Electrical resistivity of the soil can be considered as a proxy for the spatial and temporal variability of many other soil physical properties (i.e. structure, water content, or fluid composition). Because the method is non-destructive and very sensitive, it offers a very attractive tool for describing the subsurface properties without digging. It has been already applied in various contexts like: groundwater exploration, landfill and solute transfer delineation, agronomical management by identifying areas of excessive compaction or soil horizon thickness and bedrock depth, and at least assessing the soil hydrological properties. The surveys, depending on the areas heterogeneities can be performed in one-, two- or three-dimensions and also at different scales resolution from the centimetric scale to the regional scale. In this review, based on many electrical resistivity surveys, we expose the theory and the basic principles of the method, we overview the variation of electrical resistivity as a function of soil properties, we listed the main electrical device to performed one-, two- or three-dimensional surveys, and explain the basic principles of the data interpretation. At least, we discuss the main advantages and limits of the method.

/pdf/electrical-resistivity-survey-in-soil-science-a-review-52naoumd0b.pdf

Electrical resistivity survey in soil science: a review .

Tutorial : 2-D and 3-D electrical imaging surveys

Two-dimensional electrical imaging surveys are now widely used in engineering and environmental surveys to map moderately complex structures. In order to adequately resolve such structures with arbitrary resistivity distributions, the regularised least-squares optimisation method with a cell-based model is frequently used in the inversion of the electrical imaging data. The L 2 norm based least-squares optimisation method that attempts to minimise the sum of squares of the spatial changes in the model resistivity is often used. The resulting inversion model has a smooth variation in the resistivity values. In cases where the true subsurface resistivity consists of several regions that are approximately homogenous internally and separated by sharp boundaries, the result obtained by the smooth inversion method is not optimal. It tends to smear out the boundaries and give resistivity values that are too low or too high. The blocky or L 1 norm optimisation method can be used for such situations. This method attempts to minimise the sum of the absolute values of the spatial changes in the model resistivity. It tends to produce models with regions that are piecewise constant and separated by sharp boundaries. Results from tests of the smooth and blocky inversion methods with several synthetic and field data sets highlight the strengths and weaknesses of both methods. The smooth inversion method gives better results for areas where the subsurface resistivity changes in a gradual manner, while the blocky inversion method gives significantly better results where there are sharp boundaries. While fast computers and software have made the task of interpreting data from electrical imaging surveys much easier, it remains the responsibility of the interpreter to choose the appropriate tool for the task based on the available geological information.

/pdf/a-comparison-of-smooth-and-blocky-inversion-methods-in-2-d-17iu0jl2na.pdf

A comparison of smooth and blocky inversion methods in 2-D electrical imaging surveys

Numerical simulations are used to compare the resolution and efficiency of 2D resistivity imaging surveys for 10 electrode arrays. The arrays analysed include polepole (PP), pole-dipole (PD), half-Wenner (HW), Wenner-α (WN), Schlumberger (SC), dipole-dipole (DD), Wenner-β (WB), γ -array (GM), multiple or moving gradient array (GD) and midpoint-potential-referred measurement (MPR) arrays. Five synthetic geological models, simulating a buried channel, a narrow conductive dike, a narrow resistive dike, dipping blocks and covered waste ponds, were used to examine the surveying efficiency (anomaly effects, signal-to-noise ratios) and the imaging capabilities of these arrays. The responses to variations in the data density and noise sensitivities of these electrode configurations were also investigated using robust (L1-norm) inversion and smoothness-constrained least-squares (L2-norm) inversion for the five synthetic models. The results show the following. (i) GM and WN are less contaminated by noise than the other electrode arrays. (ii) The relative anomaly effects for the different arrays vary with the geological models. However, the relatively high anomaly effects of PP, GM and WB surveys do not always give a high-resolution image. PD, DD and GD can yield better resolution images than GM, PP, WN and WB, although they are more susceptible to noise contamination. SC is also a strong candidate but is expected to give more edge effects. (iii) The imaging quality of these arrays is relatively robust with respect to reductions in the data density of a multi-electrode layout within the tested ranges. (iv) The robust inversion generally gives better imaging results than the L2-norm inversion, especially with noisy data, except for the dipping block structure presented here. (v) GD and MPR are well suited to multichannel surveying and GD may produce images that are comparable to those obtained with DD and PD. Accordingly, the GD, PD, DD and SC arrays are strongly recommended for 2D resistivity imaging, where the final choice will be determined by the expected geology, the purpose of the survey and logistical considerations.

