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.
Fundamentals
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.[1]
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.
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.
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
Figure 2: Showing various electrode spacings. Provided by National Research Council
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.
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.
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.
Methods
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.
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
Figure 3: Showing the electric profiling method using the Wenner array. Provided by B.Q Aziz
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.[6]
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.[3][5]
Figure 4: Overview of electric imaging that leads to creating a pseudosection. Provided by Loke et al. 2011
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.[7] Imaging can be done in both 2D and 3D.