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New developments in mobile resistivity meter instrumentation have made it possible to survey large areas with dense data coverage. The mobile system usually has a limited number of electrodes attached to a cable that is pulled along behind an operator so that a large area can be covered within a short time. Such surveys can produce three‐dimensional datasets with hundreds of thousands of electrodes positions and data points. Similarly, the inverse model used to interpret the data can have several hundred thousand cells. It is impractical to model such large datasets within a reasonable time on microcomputers used by many small companies employing standard inversion techniques. We describe a model segmentation technique that subdivides the finite‐element mesh used to calculate the apparent resistivity and Jacobian matrix values into a number of smaller meshes. A fast technique that optimizes the calculation of the Jacobian matrix values for multi‐channel systems was also developed. A one‐dimensional wavelet transform method was then used to compress the storage of the Jacobian matrix, in turn reducing the computer time and memory required to solve the least‐squares optimization equation to determine the inverse model resistivity values. The new techniques reduce the calculation time and memory required by more than 80% while producing models that differ by less than 1% from that obtained using the standard inversion technique with a single mesh. We present results using a synthetic model and a field dataset that illustrates the effectiveness of the proposed techniques. [ABSTRACT FROM AUTHOR]

It appears to be relatively common to assume that negative apparent chargeability data in time-domain induced polarisation (IP) surveying is a sign of bad data quality. Negative IP data can however occur as a consequence of the distribution of chargeable zones in the ground, which is well documented in literature. A general mechanism behind negative IP data is proposed as follows; if the chargeable zones are mainly located in zones of negative sensitivity, and there is low or no chargeability in the positive sensitivity volumes in the investigated volume, it will result in negative apparent chargeability. Numerical modelling confirms that the phenomenon will typically occur for longer electrode separation if the chargeability is concentrated in a thin layer at the surface only, but that other distributions of the chargeable bodies can also cause negative IP data. Different electrode arrays differ in tendency to produce negative IP data, where dipole–dipole and pole–dipole arrays are more prone to generate negative data than nested arrays in the modelled examples. In addition to the relative location of the chargeable zone the resistivity is important for its impact on the apparent chargeability. Field data recorded in connection with the 3rd International IP Workshop on Ile d'Oléron in April 2014 confirm that negative apparent chargeability can be caused by a thin chargeable layer at the surface. The abundant negative IP data can be explained by an inverted model with low residuals, in which the chargeability is concentrated in a thin layer with modest chargeability close to the surface. Removing the data with negative apparent chargeability before inversion results in apparently poor resolution of the bottom layer and artefacts that are not present in the inversion results from the original data set. The results clearly demonstrate that negative apparent chargeability data can be a result of the distribution of chargeable zones in relation to the sensitivity distribution, and that such data should not be edited away on a routine basis since they contain important information. [ABSTRACT FROM AUTHOR]

Previous studies show that optimized arrays generated using the ‘Compare R’ method have significantly better resolution than conventional arrays. This method determines the optimum set of arrays by selecting those that give the maximum model resolution. The number of possible arrays (the comprehensive data set) increases with the fourth power of the number of electrodes. The optimization method faces practical limitations for 2-D survey lines with more than 60 electrodes where the number of possible arrays exceeds a million. Several techniques are proposed to reduce the calculation time for such survey lines. A single-precision version of the ‘Compare R’ algorithm using a new ranking function reduces the calculation time by two to eight times while providing results similar to the double-precision version. Recent improvements in computer GPU technology can reduce the calculation time by about seven times. The calculation time is reduced by half by using the fact that arrays that are symmetrical about the center of the line produce identical changes in the model resolution values. It is further reduced by more than thirty times by calculating the Sherman–Morrison update for all the possible two-electrode combinations, which are then used to calculate the model resolution values for the four-electrode arrays. The calculation time is reduced by more then ten times by using a subset of the comprehensive data set consisting of only symmetrical arrays. Tests with a synthetic model and field data set show that optimized arrays derived from this subset produce inversion models with differences of less than 10% from those derived using the full comprehensive data set. The optimized data sets produced models that are more accurate than the Wenner–Schlumberger array data sets in all the tests. [ABSTRACT FROM AUTHOR]

