Electrode arrays

CHAPTER 2: LITERATURE REVIEW

2.6 The Resistivity method: Historical overview

2.6.3 Electrode arrays

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Since we measure the potential difference between M and N, the voltage change is therefore given by:

∆𝑉 = 𝑉_𝑀 − 𝑉_𝑁 = ^𝜌

2𝜋[( ¹

𝐴𝑀− ¹

𝑀𝐵− ¹

𝐴𝑁− ¹

𝑁𝐵)] (2.11) Therefore, the resistivity of the ground is given by the following expression:

𝜌_𝑎 =^∆𝑉

𝐼 𝐾 (2.12) Where 𝜌_𝑎 is the apparent resistivity and 𝐾 is the geometric factor for a particular electrode configuration. From equation (8), the expression for 𝐾 is as follows:

𝐾 = 2𝜋 [( ¹

𝐴𝑀− ¹

𝑀𝐵− ¹

𝐴𝑁+ ¹

𝑁𝐵)]⁻¹ (2.13) Each electrode configuration used during a resistivity survey has a unique geometric

factor that is determined by the arrangements of the electrodes. Therefore, apparent resistivity of the ground is determined by multiplying the measured resistance with the geometric factor calculated for that particular array employed during the survey.

50 (i) Wenner array

This is one of the most popular arrays in geophysical prospecting initially proposed by Wenner (1916). It is a robust arrangement that gained recognition following the pioneering work undertaken by the University of Birmingham research team (Loke, 2015). In the field, the array consists of four electrodes, two current electrodes labelled A and B, and two potential electrodes labelled M and N as shown in figure 2.8. These electrodes are spread along a straight line and uniformly spaced so that AM=MN=NB=a.

Figure 2.8: Illustrative sketch of the Wenner electrode spread (Yadav et al., 1997).

For depth probing, the electrodes are spread about a fixed center, while systematically increasing the separation along the line. In lateral mapping, however, the spacing between the electrodes is kept constant as they are moved along the survey line. The constant separation traversing is an ideal mode of resistivity data collection for the detection of anomalies. In spite of the relatively simple geometry, the Wenner array is often not preferred for most exploration work due to several factors.

The movement of all the electrodes during the survey makes this procedure more suitable for use with low sensitivity meters. However, this also makes it necessary to have long cables, which may be too expensive. One of the major drawbacks in using the Wenner array is the tedium associated with moving all the four electrodes attached to long cables.

51 (ii) Schlumberger electrode configuration

The Schlumberger array also uses four electrodes that are spread along the survey line.

However, in the Schlumberger array, the spacing between the potential electrodes (M and N) is less than the spacing between the current electrodes (i.e. A and B) (Figure 2.9).

In simple terms, the current electrodes are spaced much further than the potential electrodes. Thus during a resistivity survey, the potential electrodes are kept fixed at the center, while the current electrodes are moved further apart in symmetrical steps. This is however, a procedure commonly adopted for vertical electrical sounding in order to detect the variations of subsurface resistivity with depth.

The expansion of current electrodes allows current to penetrate into deeper layers. In practice, this procedure often leads to a gradual decrease in the amount of measurable potential difference between the potential electrodes. Thus for large values of S, it may be imperative to expand the spacing between the potential electrodes in order to maintain a detectable potential (Telford et al., 1990).

Contrary to Wenner array, this configuration is more rapid and convenient in the field since only two electrodes need to be moved. Furthermore, maintaining a fixed separation between the potential electrodes minimizes the effects of shallow subsurface resistivity variations. One major drawback of using the schlumberger spread is the requirement for a more sensitive voltmeter, and the procedure can be more confusing in the field.

Figure 2.9: An illustrative sketch of the Schlumberger array (Anomohanran, 2013).

52 (iii) Dipole-Dipole array

Like other common electrode arrays, the Dipole-Dipole consists of four electrodes that are spread along a straight line. However, in this arrangement the potential electrodes (P1-P2) are closely spaced, as well as the current electrodes (C1-C2) (figure 2.10). The distance between the potential electrodes pair (P1 and P2) is marked ‘a”, which is the same as the separation between the current electrodes pair (C1 and C2).

The individual electrode pairs are separated from each other by a distance denoted by

‘’na’’. Furthermore, this configuration is characterized by a factor denoted by ‘’n’’, which is the ratio of the distance between the C1 and P1 electrodes, to the C1-C2 (or P1-P2) electrode spacing.

Figure 2.10: Illustrative sketch of the Dipole-Dipole spread (Loke, 2015).

The survey procedure with the Dipole-Dipole array begins with a separation of ‘’1a’’

between the C1-C2 electrodes, and this also applies to the P1-P2 electrodes (Loke, 2015). During the first series of measurements, the ‘’n’’ factor is kept at a value of 1, while maintaining the C1-C2 electrode spacing fixed at ‘’1a’’. In the subsequent measurements, the ‘’n’’ factor is gradually increased from 1 until up to about 6 in order to increase the probing depth (Loke, 1997). The spacing between the current electrode pair may be increased later in order to increase the depth of probing.

The Dipole-Dipole array is also commonly used in resistivity and IP surveys due to its high sensitivity to subsurface resistivity variations directly below each electrode pair (Ewusi, 2006). In addition, the array is very sensitive to horizontal variations in subsurface resistivity.

C2 C1 P1 P2

• a • na • a •

^na

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Thus, it is mostly preferred for mapping vertical structures such as cavities and dykes.

One of the major drawbacks to this spread is the limited depth of probing; it comparatively probes to shallower depths.

(iv) Pole-Pole Array

Contrary to the Wenner, Schlumberger and Dipole-Dipole array, the pole-pole array is less commonly used in conventional resistivity surveys. From a theoretical perspective, the conventional pole-pole array consists of one current and one potential electrode, with the other two electrodes located at infinite distances as shown in figure 2.11 (Ahzegbobor, 2010). However, in practice, the pole-pole array with one current and one potential electrode is almost impossible to setup in the field.

C1

Figure 2.11: Illustrative sketch of the Pole-Pole electrode configuration.

According to Loke (2015), the pole-pole array is best approximated by placing the second current and potential electrodes at distances more than 20 times the maximum separation between the C1 and P1 electrodes. Difficulties arise, however, when trying to find suitable locations for the second current and potential electrodes (Ewusi, 2006). In addition, a larger spacing between the potential electrodes makes the array more susceptible to telluric noise that may distort the quality of the resistivity observations (Loke, 2015). Thus, this array is often adopted for surveys where small inter-electrode spacing is required, such as archeological studies. One of the principal advantages of the pole-pole array includes a wider horizontal coverage and the increased depth of probing.

C1 P1

a

54 (v) Pole-Dipole array

Similar to other conventional arrays, the pole-dipole array involves the use of four collinear electrodes. However, one of the current electrodes (C2) is placed sufficiently far from the actual survey line, while the other current electrode is aligned with the two potential electrodes. (Loke, 2015). Thus the electrodes are asymmetrically spread along the survey line (figure 2.12). According to Loke (2015), the pole-dipole array has a relatively good horizontal coverage and signal strength.

cc CC

Figure 2.12: An illustrative sketch of the pole-dipole array.