Electrical Resistivity

Basic Concept

The basis for electrical resistivity methods is that an electrical potential difference (i.e., voltage) forms around current-carrying electrodes that are implanted within a conductive medium. The voltage distribution surrounding current electrodes that are driven into the subsurface depends the electrical resistivities of the subsurface materials and their spatial variations. Thus, electrical resistivity methods can be used to detect lateral and/or vertical variations in certain subsurface electrical properties (i.e., resistivity or its inverse, conductivity).

Electrical resistivity methods involve injecting electrical current into the subsurface via two current electrodes and measuring the potential difference across two potential electrodes. A single resistivity measurement requires four electrodes coupled to the ground and yields the apparent resistivity of the materials located between the potential electrodes. Resistivity surveys typically employ multiple electrode pairs in various arrays (i.e., spatial geometries), which are selected based on site parameters and/or survey applications (Binley, 2015).

Theory

Electrical resistivity methods measure the ability of electrical current to flow through the subsurface. Thus, resistivity methods require electrical connection (i.e., galvanic coupling) with the ground, and this is achieved with the use of metal electrodes. Typically, a battery-run power supply is used to apply a direct current (DC) between two designated current electrodes implanted in the ground. For each resistivity measurement, the transmitted current and subsequent voltage induced across the potential electrodes are recorded.

Typically, a resistivity meter (i.e., combination ammeter-voltmeter) collects the data and has a calculated output displayed as the ratio of measured voltage to induced current. Ohm’s Law, which is defined as V = IR, relates current (I) and voltage (V) data to the resistance (R) of the material(s) being measured. However, resistance is not a diagnostic material criterion, as it varies with material type and shape. Thus, resistivity methods customarily present and interpret data as apparent resistivity values.

Conceptual diagram of electrical resistivity surveying — Conceptual diagram of a 1D Schlumberger array consisting of current electrodes (C+ and C-), potential electrodes (P1 and P2), a voltmeter, a battery, and a current meter. Ohms law is observed as resistivity (R) equal to voltage (V) over current (I). (USGS stock image)

Apparent resistivity (ρ_a) is the value of resistivity (in ohm-m) that an electrically homogeneous and isotropic half-space would yield given the arrangement and spacing of electrodes. Because resistivity surveys collect subsurface measurements, resistivity data represent a half-space, which excludes any space above the surface that, if added, would render a whole space. Apparent resistivity calculations involve a geometric factor, which depends on the electrode array and spacing, that corrects a measured resistance (in ohm) for a given electrode configuration (Mussett, 2000).

Many different array geometries exist. The most commonly used arrays are the Wenner, Schlumberger, reverse-Schlumberger, gradient, dipole-dipole, or combinations of these. The array employed at a site is chosen based the survey objectives, predicted resistivity structure (e.g., lateral vs vertical variation), and/or target depth. The depth of investigation (DOI) of a resistivity measurement is the depth below which data are insensitive to subsurface resistivity and generally varies with electrode array geometry.

In a uniform medium, the Wenner, dipole-dipole, and Schlumberger arrays have DOIs that are approximately 30%, 25%, and 20% of their current electrode separation, respectively. Thus, electrode spacing can be manipulated to achieve sufficient depth. However, such processes are rather general, and site-specific DOI evaluation techniques can be employed during data inversion. In such techniques, various input models are compared to output models to determine the depth beyond which subsurface resistivity are no longer constrained by the data (Oldenberg and Li, 1999).

Applications

Apparent resistivity data can be initially plotted in a pseudosection, which displays data relative to traverse position and depth below land surface. Each apparent resistivity value is plotted at the intersection point of 45° lines drawn from midpoints of the corresponding current and potential electrode pairs. Though useful, pseudosections have limited value. Thus, electrical resistivity data are often analyzed further using numerical inversion algorithms (see inverse modeling) to determine depth-dependent resistivity variations in two-dimensional profiles (i.e., tomographs) and/or three-dimensional volumes.

Each resistivity measurement represents the weighted average of the resistivity over a large volume of material whereby the material nearer to the electrodes contribute more heavily. Thus, when dealing with large areas of investigation that incorporate long electrode spacing, resistivity data typically do not produce high resolution interpretations. Generally, the survey resolution is one half the electrode spacing. But while electrode spacing can be reduced to improve resolution, increasing resolution subsequently reduces the DOI.

