A Comparison Of 11 Classical Electrode Arrays

 

Electrode arrays can be defined as various arrangements of electrodes used to perform geophysical resistivity measurements. These arrays were developed before computers and modern algorithms were available in order to make field measurements more efficient and data interpretation easier. Even with today’s automatic resistivity imaging instruments, these arrays are still used in order to ensure an even coverage of data points.

 

There are a number of different arrays, but only a few have been important and frequently used. These include the Schlumberger array, the Wenner array, and the dipole-dipole array. Other less commonly used arrays are pole-dipole, pole-pole, square, bipole-bipole, equatorial, gradient, and azimuthal.  In the paper below, we’ll provide an overview of each of these arrays.

A Comparison Of 11 Classical Electrode Arrays

1. Wenner Array

The Wenner array was invented by an American physicist named Frank Wenner (1873-1954). It is most often used for mineral ore, groundwater exploration, electrical grounding studies and in the soil test method according to ASTM G57 [ASTM G57-06(2012), Standart Test Method for Field Measurments of Soil Resistivity Using the Wenner Four-Eñectrode Method, ASTM International, West Conshohocken, PA, 2012www.astm.org.]

In the Wenner array, there is an equal spacing “a” between the four electrodes AMNB. Because the field crew only needs to consider an equal electrode spacing for all four electrodes makes the Wenner method accessible to a non-technical field crew to perform.

The Wenner array can be used for profiling (also known as electrical trenching) or for vertical electrical sounding (also known as VES or electrical drilling), and there are benefits and drawbacks for each. The advantage of the Wenner method is apparent when you perform a profiling survey, because in this implementation you will move only one electrode for each measurement.

 

It’s important to note that you can use a combination of arrays in many instances. For example, if you’re looking for groundwater but know there’s a rock beneath the soil, you’d first want to determine the depth-to-bedrock using VES with the Schlumberger array. Once you’ve determined this, you could move the electrodes for the Wenner array and set the correct depth sensing for profiling needed to penetrate the rock. When the Wenner array then moves over a fracture, it could indicate a low-resistive area, thus indicating the presence of water.

 

2. Schlumberger Array

The Schlumberger array was named for Conrad Schlumberger, the founder of the modern-day Schlumberger oilfield services company and pioneer of electrical methods in the early 1900s. During this period, both the Schlumberger and Wenner arrays were used extensively for mineral and groundwater exploration.

Most arrays use four electrodes: two current electrodes that inject the current into the ground, and two electrodes that measure the resulting potential. In the Schlumberger array, the four electrodes are placed in a line, centered around a midpoint. The two outer electrodes are the current electrodes and the two inner electrodes are the potential electrodes. Schlumberger is the best method used for vertical electrical sounding for practical reasons. It is less labor-intensive than the Wenner array (see below) because you only need to move the two transmitting electrodes for each new reading, whereas the Wenner requires moving all four electrodes for each new measurement.

3. Dipole-Dipole Array

The dipole-dipole array, consisting of a current electrode pair and a potential electrode pair, was originally used for mineral exploration with the induced polarization (IP) method.

 

  

In order to get an idea of the earth’s cross-section, the result of a survey are plotted in a so-called pseudo-section, where the apparent resistivity data is plotted at the midpoint between the two dipoles and at a depth of 18% of the dipole-to-dipole separation [Edwards, 1977, A modified pseudosection for resistivity adn IP: Geophyscics, v. 42, no. 5, p. 1020-1036]. The values are then contoured and colorized to represent a rough image of the subsurface. It is the job of modern inversion software to recalculate all these apparent resistivity values to “true” resistivity so that a realistic image of the ground can be created.

 

When compared to the Wenner array, which provides a big picture, the dipole-dipole array provides great detail. The disadvantage is that it doesn’t reach very deep as the receiving dipole will lose the signal if they’re placed too far from the transmitting dipole.

4. Pole-Dipole Array

The Pole-Dipole array is similar to the Schlumberger Array in that the receiver dipole is a tenth of the size of the transmitter dipole (electrodes A and B). Unlike the Schlumberger array, with the Pole-Dipole array, when measuring in the center of the transmitting dipole the receiver is moved outside the transmitter dipole and beyond. The B-electrode is considered to be at a mathematical infinity when it is at a distance of beyond 5-10 times the size of the survey area of the receiver dipole.

 

After placing the remote B-electrode at infinity, you then move the potential electrodes (the receiver dipole; electrodes M and N) to a position one dipole spacing away from the current A-electrode and take a reading. Then the receiver dipole is moved one additional dipole size away from the A-electrode, and another reading is taken. This continues until you begin losing signal between the current and the potential electrodes.

