It is closely related to the medical imaging technique electrical impedance tomography (EIT), and mathematically is the same inverse problem.
In contrast to medical EIT, however, ERT is essentially a direct current method.
Early work on the mathematical problem in the 1930s assumed a layered medium (see for example Langer, Slichter).
When adequate computers became widely available, the inverse problem of ERT could be solved numerically.
In this context it is usually called Electrical Resistance Tomography, emphasising the quantity that is measured rather than imaged.
It has applications in numerous fields, including: Environmental Studies: Geotechnical Engineering: Archaeology and Cultural Heritage: Mining and Mineral Exploration: Hydrogeology: Engineering and Infrastructure: Oil and Gas Exploration: Agriculture: