**2. Basic theory of resistivity methods**

areas extend to old mining areas or karst regions. In fact, risks of collapse and pollutants transportation can lead to unwanted and hazardous events. Caves are also used as reservoirs, deposits of gas, hazardous and toxic residues and, therefore, cavity monitoring and four-

Cavity location is often done by surface mapping, documents, local and oral descriptions. Therefore, before engaging in expensive and comprehensive exploration programmes, it is important to review all the relevant available information. However, often local records are difficult to obtain, particularly in old mining areas. It is also possible that no information is available in regions with no evidence of caves at the surface or in cases of fast cavity develop-

Often invasive exploration methods (excavation, drilling) are used. These invasive methods must be carefully planned to reach the targets at a suitable cost and, furthermore, operations

Other approach uses indirect investigation techniques from the surface that is geophysical exploration methods. However, the efficiency of these methods depends, among other factors, on the contrast between the physical properties of the cavities and those of the surround-

Fortunately, in most cases there is a contrast between the velocity of seismic wave propagation, density, electrical and magnetic properties of the cavities and those of the rock formations where they are installed [3] and, thus, geophysical exploration methods can be used and adapted to cavity detection and location [4]. However, the relation between the dimensions of the cavities and their depth can also be a major limitation factor for the use of geophysics. In fact, cavities can be too small or too deep to be detected in spite of a large contrast in physical properties [5]. Since these limitations are overcome, the main objective of the use of geophysical methods in cavity location is to provide information and restrict the area to investigate by direct methods, to guide later exploration operations and to diminish costs while preserving the targets [6].

In this contribution, the application of geophysical methods in cavity exploration is focused

There many examples of the use of 2D and 3D ERT in cavity location [7, 8]. As in any other geophysical method, the success of cavity detection by resistivity methods depends on factors such as depth, size and contrast between the resistivity of the cavity and that of the surrounding media [5]. Cavities can be more conductive or more resistive then the rocks that surround them. Cavities filled with water are more conductive then the surrounding media. However, when empty they are more resistive as air is not an electricity conductor. Thus, in the first case, cavity response to resistivity methods is a conductive anomaly whilst, in the second

The nature of the surrounding media is another factor to consider. Usually, resistivity fieldwork consists on recording data in one unique direction. Therefore, two-dimensional effects arising from local geology such as contacts, schistosity, etc., can induce orientational variation

on the use of 2D resistivity methods—electrical resistivity tomography (ERT).

dimensional (4D) studies must be considered for safety reasons.

ment, such as sinkholes.

ing media [2].

118 Cave Investigation

must not interfere and damage the caves [1].

case, the response will be a resistive anomaly.

on surface resistivity data and complicate cavity detection.

Resistivity measurements are traditional geophysical methods. There are extensive textbooks presenting the theory of electrical methods [9] and their use in engineering and environmental investigations [10].

In broad terms, resistivity methods consist on passing a DC current into the ground using two current electrodes and measuring the generated electrical potential between two potential electrodes, **Figure 1**.

**Figure 1.** Resistivity fieldwork; 1, battery; 2, ammeter; 3, voltmeter; 4, current electrodes; 5, potential electrodes; dashed lines, current lines in the ground.

In the past, resistivity field operations were slow and tedious but the development of computer controlled multi-electrode resistivity metres and cables, **Figure 2**, enables fast field operations and the recording of large data sets.

Usually, field measurements use four in-line electrode arrays. The commonest in-line electrode arrays are the Wenner (left of **Figure 3**) and Schlumberger (right of **Figure 3**).

**Figure 2.** Resistivity equipment: left, automated resistivity metre and cables; right, stainless steel electrodes.

**Figure 3.** Resistivity arrays: left, Wenner; right, Schlumberger.

In the Wenner array, the electrodes are equally spaced, 'a', whilst in the Schlumberger array the distance AB, between the current electrodes, is larger than the distance between the potential electrodes MN. Once the potential difference, V, and the current, I, are measured the resistivity of the ground, *ρ*, is

$$\rho = 2\pi a \frac{\Delta V}{I} \quad \text{for the Wiener array} \tag{1}$$

and

$$
\rho = \frac{\Lambda V}{\mathcal{I}} \pi \frac{(b+a)}{\mathcal{A}} \quad \text{for the Schlumbberger array} \tag{2}
$$

The construction of an ERT requires the use of Wenner and Schlumberger arrays of different sizes along an acquisition line of electrodes, **Figure 4**.

