3 common electrode configuration of resistivity surveys

Electrode array configuration defines how much distance should put either current electrodes or potential electrodes so that to obtain the expected resistivity information about the given geological terrain. So this is a task that you need to consider when you set up your geophysical survey design. There are many types of array configuration that you can use depending on your survey objective, however this post will only provide to you the basics of three (3) commonly used array configurations in most electrical surveys.

First of all we have to consider the concept laid behind the electrode array configuration as simple as possible.

When we consider the figure in a homogeneous and isotropic half-space, when the current is passed into the ground by current electrodes, it will behave to spread out at radial distance r, so the Potential gradient between electrodes can be given as,

∆V/∆r = -pJ

Since, J = current density (I/a), Also A = 2πr2 since radial assume hemispherical shape

Then ∆V/∆r = -pI/2πr2

When taking small changes ∆V=dV, ∆r=dr, then rearrange

dV = -pIdr/2πr2

If we Integrate, ∫dV = ∫-pIdr/2πr2

V = pI/2πr

V - Potential due to single source electrode.p - resistivity, I - electric Current

If we consider the figure below,

Figure: A simple representation of electrodes configuration (Reynolds, 1997)

VMN = VM - VN

∆VMN = pI/2π[(1/AM -1/BM) - (1/AN -1/BN)].

Make the subject the resistivity (p),

p = 2π∆VMN/I[(1/AM -1/BM) - (1/AN -1/BN)].

But ∆VMN/I = R, and 2π[(1/AM -1/BM) - (1/AN -1/BN)]-1 = K

K - Geometric Factor, R - Resistance.

p = RK

Geometric factor is the one that should be taken into consideration as each array has its own geometry.

Hope you grasped the concept on that, then here down are the three (3) mostly applied electrode array configuration in electrical surveys.

Schlumberger design

Here in this configuration, its four electrodes all lie along a line at which current electrodes (C1(+) and C2(-)) send down electric current and the potential electrodes (P1(+) and P2(-)) are symmetrical with respect to the midpoint of the survey spread. As seen in the figure 1 below Potential electrodes separation (b) is kept small such as a>5b and constant during the surveying while the current electrode separation is gradually increased as survey is proceeding so that the electric field at the center of two current electrodes is obtained.

Figure 1: Schlumberger array configuration

The geometric factor for the Schlumberger array is
K = πa2/b [1 - b2/4a2]

wenner design

In this array configuration the separation between adjacent electrodes is equal. So as the survey is proceeding all electrodes are shifted into new points.

Figure 2: Wenner array configuration

The geometric factor (K) for Normal Wenner array configuration as represented in figure 2 above is given as K = 2πa

Dipole-dipole design

In this configuration, the current electrodes and Potential electrodes are separated by large distances but much smaller compared to the survey spread. As shown in figure 3, Then a single dipole source can be approximated like the electric dipole moment as we can use the similarity of electrostatic and electric conduction to derive the equations for the dipole array.
B = Idab

Figure 3: Dipole-dipole array configuration.

Here we define vector dAB as the distance between point A to B; analogous to the separation between point electric charges.,

VE = - pB⋅r'/2πr2
where r represents the distance from the source to the measurement location.

p represents the average resistivity of the medium.
The geometric factor (K) for Normal Dipole-dipole array configuration as represented in figure 2 above is given as K = πn(n+1)(n+2)a

All in all each array design has pros and cons, so the selection of which array you have to apply remains as subject of survey objective such as schlumberger design is more useful for small scale (shallow) surveys with dimensions up to 10 km while Dipole-dipole arrays are more practical for deep subsurface investigations.

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You can check here below the simple lists of equipment and tools that can suit your Project!

BASIC RESISTIVITY EQUIPMENTS and TOOLS

- Electrical resistivity meter

- Handheld GPS receiver

- glass-Fiber tape

- Geological Hammer (The friend of Geologists)

NEED METAL DETECTORS

- Lightweight, High accuracy Metal Detector.