Comparable to other potential-field geophysical methods, electrical resistivity methods deal with issues of data equivalence, where a particular voltage distribution at the ground surface may not have a unique interpretation (i.e., various subsurface resistivity structures can produce similar datasets). Therefore, inverse modeling, advanced interpretation, and incorporating all known site information is required for the most comprehensive survey results that lead to the most geologically reasonable interpretations of the subsurface structure.

The mineral grains that comprise soil and rock are essentially nonconductive (i.e., highly resistive). Resistivity tends to decrease with the presence of certain ore minerals, fine grain materials (e.g., clay minerals), and high temperatures. However, subsurface resistivity prominently depends on the amount of fluid present in pores and/or fractures and the dissolved solids within it the fluid. Thus, resistivity surveys are typically used to map the variations of rocks and/or sediments that occur concurrently with changes in porosity.

Additionally, electrical resistivity methods have been successfully applied to the following:

Groundwater prospecting/Aquifer characterization studies
Salt-water/Contamination studies
Saturation and salinity estimation
Time-series/Infiltration/Remediation monitoring
Mineral exploration
Fault/fracture zone identification
Archaeological surveys
Karst investigations/Void detection
Assessing anisotropy through azimuthal surveys

Picture of electrical resistivity field data acquisition — ERT survey conducted in June 2017 to assess the potential for unconventional oil and gas (UOG) waste water retention along the North Dakotan Blacktail Creek corridor as part of a larger evaluation of a post-spill period. (https://doi.org/10.5066/P961J30G)

Examples/Case studies

Aylsworth Jr, R.L., Van Dam, R.L., Larson, G.J., and Jessee, M.A., 2016, Characterizing large-scale glaciotectonic sediment deformation using electrical resistivity methods: Journal of Geophysics and Engineering, v. 13:2, p. S39-S49, doi:10.1088/1742-2132/13/2/S39.

Abstract: Large-scale sediment deformation structures formed by glaciotectonic processes have been identified south of Ludington, USA. Here, several apparent clay diapirs rise from below beach level to near the top of an approximately 60 m high bluff along the eastern shore of Lake Michigan. Throughout the area, the surface topography and locations of springs indicate a complicated subsurface structure and a preferred pattern of groundwater drainage. Since public borehole information is sparse, it is not known whether the structures exposed in the bluff are true diapirs or ridges, and if the latter, what is their orientation. In this paper we present the results of field, laboratory, and modeling studies to characterize the inland extent and orientation of these deformation structures using galvanic-source electrical geophysical methods. We exploit the large electrical contrast between a sandy sedimentary layer and an underlying clayey silt sedimentary layer in which the deformation occurred. Constant-spread traverses and multi-electrode tomographic data demonstrate that at least one of the narrow structures extends a significant distance inland.

Chambers, J.E., Kuras, O., Meldrum, P.I., Ogilvy, R.D., and Hollands, J., 2006, Electrical resistivity tomography applied to geologic, hydrogeologic, and engineering investigations at a former waste-disposal site: Geophysics, v. 71:6, p. 1ND-Z126, doi:10.1190/1.2360184.

Abstract: A former dolerite quarry and landfill site was investigated using 2D and 3D electrical resistivity tomography (ERT), with the aims of determining buried quarry geometry, mapping bedrock contamination arising from the landfill, and characterizing site geology. Resistivity data were collected from a network of intersecting survey lines using a Wenner-based array configuration. Inversion of the data was carried out using 2D and 3D regularized least-squares optimization methods with robust (L1-norm) model constraints. For this site, where high resistivity contrasts were present, robust model constraints produced a more accurate recovery of subsurface structures when compared to the use of smooth (L2-norm) constraints. Integrated 3D spatial analysis of the ERT and conventional site investigation data proved in this case a highly effective means of characterizing the landfill and its environs. The 3D resistivity model was successfully used to confirm the position of the landfill boundaries, which appeared as electrically well-defined features that corresponded extremely closely to both historic maps and intrusive site investigation data. A potential zone of leachate migration from the landfill was identified from the electrical models; the location of this zone was consistent with the predicted direction of groundwater flow across the site. Unquarried areas of a dolerite sill were imaged as a resistive sheet-like feature, while the fault zone appeared in the 2D resistivity model as a dipping structure defined by contrasting bedrock resistivities.

Fadillah, T., Gross, L., and Schaa, R., 2018, Estimation of Aquifer Properties Using Surface Based Electrical Resistivity Tomography, doi:10.3997/2214-4609.201800374.