**Figure 4.** Construction of an electrical resistivity tomography—ERT.

As depicted in **Figure 4**, the first line is obtained by moving the electrode array, using an electrode spacing 'a', along the line of electrodes. The measurements are plotted in accordance with the centre of the array and the spacing 'a' used, first line in **Figure 4**. The first measurement corresponds to the red dot 1, station 1.

When line 1 is finished, field measurements resume with line 2. Now, the electrode array spacing is '2a' and data are plotted against the position of the centre of the array and the new spacing '2a'. The first measurement corresponds to the red dot 2, station 2.

The procedure continues until reaching the number of lines required to obtain an image— ERT—of the ground.

To optimize field measurements, it is usual to combine Wenner and Schlumberger arrays. The complete procedure is controlled by an automated multi-electrode resistivity metre previously programmed to carry out the complete sequence of field measurements and to store all field information.

Once all data are stored, they can be modelled using appropriate software [11, 12] and detailed information about the ground is obtained.

In the Wenner array, the electrodes are equally spaced, 'a', whilst in the Schlumberger array the distance AB, between the current electrodes, is larger than the distance between the potential electrodes MN. Once the potential difference, V, and the current, I, are measured the

**Figure 2.** Resistivity equipment: left, automated resistivity metre and cables; right, stainless steel electrodes.

The construction of an ERT requires the use of Wenner and Schlumberger arrays of different

<sup>I</sup> for the Wenner array (1)

(*<sup>b</sup>* <sup>+</sup> *<sup>a</sup>* ) \_\_\_\_\_ *<sup>a</sup>* for the Schlumberger array (2)

Δ*V*

Δ*V* <sup>I</sup> *π*

sizes along an acquisition line of electrodes, **Figure 4**.

**Figure 4.** Construction of an electrical resistivity tomography—ERT.

resistivity of the ground, *ρ*, is

*ρ* = \_\_\_

and

120 Cave Investigation

*ρ* = 2*πa* \_\_\_

**Figure 3.** Resistivity arrays: left, Wenner; right, Schlumberger.

Often cavities are installed in heterogeneous and complex media. In these cases, resistivity measurements can vary with the orientation of the line of electrodes, as shown in **Figure 4**. In such cases, the orientational variation of resistivity data can hinder the location of cavities and, possibly, mask their presence.

In the presence of anisotropic media, steeply dipping schists are a good approximation, it is usual to consider two resistivities: one *ρ*<sup>l</sup> the longitudinal resistivity, in the direction of the strike, and another *ρ*<sup>t</sup> , transverse resistivity, perpendicular to the strike [13], **Figure 5**.

As the longitudinal and transverse resistivity values are different, it is possible to define a mean resistivity *ρm*:

$$
\rho\_m = \sqrt{\rho\_l \rho\_l} \tag{3}
$$

and an anisotropy coefficient, λ, the square root of the ratio between *ρ*<sup>t</sup> and *ρ*<sup>l</sup> :

$$
\lambda = \sqrt{\rho\_r/\rho\_l} \tag{4}
$$

**Figure 5.** Anisotropic medium: *ρ*<sup>l</sup> , longitudinal resistivity; *ρ*<sup>t</sup> , transverse resistivity; A, current electrode; M, potential electrode; θ, array orientation.

In the field, resistivity values can vary largely with the orientation θ of the line of electrodes, **Figure 5**, and the coefficient of anisotropy can reach values larger than 2 [9, 13].

The influence of anisotropy on resistivity measurements has been investigated [14, 15] and, herein, a case study on the location of old mining cavities in anisotropic media will be presented [16].