ABSTRACT The use of optimized arrays generated using the 'Compare R' method for cross-borehole resistivity measurements is examined in this paper. We compare the performances of two array optimization algorithms, one that maximizes the model resolution and another that minimizes the point spread value. Although both algorithms give similar results, the model resolution maximization algorithm is several times faster. A study of the point spread function plots for a cross-borehole survey shows that the model resolution within the central zone surrounded by the borehole electrodes is much higher than near the bottom end of the boreholes. Tests with synthetic and experimental data show that the optimized arrays generated by the 'Compare R' method have significantly better resolution than a 'standard' measurement sequence used in previous surveys. The resolution of the optimized arrays is less if arrays with both current (or both potential) electrodes in the same borehole are excluded. However, they are still better than the 'standard' arrays. [ABSTRACT FROM AUTHOR]

Time-lapse resistivity surveys are commonly used to monitor temporal changes in the subsurface. In certain cases, it is known from other information that the resistivity will only decrease or increase with time. The 4-D resistivity smoothness-constrained inversion method reduces artifacts due to noise by including a temporal roughness filter constraint that ensures the temporal changes vary in a smooth manner. A least-squares optimization method is used to find a solution by attempting to locate the minimum of an objective function that consists of the data misfit and model (spatial and temporal) roughness. In some cases, the 4-D time-lapse inverse models show an increase in the resistivity with time in parts of the subsurface where it is only expected to decrease (or vice versa). We compare two methods, the barrier function and transformation methods, that attempt to minimize or eliminate these artifacts. We incorporate the barrier function constraint into the 4-D inverse method by using a modified difference matrix as a temporal roughness filter. The barrier function constraint includes an additional term that increases the objective function value greatly if the model values cross the allowed thresholds. This greatly minimizes the artifacts but does not completely eliminate them. It has the advantage that there are minimal changes in the objective function in regions of model space that are not close to the imposed thresholds. The method of transformations changes the model parameter such that the additional positivity or negativity constraints are implicitly included in the transformed model parameter. It has the advantage that it can completely eliminate the artifacts. However, it modifies the entire objective function which could be a disadvantage in some cases. We also explore a combination of the two methods, using the barrier function method to generate an initial model that minimizes the artifacts followed by the transformation method. This hybrid technique completely removes the residual artifacts left by the barrier method, and produces an inverse model which is closer to the true model for a synthetic data set. We also describe a post-inversion modification of the L-curve method to determine the optimum model that takes into account the non-linear nature of the inverse problem and the forward modelling method. The technique gave an estimate of the noise level for a field data set and produced a model which is consistent with independent hydrological measurements at the test site. • 4-D ERT inversion. • Asymmetric time constraints. • Barrier function methods. • Transformation methods. • Post-inversion L-curve analysis. [ABSTRACT FROM AUTHOR]

Abstract: There have been major improvements in instrumentation, field survey design and data inversion techniques for the geoelectrical method over the past 25years. Multi-electrode and multi-channel systems have made it possible to conduct large 2-D, 3-D and even 4-D surveys efficiently to resolve complex geological structures that were not possible with traditional 1-D surveys. Continued developments in computer technology, as well as fast data inversion techniques and software, have made it possible to carry out the interpretation on commonly available microcomputers. Multi-dimensional geoelectrical surveys are now widely used in environmental, engineering, hydrological and mining applications. 3-D surveys play an increasingly important role in very complex areas where 2-D models suffer from artifacts due to off-line structures. Large areas on land and water can be surveyed rapidly with computerized dynamic towed resistivity acquisition systems. The use of existing metallic wells as long electrodes has improved the detection of targets in areas where they are masked by subsurface infrastructure. A number of PC controlled monitoring systems are also available to measure and detect temporal changes in the subsurface. There have been significant advancements in techniques to automatically generate optimized electrodes array configurations that have better resolution and depth of investigation than traditional arrays. Other areas of active development include the translation of electrical values into geological parameters such as clay and moisture content, new types of sensors, estimation of fluid or ground movement from time-lapse images and joint inversion techniques. In this paper, we investigate the recent developments in geoelectrical imaging and provide a brief look into the future of where the science may be heading. [Copyright &y& Elsevier]