/pdf/a-numerical-comparison-of-2d-resistivity-imaging-with-10-1kfer57nmn.pdf

A numerical comparison of 2D resistivity imaging with 10 electrode arrays

Recent developments in the direct-current geoelectrical imaging method

A fast inversion technique for the interpretation of data from resistivity tomography surveys has been developed for operation on a microcomputer. This technique is based on the smoothness-constrained least-squares method and it produces a two-dimensional subsurface model from the apparent resistivity pseudosection. In the first iteration, a homogeneous earth model is used as the starting model for which the apparent resistivity partial derivative values can be calculated analytically. For subsequent iterations, a quasi-Newton method is used to estimate the partial derivatives which reduces the computer time and memory space required by about eight and twelve times, respectively, compared to the conventional least-squares method. Tests with a variety of computer models and data from field surveys show that this technique is insensitive to random noise and converges rapidly. This technique takes about one minute to invert a single data set on an 80486DX microcomputer.

Rapid least-squares inversion of apparent resistivity pseudosections by a quasi-Newton method1

Techniques to reduce the time needed to carry out 3D resistivity surveys with a moderate number (25 to 100) of electrodes and the computing time required to interpret the data have been developed. The electrodes in a 3D survey are normally arranged in a square grid and the pole-pole array is used to make the potential measurements. The number of measurements required can be reduced to about one-third of the maximum possible number without seriously degrading the resolution of the resulting inversion model by making measurements along the horizontal, vertical and 45° diagonal rows of electrodes passing through the current electrode. The smoothness-constrained least-squares inversion method is used for the data interpretation. The computing time required by this technique can be greatly reduced by using a homogeneous half-space as the starting model so that the Jacobian matrix of partial derivatives can be calculated analytically. A quasi-Newton updating method is then used to estimate the partial derivatives for subsequent iterations. This inversion technique has been tested on synthetic and field data where a satisfactory model is obtained using a modest amount of computer time. On an 80486DX2/66 microcomputer, it takes about 20 minutes to invert the data from a 7 by 7 electrode survey grid. using the techniques described below, 3D resistivity surveys and data inversion can be carried out using commercially available field equipment and an inexpensive microcomputer.

Practical techniques for 3D resistivity surveys and data inversion1

The use of optimised resistivity tomography surveys to acquire field data imposes extra constraints on the design strategy beyond maximising the quality of the resulting tomographic image. In this paper, methods are presented to 1) minimise electrode polarisation effects; 2) make efficient use of parallel measurement channels; and 3) incorporate data noise estimates in the optimisation process. 1) A simulated annealing algorithm is used to rearrange the optimised measurement sequences to minimise polarisation errors. The method is developed using random survey designs, and is demonstrated to be effective for use with single and multi-channel optimised surveys. 2) An optimisation algorithm is developed to design surveys by successive addition of multi-channel groups of measurements rather than individual electrode configurations. The multi-channel surveys are shown to produce results nearly as close to optimal as equivalent single channel surveys, while reducing data collection times by an order of magnitude. 3) Random errors in the data are accounted for by weighting the electrode configurations in the optimisation process according to a simple error model incorporating background and voltage-dependent noise. The use of data weighting produces optimised surveys that are more robust in the presence of noise, while maintaining as much of the image resolution of the noise-free designs as possible. All the new methods described in this paper are demonstrated using both synthetic and real data, the latter having been measured on an active landslide using a permanently installed geoelectrical monitoring system.

Practical aspects of applied optimized survey design for electrical resistivity tomography

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.

/pdf/computation-of-optimized-arrays-for-3-d-electrical-imaging-3b0045rinn.pdf

Computation of optimized arrays for 3-D electrical imaging surveys

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.

/pdf/optimized-arrays-for-2d-cross-borehole-electrical-tomography-1ihbkwyn25.pdf

M.H. Loke

Papers

Rapid least-squares inversion of apparent resistivity pseudosections by a quasi-Newton method1

Practical techniques for 3D resistivity surveys and data inversion1

Practical aspects of applied optimized survey design for electrical resistivity tomography

Computation of optimized arrays for 3-D electrical imaging surveys

Optimized arrays for 2D cross‐borehole electrical tomography surveys