# Electric resistivity surveys

Electric resistivity methods are a group composed by a large and diverse range of methods used in prospection geophysics to differentiate the subsurface according to its electromagnetic properties. In the early days, explorations were carried out to detect very conductive base metal massive sulfide ore deposits contained in highly resistive host rocks. Because of the high contrasts, ore exploration surveys have been the prime application of resistivity methods, as is also the case of magnetometry methods, since most of the ore grades are conductive. Later on, where more sensitive measuring configurations were constructed, resistivity methods also started to be used also in other fields like oil and gas prospection.

Current flow I through a piece of conductive material over which a potential difference V has been applied.

An electric current is a flow of electrically charged particles (either electrons or ions). By convention a current is considered to flow from positive (source) to negative (sink), though in the wire the current is due to electrons moving from negative to positive. The SI unit for measuring an electric current is the Ampere [A], which is the flow of electric charge across a surface at the rate of one coulomb per second. Then, a current is the result of a potential difference [V] imposed over a closed loop and the magnitude of its flow depends on the resistance of the loop's material. For most materials, including most rocks, the current trough the resistor increases linearly proportional to the voltage across it, obeying Ohm's law. This proportionality constant R is known as resistance and is a property inherent to the material and, according to Ohm's law can be obtained experimentally as the ratio between the potential difference V and the current I as:

${\displaystyle R={\frac {\Delta V}{I}}}$,

However, the resistance given by a certain material depends not only on it's electrical properties, namely conductivity, but also on its geometrical structure, as illustrated in the figure on the right.

${\displaystyle R={\frac {L}{\sigma A}}}$,

## Resistivity surveys

Geo-electric resistivity is a geophysical method where two electrodes, known as current electrodes, are used to inject an electric current intro the ground and the potential difference is measured between two distant electrodes, known as potential electrodes. Thus, based on the known input current, the voltage measured and the array geometry, an "apparent" resistivity can be computed.

Standard four electrode configuration in homogeneous half space media.

## Array configurations

### Pole-Pole array

Pole-Pole array configuration in homogeneous half space media.

The name Pole-Pole already indicates that both, current injection and potential electrodes are modeled as single poles. In practice this is not possible, since current needs a closed loop to flow, but from last equation we may conclude that when the position of one of the electrodes is very large compared to the others, two of the distance terms become very small and can then be neglected.

Therefore, the measured voltage differences is: ${\displaystyle \Delta V={\frac {I}{2\pi \sigma a}}}$

In practice the far away electrodes are put more than 20 times the largest electrode spacing away.

### Pole-Dipole array

As the name indicates, one of the current electrodes is the far away electrode, while the potential electrodes are both used in the line of measurements. Thus, there is an extra degree of freedom to place the other three electrodes in the line of measurements. Let us denote the distance between the two potential electrodes a and the distance between the current electrode and the closest potential electrode na.

Thus, the potential difference measured is: ${\displaystyle \Delta V={\frac {I}{2\pi \sigma an(n+1)}}}$

Pole-Dipole array configuration in homogeneous half space media.

In this case, the effect of the distant electrode is negligible and the electric field of the near electrode resembles that of a point source rather than the field of a dipole. A commonly used configuration consists of a combination of two pole-dipole arrays: one forward and one reversed. This configuration is mainly used in profiling, where changes in resistivities are clearly mapped. It is characterized by a high Signal to Noise Ratio.

### Dipole-Dipole array

This is the most sensitive array of those mentioned and therefore also the most prone to the noise. In this configuration, all four electrodes are put in the line at measurable distances from each other. In this array, both current electrodes are next to each other at distance a, while the potential electrodes are also next to each other at distance a and separated from the current electrode pair at a distance na.

Therefore, the potential difference measured is: ${\displaystyle \Delta V={\frac {I}{2\pi \sigma an(n+1)(n+2)}}}$

Dipole-Dipole array configuration in homogeneous half space media.

### Wenner Arrays

This potential array is characterized by a relatively large distance between the potential electrodes compared with the potential-to-current electrodes distance. This array is suitable for areas with poor grounding conditions or areas where a high amount of noise is expected. The Wenner array has lost most of its popularity because the electrode distances are fixed and the potential electrodes must be at the same distance as the current electrodes. However, it is still used in situations where signal strength is the most important factor, like in situations where the current electrodes are put in a very highly resistive top layer.

The potential difference measured is: ${\displaystyle \Delta V={\frac {I}{2\pi \sigma a}}}$

Wenner array configuration: all the distances between electrodes are equal.

### Schlumberger Arrays

In this configuration, the potential electrodes are placed at the center of the electrode array with a small separation, typically less than one fifth the current electrodes spacing. The current electrodes separation is gradually increased during the survey while the potential electrodes remain unchanged until the measured voltage becomes too small to be detected. Schlumberger soundings generally have better resolution, greater probing depth, and less time-consuming field deployment compared to Wenner arrays. The two most outstanding disadvantages are: longer current electrode wires are required and the recording instrument needs to be very sensitive.

The potential difference measured is: ${\displaystyle \Delta V={\frac {I}{\pi \sigma an(n+1)}}}$

Schlumberger array configuration: let the distance between current electrodes be 2L and the distance between potential electrodes be 2a, while the mid-point of both current and potential electrodes coincide.