Applications of Electrical Resistivity Tomography (ERT) in Non-Destructive Testing (NDT)

Fabian Knoll, winter semester 2023/2024

The Electrical Resistivity Tomography (ERT) is used to identify variations in the electrical characteristics of a subsurface or material.^[3] This method is based on the response of the probed medium to an injected electrical current.^[4] The response can vary due to many factors, including mineral composition, fluid content, and the degree of water saturation in the medium. But the main reason for changes in the resistivity is the porosity, due to the transportation of ions through the pore space.^[5] Based on the application field or the task ERT can be used either destructive or non-destructive. For mineral exploration and hydrological investigations a destructive version of this method is used. In these fields the ERT-method is used invasive, spike electrodes are used to insert the current and measure the potential difference. To use these spike electrodes either holes need to be drilled or the spike electrodes get sticked in the ground and therefore, damage the probed medium. Fields where the ERT-method is used non‑destructive are cultural heritage and, depending on the task, archaeology. For measurements in those fields, specially designed plate-electrodes are used to keep the probed part unharmed. The current gets injected into the medium through a flat plate which is placed on the surface of the material and therefore, there is no need for holes or any harm of the part to be checked.^[6] As shown in (Athanasiou et al., 2007) the type of electrodes does not affect the ERT results if used correctly.

1.1. Physical principles

The main physical principle behind the method is Ohm´s law. This law states that the electrical potential difference V is related to the electrical resistance R and the electrical current I as shown in Equation 1.^[7]

(1)	$\begin{array}{l}\displaystyle V=IR\end{array}$

Equation 1: Ohm´s law

The method involves injecting artificially generated electric currents into the ground and measuring the resulting potential differences at the surface. Variances in potential differences from the anticipated pattern in homogeneous ground offer insights into the nature and electrical characteristics of subsurface irregularities.^[3] While the electrical current can be varied, the resistance of the material is calculated between the potential differences and the known current, which is inserted into the subsurface. It is determined as the resistance in ohms across the opposite faces of a unit cube of the material. The resistance R for a conducting cylinder with resistivity ρ, length l, and cross-sectional area A is defined by the given formula as shown in Equation 2.^[4]

(2)	$\begin{array}{l}\displaystyle R=ρ*\frac{l}{A}\end{array}$

Equation 2: Resistance of a cylinder

The parameters of resistivity, as mentioned in Equation 1 and Equation 2, are shown in Figure 1.

Figure 1: The parameters of resistivity

Source: adapted from Kearey, P., Brooks, M., & Hill, I. (2002). An introduction to geophysical exploration (3rd ed). Blackwell Science.

While the resistivity in certain minerals, for example, native metals, is conducted via the passage of electrons, rock-forming minerals are insulators. Therefore, an electrical circuit can only be completed due to the passage of ions in pore fluids, and furthermore, most rocks do not conduct electricity by electronic processes; instead electrolytic processes are the reason.^[3] Equation 1 and Equation 2 combined results in Equation 3.

(3)	$\begin{array}{l}\displaystyle V=ρI\frac{l}{A}\end{array}$

Equation 3: Ohm´s law and resistivity combined

By dividing the potential by the length and building the partial differentials, the potential gradient is given by Equation 4.

(4)	$\begin{array}{l}\displaystyle \frac{δV}{δl}=ρ*\frac{I}{δA}\end{array}$

Equation 4: Potential gradient

Figure 2 shows the simplest case - a homogeneous subsurface and a single point current source on the surface. The current flows radially away from the single point source and the potential is reciprocal connected with the distance from the current source and therefore, the cross-sectional surface have a hemisphere shape, and this results in Equation 5. Due to a drop in the potential as the current passes through the material the equation has to be corrected by adding a minus.^[5]

Figure 2: Flow of current from a point current source and resulting potential

Source: adapted from Leucci, G. (2019). Nondestructive testing for archaeology and cultural heritage:
A practical guide and new perspectives. Springer.

(5)	$\begin{array}{l}\displaystyle -\frac{δV}{δr}=ρ*\frac{I}{2πr^2}\end{array}$

Equation 5: Potential gradient hemisphere shape

Multiplying Equation 5 by δr and integrating it delivers Equation 6.

(6)	$\begin{array}{l}\displaystyle V_r=∫δV=∫-ρ*\frac{I}{2πr^2}δr=ρ\frac{I}{2πr}+c\end{array}$

Equation 6: Potential of a hemisphere shape with integration constant

When the r gets infinite (r=∞) the potential reaches its minimum at and therefore, the integration constant is zero and the potential can be defined as in Equation 7.^[3]

(7)	$\begin{array}{l}\displaystyle V_r=ρ\frac{I}{2πr}\end{array}$

Equation 7: Potential of a hemisphere shape

With Equation 7 the potential at any point on or below the surface can be calculated. In Figure 2 there are hemispherical surfaces shown. At any point in this surface there is the same potential and therefore, these surfaces are called equipotential surfaces.^[3]

In practice, it is established for all resistivity measurements to use at least one positive and one negative current source as shown in Figure 3.^[5]

Figure 3: Resistivity measurement with four electrodes

Source: adapted from Kearey, P., Brooks, M., & Hill, I. (2002). An introduction to geophysical exploration (3rd ed). Blackwell Science.

