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

Direct current (DC) resistivity (here referred to as resistivity) and induced polarization (IP) methods allow, respectively, the determination of the spatial distribution of the low-frequency resistive and capacitive characteristics of soil. Since both properties are affected by lithology, pore fluid chemistry, and water content (see Chapter 4 of this volume), these methods have significant potential for hydrogeophysical applications. The methods can be applied at a wide range of laboratory and field scales, and surveys may be made in arbitrary geometrical configurations (e.g., on the soil surface and down boreholes). In fact, resistivity methods are one of the most widely used sets of geophysical techniques in hydrogeophysics. These surveys are relatively easy to carry out, instrumentation is inexpensive, data processing tools are widely available, and the relationships between resistivity and hydrological properties, such as porosity and moisture content, are reasonably well established. In contrast, applications of induced polarization methods in hydrogeophysics have been limited. As noted by Slater and Lesmes (2002), this is partly because of the more complex procedure for data acquisition, but also because the physicochemical interpretation of induced polarization parameters is not fully understood.

DC Resistivity and Induced Polarization Methods

https://lucris.lub.lu.se/ws/files/4380044/4934427.pdf

A comparison of the Gauss–Newton and quasi-Newton methods in resistivity imaging inversion

A contaminated site at Lernacken in southern Sweden, formerly used for sludge disposal, was investigated using a 3-D resistivity imaging technique. The data acquisition was carried out using a roll-along technique for 3-D data acquisition that allows using standard multielectrode equipment designed for engineering and environmental applications. The technique allows for the measurement of large true 3-D resistivity data sets, and data were measured using two perpendicular electrode-orientation directions with only one layout of the cables. The data were plotted as two sets of pseudo depth slices using the two electrode orientation directions, which resulted in markedly different plots. The complete data set was inverted to form a resistivity-depth model of the ground using a 3-D least-squares smoothness constrained inversion technique. The results obtained were compared to other geophysical and background data, and a good agreement was found. The results show that the 3-D roll-along technique in combination with 3-D inversion can be highly useful for engineering and environmental applications. However, multichannel measurement equipment is necessary to speed up the data acquisition process for routine application.

/pdf/a-3-d-resistivity-investigation-of-a-contaminated-site-at-3768kc7cua.pdf

A 3-D resistivity investigation of a contaminated site at Lernacken, Sweden

Three-dimensional resistivity surveys and their associated inversion models are required to accurately resolve structures exhibiting very complex geology. In the same light, 3D resistivity surveys collected at multiple times are required to resolve temporally varying conditions. In this work we present 3D data sets, both synthetic and real, collected at different times. The large spatio-temporal
data sets are then inverted simultaneously using a least-squares methodology that incorporates roughness filters in both the space and time domains. The spatial roughness filter constrains the model resistivity to vary smoothly in the x-, y- and z-directions. A temporal roughness filter is also applied that minimizes changes in the resistivity between successive temporal inversion models and the L-curve method is used to determine the optimum weights for both spatial and temporal roughness filters. We show that the use of the temporal roughness filter can accurately resolve changes in the resistivity even in the presence of noise. The L1- and L2-norm constraints for the temporal roughness filter are first examined using a synthetic model. The synthetic data test shows that the L1-norm temporal constraint produces significantly more accurate results when the resistivity changes abruptly with time. The model obtained with the L1-norm temporal constraint is also less sensitive to random noise compared with independent inversions (i.e., without any temporal constraint) and the L2-norm temporal constraint. Anomalies that are common in models using independent
inversions and the L2-norm and L1-norm temporal constraints are likely to be real. In contrast, anomalies present in a model using independent inversions but that are significantly reduced with the L2-norm and L1-norm constraints are likely artefacts. For field data sets, the method successfully recovered temporal changes in the subsurface resistivity from a landfill monitoring survey due to rainwater infiltration, as well as from an experiment to map the migration of sodium cyanide solution from an injection well using surface and borehole electrodes in an area with significant topography.

/pdf/smoothness-constrained-time-lapse-inversion-of-data-from-3d-5fdbg000mq.pdf

Smoothness-constrained time-lapse inversion of data from 3D resistivity surveys

To “A 3‐D resistivity investigation of a contaminated site at Lernacken, Sweden” (Torleif Dahlin, Christian Bernstone, and Meng Heng Loke, GEOPHYSICS, 67, 1692–1700).

M. H. Loke

Papers

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

A comparison of the Gauss–Newton and quasi-Newton methods in resistivity imaging inversion

A 3-D resistivity investigation of a contaminated site at Lernacken, Sweden

Smoothness-constrained time-lapse inversion of data from 3D resistivity surveys

To “A 3‐D resistivity investigation of a contaminated site at Lernacken, Sweden” (Torleif Dahlin, Christian Bernstone, and Meng Heng Loke, GEOPHYSICS, 67, 1692–1700).