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Electrical resistivity tomography (ERT) or electrical resistivity imaging (ERI) is a geophysical technique for
imaging Imaging is the representation or reproduction of an object's form; especially a visual representation (i.e., the formation of an image). Imaging technology is the application of materials and methods to create, preserve, or duplicate images. ...
sub-surface structures from electrical resistivity measurements made at the surface, or by
electrode An electrode is an electrical conductor used to make contact with a nonmetallic part of a circuit (e.g. a semiconductor, an electrolyte, a vacuum or air). Electrodes are essential parts of batteries that can consist of a variety of materials ...
s in one or more
borehole A borehole is a narrow shaft bored in the ground, either vertically or horizontally. A borehole may be constructed for many different purposes, including the extraction of water ( drilled water well and tube well), other liquids (such as petrol ...
s. If the electrodes are suspended in the boreholes, deeper sections can be investigated. It is closely related to the medical imaging technique electrical impedance tomography (EIT), and mathematically is the same
inverse problem An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the ...
. In contrast to medical EIT, however, ERT is essentially a direct current method. A related geophysical method, induced polarization (or spectral induced polarization), measures the transient response and aims to determine the subsurface chargeability properties. Electrical resistivity measurements can be used for identification and quantification of depth of groundwater, detection of clays, and measurement of groundwater conductivity.


History

The technique evolved from techniques of electrical prospecting that predate digital computers, where layers or anomalies were sought rather than images. Early work on the mathematical problem in the 1930s assumed a layered medium (see for example Langer, Slichter).
Andrey Nikolayevich Tikhonov Andrey Nikolayevich Tikhonov (russian: Андре́й Никола́евич Ти́хонов; October 17, 1906 – October 7, 1993) was a leading Soviet Russian mathematician and geophysicist known for important contributions to topology, ...
who is best known for his work on regularization of inverse problems also worked on this problem. He explains in detail how to solve the ERT problem in a simple case of 2-layered medium. During the 1940s, he collaborated with geophysicists and without the aid of computers they discovered large deposits of copper. As a result, they were awarded a State Prize of Soviet Union. When adequate computers became widely available, the inverse problem of ERT could be solved numerically. The work of Loke and Barker at
Birmingham University , mottoeng = Through efforts to heights , established = 1825 – Birmingham School of Medicine and Surgery1836 – Birmingham Royal School of Medicine and Surgery1843 – Queen's College1875 – Mason Science College1898 – Mason Univers ...
was among the first such solution and their approach is still widely used. With the advancement in the field of Electrical Resistivity Tomography (ERT) from 1D to 2D and nowadays 3D, ERT has explored many fields. The applications of ERT include fault investigation, ground water table investigation, soil moisture content determination and many others. In industrial process imaging ERT can be used in a similar fashion to medical EIT, to image the distribution of conductivity in mixing vessels and pipes. In this context it is usually called ''
Electrical Resistance Tomography Electrical impedance tomography (EIT) is a noninvasive type of medical imaging in which the electrical conductivity, permittivity, and impedance of a part of the body is inferred from surface electrode measurements and used to form a tomographic ...
'', emphasising the quantity that is measured rather than imaged.


Operating procedure

Soil resistivity Soil resistivity is a measure of how much the soil resists or conducts electric current. It is a critical factor in design of systems that rely on passing current through the Earth's surface. It is a very important parameter for finding the best l ...
, measured in ohm-centimeters (Ω⋅cm), varies with moisture content and temperature changes. In general, an increase in soil moisture results in a reduction in soil resistivity. The pore fluid provides the only electrical path in sands, while both the pore fluid and the surface charged particles provide electrical paths in clays. Resistivities of wet fine-grained soils are generally much lower than those of wet coarse-grained soils. The difference in resistivity between a soil in a dry and in a saturated condition may be several orders of magnitude.Budhu, M. (2011) Soil Mechanics and Foundation. 3rd Edition, John Wiley & Sons, Inc., Hoboken. see chapter 3.5.1 Soils Exploration Methods The method of measuring subsurface resistivity involves placing four electrodes in the ground in a line at equal spacing, applying a measured AC current to the outer two electrodes, and measuring the AC voltage between the inner two electrodes. A measured resistance is calculated by dividing the measured voltage by the measured current. This resistance is then multiplied by a geometric factor that includes the spacing between each electrode to determine the apparent resistivity. Electrode spacings of 0.75, 1.5, 3.0, 6.0, and 12.0 m are typically used for shallow depths (<10 m) of investigations. Greater electrode spacings of 1.5, 3.0, 6.0, 15.0, 30.0, 100.0, and 150.0 m are typically used for deeper investigations. The depth of investigation is typically less than the maximum electrode spacing. Water is introduced to the electrode holes as the electrodes are driven into the ground to improve electrical contact.


See also

*
Electrical capacitance tomography Electrical capacitance tomography (ECT) is a method for determination of the dielectric permittivity distribution in the interior of an object from external capacitance measurements. It is a close relative of electrical impedance tomography and i ...
* Electrical impedance tomography *
Magnetotellurics Magnetotellurics (MT) is an electromagnetic geophysical method for inferring the earth's subsurface electrical conductivity from measurements of natural geomagnetic and geoelectric field variation at the Earth's surface. Investigation depth ...
* Seismo-electromagnetics * Telluric current * Vertical electrical sounding * Geophysical Imaging


References

* * * * *A.P. Calderón, On an inverse boundary value problem, in Seminar on Numerical Analysis and its Applications to Continuum Physics, Rio de Janeiro. 1980
Scanned copy of paper
* * * {{Authority control Geophysical imaging Inverse problems Impedance measurements Multidimensional signal processing