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Calculating the electric potential for 3-D resistivity inversion algorithms can be time consuming depending on the structure of the mesh. There have been generally two approaches to generating finite-element meshes. One approach uses a structured rectangular mesh with hexahedral elements on a rectangular model grid. The distribution of model cells can be designed to follow known boundaries, and directional roughness constraints can be easily imposed. A 1-D wavelet transform that takes advantage of the regular arrangement of the model cells can also be used to reduce the computer time and memory required to solve the smoothness-constrained least-squares equation. However, the structured rectangular mesh uses an unnecessarily fine mesh in parts of the model that are far away from the electrodes where the potential changes gradually. A second approach uses an unstructured mesh with tetrahedral elements created automatically by a mesh generation program with finer elements nearer the electrodes and coarser elements in the more remote regions. This generates a mesh with a much smaller number of nodes. The disadvantage is that an irregular model grid is normally used. We examine an alternative approach that combines structured and unstructured meshes. We employ a regular model grid with a finer mesh near the surface and a coarser mesh in deeper regions using a combination of hexahedral and tetrahedral elements. The semi-structured mesh reduces the calculation time by more than three times compared with a structured mesh. An adaptive semi-structured mesh that also uses a coarser mesh for model cells near the surface if they are more than one unit electrode spacing from the nearest electrode was also developed for surveys with non-uniform data coverage. For the Bonsall Leys field survey, which used a capacitively coupled mobile system and collected a data set with nearly a million electrode positions, the adaptive mesh reduces the calculation time by about 80%. The calculat

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.

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.

Resistivity monitoring surveys are used to detect temporal changes in the subsurface using repeated measurements over the same site. The positions of the electrodes are typically measured at the start of the survey program and possibly at occasional later times. In areas with unstable ground, such as landslide‐prone slopes, the positions of the electrodes can be displaced by ground movements. If this occurs at times when the positions of the electrodes are not directly measured, they have to be estimated. This can be done by interpolation or, as in recent developments, from the resistivity data using new inverse methods. The smoothness‐constrained least squares optimisation method can be modified to include the electrode positions as additional unknown parameters. The Jacobian matrices with the sensitivity of the apparent resistivity measurements to changes in the electrode positions are then required by the optimisation method. In this paper, a fast adjoint‐equation method is used to calculate the Jacobian matrices required by the least squares method to reduce the calculation time. In areas with large near‐surface resistivity contrasts, the inversion routine sometimes cannot accurately distinguish between electrode displacements and subsurface resistivity variations. To overcome this problem, the model for the initial time‐lapse dataset (with accurately known electrode positions) is used as the starting model for the inversion of the later‐time dataset. This greatly improves the accuracy of the estimated electrode positions compared to the use of a homogeneous half‐space starting model. In areas where the movement of the electrodes is expected to occur in a fixed direction, the method of transformations can be used to include this information as an additional constraint in the optimisation routine.

Resistivity monitoring surveys are used to detect temporal changes in the subsurface using repeated measurements over the same site. The positions of the electrodes are typically measured at the start of the survey program and possibly at occasional later times. In areas with unstable ground, such as landslide‐prone slopes, the positions of the electrodes can be displaced by ground movements. If this occurs at times when the positions of the electrodes are not directly measured, they have to be estimated. This can be done by interpolation or, as in recent developments, from the resistivity data using new inverse methods. The smoothness‐constrained least squares optimisation method can be modified to include the electrode positions as additional unknown parameters. The Jacobian matrices with the sensitivity of the apparent resistivity measurements to changes in the electrode positions are then required by the optimisation method. In this paper, a fast adjoint‐equation method is used to calculate the Jacobian matrices required by the least squares method to reduce the calculation time. In areas with large near‐surface resistivity contrasts, the inversion routine sometimes cannot accurately distinguish between electrode displacements and subsurface resistivity variations. To overcome this problem, the model for the initial time‐lapse dataset (with accurately known electrode positions) is used as the starting model for the inversion of the later‐time dataset. This greatly improves the accuracy of the estimated electrode positions compared to the use of a homogeneous half‐space starting model. In areas where the movement of the electrodes is expected to occur in a fixed direction, the method of transformations can be used to include this information as an additional constraint in the optimisation routine.

