Electric resistivity methods
Electric resistivity methods are a form of geophysical surveying that aids in imaging the subsurface. These methods utilize differences in electric potential to identify subsurface material.
Resistivity is fundamentally related to Ohm's Law measuring Resistance. Resistance is defined as the voltage divided by the current (R = V/I) and the value of a material's resistance depends on the resistivity of that material.
Resistivity is the value of resisting power of a certain material to the flow of a moving current.
Resistivity (ρ) values are related by the equation describing current refraction.
This law acts opposite that of Snell's Law in that the current traveling from a layer of lower resistivity to a layer of higher resistivity would travel at a smaller refraction angle.
Configuration and electrode spacing
The basic setup for a resistivity survey involves using a resistivity meter and four electrodes.
The resistivity meter is a device that acts as both a voltmeter (measuring V) and an ammeter (measuring I) and records resistance values (V/I).
These resistance values are converted to apparent resistivity values using the formula:
where ρa = apparent resistivity and k = geometric factor. The geometric factor varies based on the geometry of each electrode spacing setup.
In typical field work, data is acquired as an apparent resistivity value and later interpreted to obtain true resistivity.
The Wenner Array
Among the four electrodes used with the resistivity meter, two are used to pass the current through while the other two measure the change in potential.
In the Wenner Array, the spacing between each of the four electrodes is the same. The amount of spacing can be changed depending on the depth of the survey. Generally, the depth the survey can measure is related to 1/2 the distance between the outer electrodes. This array is one of the most commonly used. 
The Schlumberger Array
With the Schlumberger array, only the outer two electrodes (the electrodes supplying and receiving the current) are moved. The advantage of this is that it is much
faster because only two electrodes have to be moved rather than the 4 with the Wenner array.
In field work, the outer electrodes would keep being moved until the recorded potential is a minimum value. At that point the set up is established in another location and the survey is continued.
The Gradient Array
With the gradient array, the spacing of the outer two electrodes is kept constant while the two inner electrodes (the potential electrodes) are moved. The spacing between the inner electrodes is constant but they are moved as a pair in the space between the outer electrodes and measure the potential as they go.
Other array spacings
These are not the only array spacings a resistivity survey can have. Others include the dipole-dipole array, the pole-dipole array, pole-pole array, the Lee-partition array, and the square array. Each of these various arrays differs in electrode spacing and the movement of either the current or potential electrodes.
Some of the array spacings are depicted on the right.
The three main methods of electric resistivity surveys are vertical electric sounding (VES), electric profiling, and electric imaging. Each of these utilize one of the array configurations mentioned above.
Vertical Electric Sounding
VES is one of the more commonly used and cost effective resistivity survey methods. Current is moved through the subsurface from one current electrode to the other and the potential as the current moves is recorded. From this information, resistivity values of various layers is acquired and layer thickness can be identified.
The apparent resistivity values determined are plotted as a log function versus the log of the spacing between the electrodes. These plotted curves identify thickness of
layers. If there are multiple layers (more than 2), the acquired data is compared to a master curve to determine layer thickness.
There are a few limitations with VES. First, the depth of the survey is limited to the electrode spacing. Second, layers may vary in resistivity horizontally. This is where a
method like electric profiling would be better to use. Lastly, the layers must have consistent thickness. If there is a case where the middle layer is much thinner than the layers above and below it then the resistivity results will be inaccurate. The resistivity of the thin middle layer will affect the reading. This is termed equivalence.
Where VES focuses on determining resistivity variations on a vertical scale, electric profiling seeks to determine resistivity variations on a horizontal scale. Profiling can use the same electrode spacing configurations as VES. Since changing the spacing between electrodes only affects the depth at which the survey can reach, the profiling method does not involve manipulating electrode spacing. Instead, the electrode spacing is kept constant and the entire survey is moved along a line or a "profile" to measure horizontal changes in resistivity.
In many cases resistivity can change as both depth and horizontal distance increase. Both VES and electric profiling are limited to surveying in one direction. Electric imaging is able to survey both vertical and horizontal changes in resistivity. This method essentially combines the other two methods. Electrode spacing is increased and the survey is moved along a profile in order to measure both vertical and horizontal resistivity. These values are then used to create a pseudosection.
The pseudosection can be used to generate an image of the subsurface. Imaging can be done in both 2D and 3D.
There are many applications for electric resistivity methods including groundwater detection, mineral identification, waste exploration, oil identification, and several others.
For example, with waste detection, electric resistivity techniques may provide a more environmentally friendly way of acquiring data. Electric surveys are used instead of drilling methods to eliminate the chance of drilling into the waste and risking leakage. Waste detection studies generally focus on a landfill site and are used to determine the extent of the leakage (leachate) of the waste.
The example shown here is from a study in Arizona where electric imaging was used to identify the waste depth as well as how close it lies to groundwater.
Resistivity surveys can offer an alternative imaging technique that works well to identify subsurface material. However, as with other geophysical methods, there are some limitations. For example, with VES surveys there is a limit to how far the detectable depth is. This mostly relies on the maximum separation of current electrodes. Additionally, VES generally works with horizontal layers so if the area has steep topographic variation then the survey will be difficult.
A lot of the surveys are time consuming and labor intensive. As seen with electric profiling there is a constant need to move the electrodes along a certain profile.
To seek an accurate subsurface image surveyors tend to use a multitude of survey techniques in order to eliminate the effect of some of these errors. Resistivity methods are simply some of the many tools used to do this.
 Ohm's Law
 Snell's Law
 Geometric factor
 Using Resistivity for Oil detection
 Electric Resistivity Surveys
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