Abstract: Four different methods to automatically select an optimal set of array configurations that gives the maximum subsurface resolution with a limited number of measurements for 2D electrical imaging surveys were tested. The first (CR) method directly calculates the change in the model resolution for each new array added to the base data set, and uses this to select array configurations that gave the maximum model resolution. However this method is the slowest. The algorithm used by the CR method for calculating rank-one updates was optimized to reduce computational time by a factor of eighty. The sequence of calculations was modified to reduce the traffic between the computer main memory and the CPU registers. Further code optimizations were made to take advantage of the parallel processing capabilities of modern CPUs. The second (ETH) and third (BGS) methods use approximations based on the sensitivity values to estimate the change in the model resolution matrix. The ETH and BGS methods, respectively, use the first and second power of the sensitivity values to calculate approximations of the model resolution. Both methods are about an order of magnitude faster than the CR method. The results obtained by the BGS method are significantly better than the ETH method, and it approaches that of the CR method. The fourth method (BGS–CR) uses a combination of the BGS and CR methods. It produces results that are almost identical to the CR method but is several times faster. The different methods were tested using data from synthetic models and field surveys. The models obtained from the inversion of the data sets generated by the four different methods confirm that the models generated by the CR method have the best resolution, followed by the BGS–CR, BGS and ETH methods. [ABSTRACT FROM AUTHOR]

Electrical impedance tomography (EIT) was used to monitor the movement of a fluorinated hydrocarbon dense nonaqueous phase liquid (DNAPL) through a saturated porous medium within a laboratory column. Impedance measurements were made using a horizontal plane of 12 electrodes positioned at regular intervals around the centre of the column. A 2D inversion algorithm, which incorporated the cylindrical geometry of the column, was used to reconstruct resistivity and phase images from the measured data. Differential time-lapse images of DNAPL movement past the plane of electrodes were generated by the cell-by-cell subtraction of resistivity and phase baseline models from those associated with the DNAPL release stage of the experiment.The DNAPL pulse was clearly delineated as resistive anomalies in the differential time-lapse resistivity images. The spatial extent of the resistive anomalies indicated that in addition to vertical migration, some lateral spreading of the DNAPL had occurred. Residual contamination could be detected after quasi-static conditions were reestablished. Residual DNAPL saturation was estimated from the resistivity model data by applying Archie''s second equation.Despite significant measured phase changes due to DNAPL contamination, the differential phase images revealed only weak anomalies associated with DNAPL flow; these anomalies could be seen only in the initial stages of the experiment during peak flow through the plane of electrodes. [Copyright &y& Elsevier]

The smoothness-constrained least-squares method is widely used for two-dimensional (2D) and three-dimensional (3D) inversion of apparent resistivity data sets. The Gauss–Newton method that recalculates the Jacobian matrix of partial derivatives for all iterations is commonly used to solve the least-squares equation. The quasi-Newton method has also been used to reduce the computer time. In this method, the Jacobian matrix for a homogeneous earth model is used for the first iteration, and the Jacobian matrices for subsequent iterations are estimated by an updating technique. Since the Gauss–Newton method uses the exact partial derivatives, it should require fewer iterations to converge. However, for many data sets, the quasi-Newton method can be significantly faster than the Gauss–Newton method. The effectiveness of a third method that is a combination of the Gauss–Newton and quasi-Newton methods is also examined. In this combined inversion method, the partial derivatives are directly recalculated for the first two or three iterations, and then estimated by a quasi-Newton updating technique for the later iterations.The three different inversion methods are tested with a number of synthetic and field data sets. In areas with moderate (less than 10:1) subsurface resistivity contrasts, the inversion models obtained by the three methods are similar. In areas with large resistivity contrasts, the Gauss–Newton method gives significantly more accurate results than the quasi-Newton method. However, even for large resistivity contrasts, the differences in the models obtained by the Gauss–Newton method and the combined inversion method are small. As the combined inversion method is faster than the Gauss–Newton method, it represents a satisfactory compromise between speed and accuracy for many data sets. [Copyright &y& Elsevier]

The geoelectrical imaging method is a tool for mapping the intrusion boundary between fresh water and saline water due to its inherent capability to delineate the lateral changes in pore-water salinity. A new field survey technique that can be used for environmental and geotechnical investigations has been developed. This study evaluates the multiscale survey technique as a tool employed in electrical imaging to detect the salt-water intrusion boundary in Yan, State of Kedah, northwest Malaysia. The technique was incorporated into these surveys, and it has proved to be a robust method for accurately mapping the fresh-water/saline-water boundary. The resulting resistivity sections from these surveys were consistent with both the available geological and borehole information from the area and the previous resistivity surveys conducted by the Geological Survey of Malaysia at those sites. [ABSTRACT FROM AUTHOR]