Adaptive optimal experimental design methods use previous data and results to guide the choice and design of future experiments. This paper describes the formulation of an adaptive survey design technique to produce optimal resistivity imaging surveys for time-lapse geoelectrical monitoring experiments. These survey designs are time-dependent and, compared to dipole-dipole or static optimized surveys that do not change over time, focus a greater degree of the image resolution on regions of the subsurface that are actively changing. The adaptive optimization method is validated using a controlled laboratory monitoring experiment comprising a well-defined cylindrical target moving along a trajectory that changes its depth and lateral position. The algorithm is implemented on a standard PC in conjunction with a modified automated multichannel resistivity imaging system. Data acquisition using the adaptive survey designs requires no more time or power than with comparable standard surveys, and the algorithm processing takes place while the system batteries recharge. The results show that adaptively designed optimal surveys yield a quantitative increase in image quality over and above that produced by using standard dipole-dipole or static (time-independent) optimized surveys

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.

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.

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.

Adaptive optimal experimental design methods use previous data and results to guide the choice and design of future experiments. This paper describes the formulation of an adaptive survey design technique to produce optimal resistivity imaging surveys for time-lapse geoelectrical monitoring experiments. These survey designs are time-dependent and, compared to dipole–dipole or static optimized surveys that do not change over time, focus a greater degree of the image resolution on regions of the subsurface that are actively changing. The adaptive optimization method is validated using a controlled laboratory monitoring experiment comprising a well-defined cylindrical target moving along a trajectory that changes its depth and lateral position. The algorithm is implemented on a standard PC in conjunction with a modified automated multichannel resistivity imaging system. Data acquisition using the adaptive survey designs requires no more time or power than with comparable standard surveys, and the algorithm processing takes place while the system batteries recharge. The results show that adaptively designed optimal surveys yield a quantitative increase in image quality over and above that produced by using standard dipole–dipole or static (time–independent) optimized surveys.

The ‘Compare R’ method is used to automatically generate optimized arrays for two-dimensional resistivity surveys with electrodes arranged along parallel lines on the surface and the subsurface. The resolution at depth is greatly improved by carrying out measurements with at least one line of electrodes below the surface using a direct push installation technique. The performance of the optimized arrays is compared with a standard measurement sequence created manually that was used for previous surveys. Tests were conducted using a synthetic model and a field survey in an area with karst geology that has some ground truth. Both tests show that the optimized arrays have significantly better resolution compared with a standard measurement sequence. We also show that artefacts in the inversion model can be reduced by using higher damping factors near the positions of the subsurface electrodes.

The ‘Compare R’ method is used to automatically generate optimized arrays for two-dimensional resistivity surveys with electrodes arranged along parallel lines on the surface and the subsurface. The resolution at depth is greatly improved by carrying out measurements with at least one line of electrodes below the surface using a direct push installation technique. The performance of the optimized arrays is compared with a standard measurement sequence created manually that was used for previous surveys. Tests were conducted using a synthetic model and a field survey in an area with karst geology that has some ground truth. Both tests show that the optimized arrays have significantly better resolution compared with a standard measurement sequence. We also show that artefacts in the inversion model can be reduced by using higher damping factors near the positions of the subsurface electrodes.

Adaptive optimal experimental design methods use previous data and results to guide the choice and design of future experiments. This paper describes the formulation of an adaptive survey design technique to produce optimal resistivity imaging surveys for time-lapse geoelectrical monitoring experiments. These survey designs are time-dependent and, compared to dipole–dipole or static optimized surveys that do not change over time, focus a greater degree of the image resolution on regions of the subsurface that are actively changing. The adaptive optimization method is validated using a controlled laboratory monitoring experiment comprising a well-defined cylindrical target moving along a trajectory that changes its depth and lateral position. The algorithm is implemented on a standard PC in conjunction with a modified automated multichannel resistivity imaging system. Data acquisition using the adaptive survey designs requires no more time or power than with comparable standard surveys, and the algorithm processing takes place while the system batteries recharge. The results show that adaptively designed optimal surveys yield a quantitative increase in image quality over and above that produced by using standard dipole–dipole or static (time–independent) optimized surveys.