The potential value for point C and D in the medium in this case is given by following equations, where r_xy and R_xy are the distances between a current source and one point of the measurement:

$\begin{array}{l}\displaystyle V_C=ρ\frac{I}{2π}*(\frac{1}{r_A_C}-\frac{1}{r_B_C})\end{array}$

$\begin{array}{l}\displaystyle V_D=ρ\frac{I}{2π}*(\frac{1}{R_A_D}-\frac{1}{R_B_D})\end{array}$

Because monitoring absolute potentials is very difficult the difference between these two potentials is measured resulting in Equation 8.^[3]

$\begin{array}{l}\displaystyle ∆V=V_C-V_D=ρ\frac{I}{2π}*((\frac{1}{r_A_C}-\frac{1}{r_B_C})-(\frac{1}{R_A_D}-\frac{1}{R_B_D}))\end{array}$

$\begin{array}{l}\displaystyle ⇒ρ=\frac{2π∆V}{I((\frac{1}{r_A_C}-\frac{1}{r_B_C})-(\frac{1}{R_A_D}-\frac{1}{R_B_D}))}\end{array}$

(8)	$\begin{array}{l}\displaystyle ⇒ρ=k\frac{∆V}{I}\end{array}$

Equation 8: Resistivity based on measured potential difference

In uniform materials, resistivity stays constant, as can be seen in Equation 8. But with subsurface variations, resistivity changes with the positioning of the electrodes, yielding apparent resistivity ρ_a. Equation 8 is the key formula for calculating apparent resistivity for any electrode setup.^[3] The factor k in Equation 8 is the geometric factor, which depends on the setup of the current and potential electrodes. This factor was researched over the years and different arrangements of electrodes and arrays are developed. The advantages as well as the disadvantages of each arrangement are discussed in different papers, such as in Dahlin and Zhou (2004), Saydam and Duckworth (1978) and Szalai and Szarka (2008). The sensitivity to the target of interest, signal-to-noise ratio, investigation depth, lateral data coverage and efficiency of using the array in a multi-channel system are factors to consider by thinking about the suitability of an array for the measurement.^[1]

1.2. Advantages and disadvantages of the method

Electrical Resistivity Tomography is recognized as a versatile and essential tool for subsurface imaging and exploration, offering numerous benefits across various fields. Its non-invasive nature allows for thorough investigation of underground structures without disturbing the ground, making it particularly valuable in cultural heritage, archaeology, environmental science, and civil engineering. This characteristic is crucial for maintaining the integrity of surveyed areas, ensuring accurate evaluation and interpretation.^[1]

Electrical resistivity tomography has demonstrated its speed in producing large-scale spatial models of subsurface physical properties. It offers adequate and precise information for specific areas at a low cost due to its efficiency and short operation time. ERT is particularly preferred to minimize ground disturbance, making it well-suited for landfill investigations. Another notable advantage of ERT is its cost-effectiveness relative to alternative geophysical methods. The ability to acquire valuable subsurface information at a reasonable cost makes it an attractive option for both small-scale investigations and large-scale projects.^[2]

Despite its advantages, Electrical Resistivity Tomography is not without its limitations and challenges. Depending on several conditions, like electrical conductivity of the material, array configuration, electrode spacing, and power of electrical source one limitation can be a restricted depth penetration, which typically ranges up to a few tens of meters. This limitation may pose challenges in scenarios requiring deep subsurface exploration, limiting the applicability of ERT in certain geological contexts. Additionally, interpretation of ERT data presents another notable challenge, as it requires expertise and may be complicated by factors such as noise, geological complexity, and the 3D nature of the anomalies. Accurate interpretation necessitates a thorough understanding of subsurface processes and the ability to discern subtle variations in resistivity profiles amidst complex geological settings. Another deficit is impacts of deeper variations can be obscured due to near-surface resistivity fluctuations.^[3]

Another limitation is that not all materials can be investigated using ERT. An example of this is tarmac.^[9]

1.3. Main applications

The electrical resistivity tomography is mainly used for mineral exploration, hydrological investigations, archaeology and cultural heritage which will be described in the following.^[6]

1.3.1. Mineral exploration

Resistivity surveys have aided in uncovering buried uranium deposits and exploring various mineral resources. They are also valuable in mapping shallow oil sand deposits and bulk construction materials. Recent advancements in field equipment and surveying techniques have revolutionized mineral exploration, enabling deeper exploration in complex terrains.^[6]

1.3.2. Hydrogeological investigations

Resistivity surveys are commonly utilized in hydrogeological studies, offering valuable insights into geological structure, lithologies, and subsurface water resources. This approach provides crucial information at a fraction of the cost of extensive drilling programs. The survey results help pinpoint the minimum number of exploratory boreholes needed for aquifer tests and verifying geophysical interpretations.^[3]