Electrical resistivity tomography (ERT) surveys are widely used in geological, environmental and engineering studies. However, the effectiveness of surface ERT surveys is limited by decreasing resolution with depth and near the ends of the survey line. Increasing the array length will increase depth of investigation, but may not be possible at urban sites where access is limited. One novel method of addressing these limitations while maintaining lateral coverage is to install an array of deep electrodes. Referred to here as the Multi-Electrode Resistivity Implant Technique (MERIT), self-driving pointed electrodes are implanted at depth below each surface electrode in an array, using direct-push technology. Optimal sequences of readings have been identified with the “Compare R” method of Wilkinson. Numerical, laboratory, and field case studies are applied to examine the effectiveness of the MERIT method, particularly for use in covered karst terrain. In the field case studies, resistivity images are compared against subsurface structure defined from borings, GPR surveys, and knowledge of prior land use. In karst terrain where limestone has a clay overburden, traditional surface resistivity methods suffer from lack of current penetration through the shallow clay layer. In these settings, the MERIT method is found to improve resolution of features between the surface and buried array, as well as increasing depth of penetration and enhancing imaging capabilities at the array ends. The method functions similar to a cross-borehole array between horizontal boreholes, and suffers from limitations common to borehole arrays. Inversion artifacts are common at depths close to the buried array, and because some readings involve high geometric factors, inversions are more susceptible to noise than traditional surface arrays. Results are improved by using errors from reciprocal measurements to weight the data during the inversion. [ABSTRACT FROM AUTHOR]

The optimized ‘Compare R’ (CR) method is considered one of the best algorithms to automatically generate a set of electrode arrays that maximizes the model resolution for electrical resistivity imaging. In its original version, the calculation time to generate a set of arrays, even for a short resistivity line, required several hours. Recently, researchers spent considerable effort to reduce execution time. In addition, other modifications have been made to improve the practical aspects, such as minimizing the electrode polarization effects and incorporating errors in the data. In line with this approach, the effectiveness of the optimized arrays that are generated based on a modified version of ‘Compare-R' optimization algorithm is demonstrated through a comprehensive and quantitative comparison with the conventional Dipole-Dipole (DD) and Wenner-Schlumberger (WS) arrays. Four different synthetic models were generated and noisy data cases were considered. The results show that the optimized array has significantly better resolution and target detail than conventional arrays. This is clear in enhancing the detectability accuracy in the deepest part of the inversion models. Of the conventional arrays, the DD array provides inversion images mostly closely related to the performance of the optimized array models. [ABSTRACT FROM AUTHOR]

Abstract: We describe the application of 3D electrical resistivity tomography (ERT) to the characterisation and reserve estimation of an economic fluvial sand and gravel deposit. Due to the smoothness constraints used to regularise the inversion, it can be difficult to accurately determine the geometry of sharp interfaces. We have therefore considered two approaches to interface detection that we have applied to the 3D ERT results in an attempt to provide an accurate and objective assessment of the bedrock surface elevation. The first is a gradient-based approach, in which the steepest gradient of the vertical resistivity profile is assumed to correspond to the elevation of the mineral/bedrock interface. The second method uses an intrusive sample point to identify the interface resistivity at a location within the model, from which an iso-resistivity surface is identified that is assumed to define the interface. Validation of these methods has been achieved through direct comparison with observed bedrock surface elevations that were measured using real-time-kinematic GPS subsequent to the 3D ERT survey when quarrying exposed the bedrock surface. The gradient-based edge detector severely underestimated the depth to bedrock in this case, whereas the interface resistivity method produced bedrock surface elevations that were in close agreement with the GPS-derived surface. The failure of the gradient-based method is attributed to insufficient model sensitivity in the region of the bedrock surface, whereas the success of the interface resistivity method is a consequence of the homogeneity of the mineral and bedrock, resulting in a consistent interface resistivity. These results highlight the need for some intrusive data for model validation and for edge detection approaches to be chosen on the basis of local geological conditions. [Copyright &y& Elsevier]

Abstract: We describe the use of a fully volumetric geophysical imaging approach, three-dimensional electrical resistivity (3D ERT), for bedrock detection below mixed sand and gravel deposits typical of fluvial valley-fill terraces. We illustrate the method through an analysis of terrace deposits of the Great Ouse River (UK), where up to 4m of sand and gravel have filled the valley bottom during the latest Pleistocene. We use an edge detector to identify the steepest gradient in first-derivative resistivity profiles, which yields an estimate of bedrock depth (verified by drilling) to a precision better than 0.2m (average) and 0.4m (standard deviation). Comparison of a range of drilling techniques at the site has revealed that borehole derived interface depths suffered from levels of uncertainty similar to those associated with the 3D ERT — indicating that the reliability of bedrock interface depths determined using these two approaches is comparable in this case. The 3D ERT method provides a high spatial resolution that enabled a previously unknown erosional bedrock structure, associated with the change from deeper first terrace to second terrace deposits, to be identified in the Great Ouse valley. The method provides a relatively quick method to quantify terrace fill volume over large sites to a greater degree of precision than currently available. [Copyright &y& Elsevier]