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.

3-D electrical resistivity surveys and inversion models are required to accurately resolve structures in areas with very complex geology where 2-D models might suffer from artefacts. Many 3-D surveys use a grid where the number of electrodes along one direction (x) is much greater than in the perpendicular direction (y). Frequently, due to limitations in the number of independent electrodes in the multi-electrode system, the surveys use a roll-along system with a small number of parallel survey lines aligned along the x-direction. The ‘Compare R’ array optimization method previously used for 2-D surveys is adapted for such 3-D surveys. Offset versions of the inline arrays used in 2-D surveys are included in the number of possible arrays (the comprehensive data set) to improve the sensitivity to structures in between the lines. The array geometric factor and its relative error are used to filter out potentially unstable arrays in the construction of the comprehensive data set. Comparisons of the conventional (consisting of dipole-dipole and Wenner–Schlumberger arrays) and optimized arrays are made using a synthetic model and experimental measurements in a tank. The tests show that structures located between the lines are better resolved with the optimized arrays. The optimized arrays also have significantly better depth resolution compared to the conventional arrays.

3-D electrical resistivity surveys and inversion models are required to accurately resolve structures in areas with very complex geology where 2-D models might suffer from artefacts. Many 3-D surveys use a grid where the number of electrodes along one direction (x) is much greater than in the perpendicular direction (y). Frequently, due to limitations in the number of independent electrodes in the multi-electrode system, the surveys use a roll-along system with a small number of parallel survey lines aligned along the x-direction. The ‘Compare R’ array optimization method previously used for 2-D surveys is adapted for such 3-D surveys. Offset versions of the inline arrays used in 2-D surveys are included in the number of possible arrays (the comprehensive data set) to improve the sensitivity to structures in between the lines. The array geometric factor and its relative error are used to filter out potentially unstable arrays in the construction of the comprehensive data set. Comparisons of the conventional (consisting of dipole-dipole and Wenner–Schlumberger arrays) and optimized arrays are made using a synthetic model and experimental measurements in a tank. The tests show that structures located between the lines are better resolved with the optimized arrays. The optimized arrays also have significantly better depth resolution compared to the conventional arrays.

Electrical resistivity tomography is commonly used to identify geologic features associated with sinkhole formation. In covered karst terrain, however, it can be difficult to resolve the depth to top of limestone with this method. This is due to the fact that array lengths, and hence depth of resolution, are often limited by residential or commercial lot dimensions in urban environments. Furthermore, the sediments mantling the limestone are often clay-rich and highly conductive. The resistivity method has limited sensitivity to resistive zones beneath conductive zones. This sensitivity can be improved significantly with electrodes implanted at depth in the cover sediments near the top of limestone. An array of deep electrodes is installed with direct push technology in the karst cover. When combined with a surface array in which each surface electrode is underlain by a deep electrode, the array geometry is similar to a borehole array turned on its side. This method, called the Multi-Electrode Resistivity Implant Technique (MERIT), offers the promise of significantly improved resolution of epikarst and cover collapse development zones in the overlying sediment, the limestone or at the sediment-bedrock interface in heterogeneous karst environments. With a non-traditional array design, the question of optimal array geometries arises. Optimizing array geometries is complicated by the fact that many plausible 4-electrode readings will produce negative apparent resistivity values, even in homogeneous terrain. Negative apparent resistivities cannot be used in inversions based on the logarithm of the apparent resistivity. New algorithms for seeking optimal array geometries have been developed by modifying the “Compare R” method of Wilkinson and Loke. The optimized arrays show significantly improved resolution over basic arrays adapted from traditional 2D surface geometries. Several MERIT case study surveys have been conducted in covered karst in west-central Florida, with 2

Three-dimensional surveys and inversion models are required to accurately resolve structures in areas with very complex geology where 2-D models might suffer from artifacts. Many 3-D surveys use a survey grid where the number of electrodes along one direction (x) is much greater than in the perpendicular direction (y). Frequently, due to limitations in the number of independent electrodes in the multi-electrode system, the surveys use a roll-along system with a small number of parallel survey lines aligned along the xdirection. The 'Compare R' array optimization method previously used for 2-D surveys is adapted for such 3-D surveys. Offset versions of the inline arrays used in 2-D surveys are included in the number of possible arrays (the comprehensive data set) to improve the sensitivity to structures in between the lines. By using PCs with modern graphics cards incorporating a fast Graphics Processing Unit (GPU) and using an improved single-precision 'Compare R' algorithm, the 3-D optimized arrays can be calculated within a reasonable time despite the comprehensive data set possibly have millions of arrays. A comparison with data sets using inline measurements made using conventional arrays show that structures located between the lines are much better resolved with the optimized arrays.