Abstract: Aquifer characterization such as hydraulic conductivity (K) is necessary due to groundwater sustainability for agriculture industry. The current method for calculating K is to conduct a pumping test or a permeability test. This study is trying to find an alternative method to obtain a K value by determining the correlation between water and aquifer resistivity which is conducted in the laboratory and field scale. The aquifer resistivity is gathered from Electrical Resistivity Tomography (ERT) and the water resistivity from direct measurement. The correlation can perform the Kozeny–Carman equation, which is modified from Archie and Waxman–Smits formulas, to estimate the hydraulic conductivity. The hydraulic conductivity estimation is compared with the hydraulic conductivity value from the permeability and pumping test solutions. The measurement result showed 12.63 m/day, which was similar to the permeability test with 10.3 m/day. However, the field result revealed 14.07 m/day, while the pumping test indicated 24.5 m/day. An analysis has been conducted with the fact that geological condition, grain size, and water resistivity have a significant contribution to the result. Nevertheless, the outcome of the ERT profile can be an alternative method to get an estimation of K that is more efficient, yet not offensive.

Lane Jr., J.W., Haeni, F.P., and Watson, W.M., 1995, Use of a Square‐Array Direct‐Current Resistivity Method to Detect Fractures in Crystalline Bedrock in New Hampshire: Groundwater, v. 33, no. 3, p. 476-485, doi:10.1111/j.1745-6584.1995.tb00304.x.

Abstract: Azimuthal square‐array direct‐current (dc) resistivity soundings were used to detect fractures in bedrock in the Mirror Lake watershed in Grafton County, New Hampshire. Soundings were conducted at a site where crystalline bedrock underlies approximately 7 m (meters) of glacial drift. Measured apparent resistivities changed with the orientation of the array. Graphical interpretation of the square‐array data indicates that a dominant fracture set and (or) foliation in the bedrock is oriented at 030° (degrees). Interpretation of crossed square‐array data indicates an orientation of 027° and an anisotropy factor of 1.31. Assuming that anisotropy is due to fractures, the secondary porosity is estimated to range from 0.01 to 0.10. Interpretations of azimuthal square‐array data are supported by other geophysical data, including azimuthal seismic‐refraction surveys and azimuthal Schlumberger dc‐resistivity soundings at the Camp Osceola well field. Dominant fracture trends indicated by these geophysical methods are 022° (seismic‐refraction) and 037° (dc‐resistivity). Fracture mapping of bedrock outcrops at a site within 250 m indicates that the maximum fracture‐strike frequency is oriented at 030°. The square‐array dc‐resistivity sounding method is more sensitive to a given rock anisotropy than the more commonly used Schlumberger and Wenner arrays. An additional advantage of the square‐array method is that it requires about 65 percent less surface area than an equivalent survey using a Schlumberger or Wenner array.

Maurya, P.K., Rønde, V.K., Fiandaca, G., Balbarini, N., Auken, E., Bjerg, P.L., and Christiansen, A.V., 2017, Detailed landfill leachate plume mapping using 2D and 3D electrical resistivity tomography - with correlation to ionic strength measured in screens: Journal of Applied Geophysics, v. 138, p. 1-8, doi:10.1016/j.jappgeo.2017.01.019.

Abstract: Leaching of organic and inorganic contamination from landfills is a serious environmental problem as surface water and aquifers are affected. In order to assess these risks and investigate the migration of leachate from the landfill, 2D and large scale 3D electrical resistivity tomography were used at a heavily contaminated landfill in Grindsted, Denmark. The inverted 2D profiles describe both the variations along the groundwater flow as well as the plume extension across the flow directions. The 3D inversion model shows the variability in the low resistivity anomaly pattern corresponding to differences in the ionic strength of the landfill leachate. Chemical data from boreholes agree well with the observations indicating a leachate plume which gradually sinks and increases in size while migrating from the landfill in the groundwater flow direction. Overall results show that the resistivity method has been very successful in delineating the landfill leachate plume and that good correlation exists between the resistivity model and leachate ionic strength.

Mosuro, G.O., Omosanya, K.O., Bayewy, O.O., Oloruntola, M.O., Laniyan, T.A., Atobi, O., Okubena, M., and Popoola, E., 2017, Assessment of groundwater vulnerability to leachate infiltration using electrical resistivity method: Applied Water Science, v. 7:5, p. 2195-2207, doi:10.1007/s13201-016-0393-4.