Abstract: Robust characterization and monitoring of dense nonaqueous phase liquid (DNAPL) source zones is essential for designing effective remediation strategies, and for assessing the efficacy of treatment. In this study high-resolution cross-hole electrical resistivity tomography (ERT) was evaluated as a means of monitoring a field-scale in-situ bioremediation experiment, in which emulsified vegetable oil (EVO) electron donor was injected into a trichloroethene source zone. Baseline ERT scans delineated the geometry of the interface between the contaminated alluvial aquifer and the underlying mudstone bedrock, and also the extent of drilling-induced physical heterogeneity. Time-lapse ERT images revealed major preferential flow pathways in the source and plume zones, which were corroborated by multiple lines of evidence, including geochemical monitoring and hydraulic testing using high density multilevel sampler arrays within the geophysical imaging planes. These pathways were shown to control the spatial distribution of the injected EVO, and a bicarbonate buffer introduced into the cell for pH control. Resistivity signatures were observed within the preferential flow pathways that were consistent with elevated chloride levels, providing tentative evidence from ERT of the biodegradation of chlorinated solvents. [ABSTRACT FROM AUTHOR]

Abstract: Internal erosion is one of the major reasons for embankment dam failures. Despite this, the knowledge of the temporal development of internal erosion in full scale structures is limited. Detection of internal erosion is complicated using conventional methods, and new or improved methods are appreciated. Hällby was the first Swedish embankment to get a permanently installed monitoring system intended for resistivity measurements. Daily measurements started to take place already in late 1996, which make these long term monitoring data unique. This paper includes examples of long term time series from Hällby along with some evaluation and interpretation techniques used when analysing such monitoring data. Time-lapse inversion was used to focus the variation over time and suppress artefacts due to the resistivity structure. Seasonal resistivity variations inside the dam are obvious. Increasing long term resistivity has been noticed in a particular zone in the left embankment. This zone also exhibits larger seasonal variations relative to other parts of the dam, and the variations are increasing. The observations may relate to an ongoing internal erosion process in the dam. The long term change may be indicative of a change in material properties, and the large and increasing variations may reflect higher and increasing seepage levels. In the years 2004 to 2006 the dam was upgraded and the resistivity system reinstalled. The results indicate that resistivity monitoring may have a chance of detecting development of internal erosion at an early stage. [Copyright &y& Elsevier]

Abstract: A methodology to locate automatically limits or boundaries between different geological bodies in 2D electrical tomography is proposed, using a crest line extraction process in gradient images. This method is applied on several synthetic models and on field data set acquired on three experimental sites during the European project PALEOSIS where trenches were dug. The results presented in this work are valid for electrical tomographies data collected with a Wenner-alpha array and computed with an l1 norm (blocky inversion) as optimization method. For the synthetic cases, three geometric contexts are modelled: a vertical and a dipping fault juxtaposing two different geological formations and a step-like structure. A superficial layer can cover each geological structure. In these three situations, the method locates the synthetic faults and layer boundaries, and determines fault displacement but with several limitations. The estimated fault positions correlate exactly with the synthetic ones if a conductive (or no superficial) layer overlies the studied structure. When a resistive layer with a thickness of 6 m covers the model, faults are positioned with a maximum error of 1 m. Moreover, when a resistive and/or a thick top layer is present, the resolution significantly decreases for the fault displacement estimation (error up to 150%). The tests with the synthetic models for surveys using the Wenner-alpha array indicate that the proposed methodology is best suited to vertical and horizontal contacts. Application of the methodology to real data sets shows that a lateral resistivity contrast of 1:5–1:10 leads to exact faults location. A fault contact with a resistivity contrast of 1:0.75 and overlaid by a resistive layer with a thickness of 1 m gives an error location ranging from 1 to 3 m. Moreover, no result is obtained for a contact with very low contrasts (∼1:0.85) overlaid by a resistive soil. The method shows poor results when vertical gradients are greater than horizontal ones. This kind of image processing technique should be systematically used for improving the objectiveness of tomography interpretation when looking for limits between geological objects. [Copyright &y& Elsevier]