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.

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.

There have been major improvements in instrumentation, field survey design and data inversion techniques for the geoelectrical method over the past 25 years. 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.

Electrical resistivity tomography is commonly used to identify geologic features associated with sinkhole formation. In covered karst terrain, however, it can be difficult to resolve the depth to top of limestone with this method. This is due to the fact that array lengths, and hence depth of resolution, are often limited by residential or commercial lot dimensions in urban environments. Furthermore, the sediments mantling the limestone are often clay-rich and highly conductive. The resistivity method has limited sensitivity to resistive zones beneath conductive zones. This sensitivity can be improved significantly with electrodes implanted at depth in the cover sediments near the top of limestone. An array of deep electrodes is installed with direct push technology in the karst cover. When combined with a surface array in which each surface electrode is underlain by a deep electrode, the array geometry is similar to a borehole array turned on its side. This method, called the Multi-Electrode Resistivity Implant Technique (MERIT), offers the promise of significantly improved resolution of epikarst and cover collapse development zones in the overlying sediment, the limestone or at the sediment-bedrock interface in heterogeneous karst environments. With a non-traditional array design, the question of optimal array geometries arises. Optimizing array geometries is complicated by the fact that many plausible 4-electrode readings will produce negative apparent resistivity values, even in homogeneous terrain. Negative apparent resistivities cannot be used in inversions based on the logarithm of the apparent resistivity. New algorithms for seeking optimal array geometries have been developed by modifying the “Compare R” method of Wilkinson and Loke. The optimized arrays show significantly improved resolution over basic arrays adapted from traditional 2D surface geometries. Several MERIT case study surveys have been conducted in covered karst in west-central Florida, with 2

Three-dimensional surveys and inversion models are required to accurately resolve structures in areas with very complex geology where 2-D models might suffer from artifacts. Many 3-D surveys use a survey grid where the number of electrodes along one direction (x) is much greater than in the perpendicular direction (y). Frequently, due to limitations in the number of independent electrodes in the multi-electrode system, the surveys use a roll-along system with a small number of parallel survey lines aligned along the xdirection. The 'Compare R' array optimization method previously used for 2-D surveys is adapted for such 3-D surveys. Offset versions of the inline arrays used in 2-D surveys are included in the number of possible arrays (the comprehensive data set) to improve the sensitivity to structures in between the lines. By using PCs with modern graphics cards incorporating a fast Graphics Processing Unit (GPU) and using an improved single-precision 'Compare R' algorithm, the 3-D optimized arrays can be calculated within a reasonable time despite the comprehensive data set possibly have millions of arrays. A comparison with data sets using inline measurements made using conventional arrays show that structures located between the lines are much better resolved with the optimized arrays.

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.

There have been major improvements in instrumentation, field survey design and data inversion techniques for the geoelectrical method over the past 25 years. 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.

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.

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 4 m 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 0.2 m (average) and 0.4 m (standard deviation). The 3D ERT method provides a high spatial resolution, which 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 to a greater degree of precision than currently available.

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 4 m 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 0.2 m (average) and 0.4 m (standard deviation). The 3D ERT method provides a high spatial resolution, which 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 to a greater degree of precision than currently available.