1.3.3. Archaeology and cultural heritage

The historical evolution of Electrical Resistivity Tomography is intimately linked with archaeological inquiry. While traditional resistivity mapping has long been prevalent in archaeological investigations, recent years have seen a growing adoption of detailed 2-D and 3-D resistivity imaging techniques by archaeologists seeking enhanced pre-excavation analysis capabilities. ERT has proven effective in characterizing a wide range of archaeological features, including mounds, settlements, buried structures, and monuments. Moreover, its utility extends to "rescue archaeology", where rapid surveys and excavations are conducted in areas threatened by development, as well as in cultural heritage preservation efforts. Additionally, ERT plays a significant role in the structural assessment and restoration of historical buildings constructed over ancient structures, showcasing its versatility and importance in archaeological and heritage contexts.^[6] In the following some examples of the use of ERT in the archaeology and cultural heritage are described.

The ERT was used for example by (Tejero-Andrade et al., 2018) where the aim of the investigation was to explore the interior of the El Castillo pyramid, also known as the Temple of Kukulkan, using 828 electrodes placed around its nine sections, including the base. The final 3D model, based on nine observation levels totalling 33,169 measurements, revealed two older pyramids within the main Mayan structure, offering insights into Mayan civilization. Further studies of the older substructure could unveil details about early settlement, historical evolution, and cultural influences at the site.

Another survey was conducted by (Tsourlos & Tsokas, 2011) where the aim of the survey was to investigate the space behind the south wall of the Acropolis. The survey provided crucial information regarding the preservation strategy of the Greek monument. Even though there were technical challenges, the ERT demonstrated its effectiveness by applying innovative measuring setups and software modifications. To get dense grid surveys and therefore, a maximum of information climbers were hired which installed cables on the wall. The investigation was limited to its small wall area.

The final investigation mentioned in this article is the survey of (Tsokas et al., 2008) where the area inside and outside of the Kapnikarea Church in Athens was explored. Before aqueducts, wells and cisterns were Athens' primary water sources. They remained in use until the mid-20th century, their construction being relatively simple: a cylindrical pit dug, usually about 1 meter in diameter, reaching the Athenian Schist for water. Most wells were about 15 meters deep, some even deeper. Many were filled with debris over time, due to urban changes or disasters like Persian invasions. Though buried, these wells are detectable via explorative geophysics, appearing as resistive targets due to their stone walls. The study focused on a well near Kapnikarea church, revealing voids below. Metro tunnel excavation nearby caused no issues, and the study found flat-base electrodes reliable despite higher errors, likely due to the heterogeneous near-surface stratum violating the inversion scheme's two-dimensional assumption.

1.4. References

Athanasiou, E. N., Tsourlos, P. I., Vargemezis, G. N., Papazachos, C. B., & Tsokas, G. N. (2007). Non-destructive DC resistivity surveying using flat-base electrodes. Near Surface Geophysics.
Feng, S.‑J., Bai, Z.‑B., Cao, B.‑Y., Lu, S.‑F., & Ai, S.‑G. (2017). The use of electrical resistivity tomography and borehole to characterize leachate distribution in Laogang landfill, China. Environmental Science and Pollution Research International, 24(25), 20811–20817. https://doi.org/10.1007/s11356-017-9853-0
Kearey, P., Brooks, M., & Hill, I. (2002). An introduction to geophysical exploration (3rd ed). Blackwell Science.
Leucci, G. (2019). Nondestructive testing for archaeology and cultural heritage: A practical guide and new perspectives. Springer.
Loke, M. H. (2018). Tutorial : 2-D and 3-D electrical imaging surveys.
Loke, M. H., Chambers, J. E., Rucker, D. F., Kuras, O., & Wilkinson, P. B. (2013). Recent developments in the direct-current geoelectrical imaging method. Journal of Applied Geophysics, 95, 135–156. https://doi.org/10.1016/j.jappgeo.2013.02.017
Oswin, J. (2009). A Field Guide to Geophysics in Archaeology. Scholars Portal.
Tejero-Andrade, A., Argote-Espino, D. L., Cifuentes-Nava, G., Hernández-Quintero, E., Chávez, R. E., & García-Serrano, A. (2018). ‘Illuminating’ the interior of Kukulkan's Pyramid, Chichén Itzá, Mexico, by means of a non-conventional ERT geophysical survey. Journal of Archaeological Science, 90, 1–11. https://doi.org/10.1016/j.jas.2017.12.006
Tsokas, G. N., Tsourlos, P. I., Vargemezis, G., & Novack, M. (2008). Non‐destructive electrical resistivity tomography for indoor investigation: the case of Kapnikarea Church in Athens. Archaeological Prospection, 15(1), 47–61. https://doi.org/10.1002/arp.321
Tsourlos, P. I., & Tsokas, G. N. (2011). Non‐destructive Electrical Resistivity Tomography Survey at the South Walls of the Acropolis of Athens. Archaeological Prospection, 18(3), 173–186. https://doi.org/10.1002/arp.416

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