Abstract: This aim of this work is to assess the degree of leachate infiltration at a dumpsite in Agbara industrial estate, Southwestern Nigeria using electrical resistivity techniques. Around the dumpsite were 45 vertical electrical sounding (VES) stations and 3 electrical resistivity tomography profiles. Current electrode spread varied from 300 to 600 m for the electrical sounding. Electrode configuration includes Schlumberger and Wenner array for sounding and profiling. The state of leachate contamination was tested using parameters such as aquifer vulnerability index, overburden protective capacity and longitudinal unit conductance (Si) derived from the apparent resistivity values. Four principal geoelectric layers inferred from the VES data include the topsoil, sand, clayey sand, and clay/shale. Resistivity values for these layers vary from 3 to 1688, 203 to 3642 123 to 388, and 67 to 2201 Ω m with corresponding thickness of 0.8–2.4, 2.5–140, 3–26 m and infinity, respectively. The leachate plume occurs at a maximum depth of 10 m on the 2-D inverse models of real electrical resistivity with an average depth of infiltration being 6 m in the study area. The correlation between longitudinal conductance and overburden protective capacity show that aquifers around the dumpsite have poor protective capacity and are vulnerable to leachate contamination. Leachate infiltration is favored by the absence of lithological barriers such as clay which in the study area are either mixed with sand or positioned away from the aquifer.

Nawikas, J.M., O’Leary, D.R., Izbicki, J.A., and Burgess, M.K., 2016, Selected techniques for monitoring water movement through unsaturated alluvium during managed aquifer recharge: U.S. Geological Survey Open-File Report 2016-1180, 8 p., doi:10.3133/ofr20161180.

Abstract: Managed aquifer recharge is used to augment natural recharge to aquifers. It can be used to replenish aquifers depleted by pumping or to store water during wetter years for withdrawal during drier years. Infiltration from ponds is a commonly used, inexpensive approach for managed aquifer recharge. At some managed aquifer-recharge sites, the time when infiltrated water arrives at the water table is not always clearly shown by water-level data. As part of site characterization and operation, it can be desirable to track downward movement of infiltrated water through the unsaturated zone to identify when it arrives at the water table.

Zhou, W., Beck, B.F., and Adams, A.L., 2002, Effective electrode array in mapping karst hazards in electrical resistivity tomography: Environmental Geology, v. 42:8, p. 922-928, doi:10.1007/s00254-002-0594-z.

Abstract: When conducting environmental and engineering investigations in karst terranes, engineers and geologists often supplement exploratory borehole results with data gathered from surface geophysics to reduce the site-characterization cost and establish the most useful locations for borings or samples. When conducting resistivity investigations, a frequently occurring problem is the need to determine which of the many existing electrode configurations will respond best to the material changes in karst features. Each array has its advantages and disadvantages in terms of depth of investigation, sensitivity to horizontal or vertical variations, and signal strength. In the application presented in this paper, numerical forward modeling was conducted of dipole–dipole, Schlumberger, and Wenner arrays, and they produced markedly different anomaly shapes for a conceptual model of the development of a cover-collapse sinkhole. The resolution of the three above-mentioned arrays was further evaluated along a section of I-70 near Frederick, Maryland, where a sinkhole had occurred in the median of the highway. The image from the dipole–dipole array appeared to be better than those from the Wenner and Schlumerger arrays in displaying the sinkhole collapse area. However, they are all less effective than a mixed array, in which apparent resistivities from all the three arrays are combined and processed together in the model. Because the mixed array requires a significant increase in data collection, the dipole–dipole array appears to be the most effective and less costly configuration in mapping karst hazards areas. This conclusion was then confirmed by two case studies.

References

Aylsworth Jr, R.L., Van Dam, R.L., Larson, G.J., and Jessee, M.A., 2016, Characterizing large scale glaciotectonic sediment deformation using electrical resistivity methods: Journal of Geophysics and Engineering, v. 13:2, p. S39-S49, doi:10.1088/1742-2132/13/2/S39.

Binley, A., 2015, Tools and Techniques: Electrical Methods, in Schubert, G., ed., Treatise on Geophysics: Cambridge, MA, Elsevier Science, v. 11, p. 233–259, doi:10.1016/B978-0-444-53802-4.00192-5.