Polarisation potentials are caused when metallic electrodes are used to transmit current in resistivity imaging surveys. If these electrodes are subsequently used to measure potential differences, the decaying polarisation potentials can be a source of significant error. In this paper we describe a general method to minimise the impact of polarisation errors by rearranging the resistivity measurements to maximise the time between any electrode injecting current and later measuring potential. This method does not rely on the existence of a natural ordering of the measurements and can therefore be used with arbitrary resistivity imaging arrays, specifically including those generated by automated optimisation schemes. The method uses a global minimisation algorithm ("simulated annealing") to attempt to avoid local minima without performing an exhaustive search of the configuration space. We determine the control parameters and permutation types for the method from the results of a series of numerical experiments on a randomly generated measurement sequence. We then demonstrate the efficacy of the method using real data measured with a permanently installed resistivity monitoring system on an active landslide. The results show that polarisation errors can be effectively eliminated when using optimised resistivity imaging arrays.

Polarisation potentials are caused when metallic electrodes are used to transmit current in resistivity imaging surveys. If these electrodes are subsequently used to measure potential differences, the decaying polarisation potentials can be a source of significant error. In this paper we describe a general method to minimise the impact of polarisation errors by rearranging the resistivity measurements to maximise the time between any electrode injecting current and later measuring potential. This method does not rely on the existence of a natural ordering of the measurements and can therefore be used with arbitrary resistivity imaging arrays, specifically including those generated by automated optimisation schemes. The method uses a global minimisation algorithm ("simulated annealing") to attempt to avoid local minima without performing an exhaustive search of the configuration space. We determine the control parameters and permutation types for the method from the results of a series of numerical experiments on a randomly generated measurement sequence. We then demonstrate the efficacy of the method using real data measured with a permanently installed resistivity monitoring system on an active landslide. The results show that polarisation errors can be effectively eliminated when using optimised resistivity imaging arrays.

Modern automatic multi-electrode survey instruments have made it possible to use non-traditional arrays to maximize the subsurface resolution from electrical imaging surveys. Previous studies have shown that one of the best methods for generating optimized arrays is to select the set of array configurations that maximizes the model resolution for a homogeneous earth model. The Sherman–Morrison Rank-1 update is used to calculate the change in the model resolution when a new array is added to a selected set of array configurations. This method had the disadvantage that it required several hours of computer time even for short 2-D survey lines. The algorithm was modified to calculate the change in the model resolution rather than the entire resolution matrix. This reduces the computer time and memory required as well as the computational round-off errors. The matrix–vector multiplications for a single add-on array were replaced with matrix–matrix multiplications for 28 add-on arrays to further reduce the computer time. The temporary variables were stored in the double-precision Single Instruction Multiple Data (SIMD) registers within the CPU to minimize computer memory access. A further reduction in the computer time is achieved by using the computer graphics card Graphics Processor Unit (GPU) as a highly parallel mathematical coprocessor. This makes it possible to carry out the calculations for 512 add-on arrays in parallel using the GPU. The changes reduce the computer time by more than two orders of magnitude. The algorithm used to generate an optimized data set adds a specified number of new array configurations after each iteration to the existing set. The resolution of the optimized data set can be increased by adding a smaller number of new array configurations after each iteration. Although this increases the computer time required to generate an optimized data set with the same number of data points, the new fast numerical routines has made this practical on c

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.

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.

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.

Modern automatic multi-electrode survey instruments have made it possible to use non-traditional arrays to maximize the subsurface resolution from electrical imaging surveys. Previous studies have shown that one of the best methods for generating optimized arrays is to select the set of array configurations that maximizes the model resolution for a homogeneous earth model. The Sherman–Morrison Rank-1 update is used to calculate the change in the model resolution when a new array is added to a selected set of array configurations. This method had the disadvantage that it required several hours of computer time even for short 2-D survey lines. The algorithm was modified to calculate the change in the model resolution rather than the entire resolution matrix. This reduces the computer time and memory required as well as the computational round-off errors. The matrix–vector multiplications for a single add-on array were replaced with matrix–matrix multiplications for 28 add-on arrays to further reduce the computer time. The temporary variables were stored in the double-precision Single Instruction Multiple Data (SIMD) registers within the CPU to minimize computer memory access. A further reduction in the computer time is achieved by using the computer graphics card Graphics Processor Unit (GPU) as a highly parallel mathematical coprocessor. This makes it possible to carry out the calculations for 512 add-on arrays in parallel using the GPU. The changes reduce the computer time by more than two orders of magnitude. The algorithm used to generate an optimized data set adds a specified number of new array configurations after each iteration to the existing set. The resolution of the optimized data set can be increased by adding a smaller number of new array configurations after each iteration. Although this increases the computer time required to generate an optimized data set with the same number of data points, the new fast numerical routines has made this practical on c

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.