 

The pole-dipole array is preferred to the Dipole-Dipole array when it comes to depth penetration, since depth is related to the distance that separates the A-electrode and the M-electrode.

5. Pole-Pole Array

Between dipole-dipole, pole-dipole, and pole-pole, the latter is the least common. It is only used when you need to see extremely deep in the ground at the additional logistics of placing two remote electrodes at infinity (twenty times that of the survey area). To use the pole-pole survey, you set up the electrodes like you would in a pole-dipole survey—but one of the potential electrodes is placed at infinity in the opposite direction, so one electrode is on each side of the survey area.

 

You then proceed exactly as you would with pole-dipole: The current electrode stay in the same place and the potential electrode move out to take new readings. The primary issue with using the pole-pole array is space. For example, if the survey area is 100 meters in length, the remote electrodes (B and N) would need to be placed at a distance of at least twenty times the survey area. The two infinity electrodes would then be at least 2100 meters apart. The two infinity electrodes are stationary during the entire survey, so you may have to get permission to place them on someone else’s land for the duration of the survey. You also have to consider traffic that could run over your remote electrode cables, creeks, or brush when handling the remote wire.

 

6. Equatorial Array

The equatorial array consists of the two dipoles—A-B and M-N—oriented perpendicular to the survey line and parallel to each other. The advantage of the equatorial array is that you are able to penetrate deeper into the ground than when using the dipole-dipole array, assuming the length along the survey line is the same. This can be particularly advantageous when pulling an array of electrodes behind a vehicle or in limited spaces.

7. Square Array

The square array is a special case of the equatorial array, named because the electrodes form the shape of a square and the sides of the array are all equal length. This array is used most frequently in determining the anisotropy (i.e. resistivity in different directions) of a geological formation. Instead of expanding the electrodes, the square is turned typically 15 degrees for each measurement around the center point of the square.

 

 

For example, let’s say a hydrogeologist needs to survey a rock body with a fracture system through it to locate the general fracture direction. Taking a number of readings through the square array, he can determine which direction is more conductive and thus the main direction of the fractures. Furthermore, if you needed to see deeper to gain more information on the fractures in the rock body, you could expand the size of the square and repeat the same procedure. It may, for instance, show that the fracture changes direction at a particular depth.

8. Gradient Array

The gradient array is used to measure the potential using a dipole M-N moving between two fixed current electrodes A and B. The array is used to map the electrical field caused by the two fixed current electrodes. The Schlumberger array is a variation of the gradient array.

 

The gradient array is easy to use with a multichannel resistivity system, because you can take several simultaneous measurements with the different potential electrode pairs at different locations. It permits also different sets of multiple gradient measurements which are made with the current electrodes at different locations.

9. Azimuthal Method

“Azimuth” is the direction or angle compared to north. The azimuthal method is actually less of an array and more of an electrode orientation. For example, you may measure with either a Wenner array or Schlumberger array in order to determine the resistivity of a formation in a certain direction as described for the square array.

 

When your current electrodes are at 12:00 and 6:00 you take the first reading. You may then spin the whole array around the center point and move so that the current electrodes now are at 1:00 and 7:00 then to 2:00 and 8:00 and take a reading for each new position until you’ve made half a turnaround. Evaluation of this data will give you information about fracture patterns in the formation below.

10. Mise-A-La-Masse Method

Mise-a-la-masse is a French term that literally translates to “charged mass.” Mise-a-la-masse is more of a survey method—like vertical electrical sounding or profiling—than it is an electrode array, but it’s still in the same family. It primarily uses the pole-dipole array to delineate an ore body.

 

One current electrode is placed at infinity and the other current electrode is placed in contact with the ore body at an outcrop or in a borehole. The two potential electrodes are used as a dipole to measure the electrical gradient in a profile or grid on the surface. By drawing a contour map of the data, the outline of the ore body can be displayed.  

 

11. Bipole-Bipole Array

The word bipole is used instead of dipole when the two transmitting electrodes are placed so far apart that the electric field from them can be considered a field from two separate poles. In other words, the distance between the receiver and transmitter dipoles is small in relation to the dipoles themselves.

 

Note: Strictly speaking, the field from the transmitting electrodes when using the dipole-dipole array is actually the field from a bipole (especially as it pertains to the measurements closest to the transmitting electrodes). However, this is labeled as a dipole-dipole array.

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