in heterogeneous sandy soils with the accuracy needed to routinely study their hydrological functioning.

Spatial focusing of electrical resistivity surveys considering geologic and hydrologic layering

Electrical resistivity tomography (ERT) has shown great promise for monitoring transient hydrologic processes. One advantage of ERT under those conditions is the ability of a user to tailor the spatial sensitivity of an ERT survey through selection of electrode locations and electrode combinations. Recent research has shown that quadripoles can be selected in a manner that improves the independent inversion of ERT data. Our ultimate interest lies in using ERT data along with measurements from other sensors, which typically can provide high-quality data from shallow regions of the subsurface, in a joint inversion. As a result, we do not consider the selection of quadripoles specifically for inde-pendent ERT inversion. Rather, we present an approach to focusthe spatial sensitivity of ERT surveys in specificsubsurface regions with the assumption that those data, when interpreted along with other measurements that are sensitive to those regions, will lead to more complete hydrologic characterization. Because we are interested in monitoring rapid processes, our approach is designed to efficiently identify optimal quadripoles. This is achieved by separating the optimization from the inversion grid, significantly reducing computational effort. We extend our previous work to consider the use of both surface and borehole ERT electrodes and to consider the impacts of horizontally layered electrical conductivity conditions. Results confirm the ability of the method to focus survey sensitivity while showing the importance of incorporation of prior knowledge of the subsurface electric conductivity structure in designing optimal ERT surveys.