Modern automatic multi-electrode survey instruments have made it possible to use non-traditional arrays to maximise the subsurface resolution from electrical imaging surveys. One of the best methods for generating optimised arrays is to select the array configurations that maximises the model resolution for a homogeneous earth model. The Sherman-Morrison Rank-1 update is used to calculate the change in the model resolution when a new array is added to a selected set of array configurations. This method had the disadvantage that it required several hours of computer time. The algorithm was modified to calculate the change in the model resolution rather than the entire resolution matrix. This reduces the computer time and memory required and also the round-off errors. The matrix-vector multiplications for a single add-on array were replaced with parallel matrix-matrix multiplications for 512 add-on arrays using the computer GPU for the calculations. These changes reduced the computer time by more than two orders of magnitude. The damped and smoothness-constrained least-squares formulations were used in the array optimisation model resolution equation. The smoothness-constrained method can improve the model resolution for deep extended structures where the resolution is poor.

Modern automatic multi-electrode survey instruments have made it possible to use non-traditional arrays to maximise the subsurface resolution from electrical imaging surveys. One of the best methods for generating optimised arrays is to select the array configurations that maximises the model resolution for a homogeneous earth model. The Sherman-Morrison Rank-1 update is used to calculate the change in the model resolution when a new array is added to a selected set of array configurations. This method had the disadvantage that it required several hours of computer time. The algorithm was modified to calculate the change in the model resolution rather than the entire resolution matrix. This reduces the computer time and memory required and also the round-off errors. The matrix-vector multiplications for a single add-on array were replaced with parallel matrix-matrix multiplications for 512 add-on arrays using the computer GPU for the calculations. These changes reduced the computer time by more than two orders of magnitude. The damped and smoothness-constrained least-squares formulations were used in the array optimisation model resolution equation. The smoothness-constrained method can improve the model resolution for deep extended structures where the resolution is poor.

Laboratory measurements of various materials suggest that more information can be obtained by measuring the in-phase and out-of-phase potentials at a number of frequencies. One common model used to describe the variation of the electrical properties with frequency is the Cole-Cole model. Apart from the DC resistivity (ρ) and chargeability (m) parameters used in conventional induced-polarization (IP) surveys, the Cole-Cole model has two additional parameters, i.e. the time (τ) and relaxation (c) constants. Much research has been conducted on the use of the additional Cole-Cole parameters to distinguish between different IP sources. Here, we propose a modified inversion method to recover the Cole-Cole parameters from a 2D spectral IP (SIP) survey. In this method, an approximate inversion method is initially used to construct a non-homogeneous starting model for the resistivity and chargeability values. The 2D model consists of a number of rectangular cells with constant resistivity (ρ), chargeability (m), time (τ) and relaxation (c) constant values in each cell. A regularized least-squares optimization method is then used to recover the time and relaxation constant parameters as well as to refine the chargeability values in the 2D model. We present results from tests carried out with the proposed method for a synthetic data set as well as from a laboratory tank experiment.

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.

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.

Adaptive optimal experimental design methods use previous data and results to guide the choice and design of future experiments. This paper describes the formulation of an adaptive survey design technique to produce optimal resistivity imaging surveys for time-lapse geoelectrical monitoring experiments. These survey designs are time-dependent and, compared to dipole-dipole or static optimized surveys that do not change over time, focus a greater degree of the image resolution on regions of the subsurface that are actively changing. The adaptive optimization method is validated using a controlled laboratory monitoring experiment comprising a well-defined cylindrical target moving along a trajectory that changes its depth and lateral position. The algorithm is implemented on a standard PC in conjunction with a modified automated multichannel resistivity imaging system. Data acquisition using the adaptive survey designs requires no more time or power than with comparable standard surveys, and the algorithm processing takes place while the system batteries recharge. The results show that adaptively designed optimal surveys yield a quantitative increase in image quality over and above that produced by using standard dipole-dipole or static (time-independent) optimized surveys