Electrical resistivity tomography

# Electrical resistivity tomography

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Encyclopedia
Electrical resistivity tomography (ERT) or electrical resistivity imaging (ERI) is a geophysical technique
Geophysics
Geophysics is the physics of the Earth and its environment in space; also the study of the Earth using quantitative physical methods. The term geophysics sometimes refers only to the geological applications: Earth's shape; its gravitational and magnetic fields; its internal structure and...

for imaging
Geophysical imaging
Geophysical imaging is geophysical technique that investigates the subsurface. There are many different kinds of imaging techniques, all which are based on applied physics.Types of geophysical imaging include:...

sub-surface structures from electrical measurements made at the surface, or by electrode
Electrode
An electrode is an electrical conductor used to make contact with a nonmetallic part of a circuit...

s in one or more borehole
Borehole
A borehole is the generalized term for any narrow shaft bored in the ground, either vertically or horizontally. A borehole may be constructed for many different purposes, including the extraction of water or other liquid or gases , as part of a geotechnical investigation, environmental site...

s. It is closely related to the medical imaging technique electrical impedance tomography
Electrical impedance tomography
Electrical impedance tomography is a medical imaging technique in which an image of the conductivity or permittivity of part of the body is inferred from surface electrical measurements. Typically, conducting electrodes are attached to the skin of the subject and small alternating currents are...

(EIT), and mathematically is the same inverse problem
Inverse problem
An inverse problem is a general framework that is used to convert observed measurements into information about a physical object or system that we are interested in...

. In contrast to medical EIT however ERT is essentially a direct current method. A related geophysical method, induced polarization
Induced polarization
Induced polarization is a geophysical imaging technique used to identify subsurface materials, such as ore. The method is similar to electrical resistivity tomography, in that an electric current is induced into the subsurface through two electrodes, and voltage is monitored through two other...

, measures the transient response. 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). Tikhonov
Andrey Nikolayevich Tychonoff
Andrey Nikolayevich Tikhonov was a Soviet and Russian mathematician known for important contributions to topology, functional analysis, mathematical physics, and ill-posed problems. He was also inventor of magnetotellurics method in geology. Tikhonov originally published in German, whence the...

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 geophyicists 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, and the work of Loke and Barker at Birmingham University was among the first such solution, and their approach is still widely used.

Applications of ERT include mineral prospecting
Prospecting
Prospecting is the physical search for minerals, fossils, precious metals or mineral specimens, and is also known as fossicking.Prospecting is a small-scale form of mineral exploration which is an organised, large scale effort undertaken by mineral resource companies to find commercially viable ore...

, monitoring of ground water flow and archeology.

In industrial process imaging
Industrial process imaging
Industrial Process Imaging, or Industrial Process Tomography or Process Tomography are methods use to form an image of a cross section of vessel or pipe in a chemical engineering or mineral processing, or petroleum extraction or refining plant....

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, emphasising the quantity that is measured rather than imaged.