# A Two Dimensional Flow Is Defined By Its Components Electricity and Geophysics

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## Electricity and Geophysics

The resistivity method is used for the study of horizontal and vertical discontinuities in the electrical properties of the subsurface and for the detection of three-dimensional bodies of anomalous electrical conductivity. This method is mainly used in engineering and hydrogeological investigations.

In the resistivity method, artificially generated electric currents are introduced into the subsurface and the resulting potential difference is measured at the surface. Potential difference is defined as the electrical potential difference between two points. Deviations in the pattern of potential differences from a homogeneous ground are expected, providing information on the nature of the cohesion and electrical properties of the subsurface.

The resistivity of a material is defined as the resistance in ohms between opposite faces of a unit cube of the material. The resistance offered by a material to current flow is expressed in terms of resistivity. The SI unit of resistance is the ohm-meter and the reciprocal of resistance is called conductance. Siemens/meter and MHO are some of its units of measurement.

Basic minerals and graphite conduct electricity by way of electrons. However, most rock-forming minerals are dielectric and, therefore, electricity is carried through them mainly by way of ions in the pore water. Thus most rocks conduct electricity through electrolytic rather than electronic processes. Porosity is therefore the major controlling factor of rock resistivity and resistivity increases as porosity decreases. Archie’s law shows an inverse relationship between resistivity and porosity.

Even crystalline rocks with negligible intergranular porosity are conductive along cracks and fissures. But in common rock types, there is considerable overlap between different rock types and it is not possible to identify rock types based on resistivity data alone! Apparent or effective resistivity (the resistivity of the rock and its pore water) can also be expressed in terms of resistivity and the amount of pore water present.

Resistivity method measures the magnitude of conductance, while induced polarization measures the magnitude of polarization.

Some of the major applications of resistivity survey are groundwater exploration, mineral exploration, cavity exploration, waste site exploration, oil exploration, etc.

Induced polarization methods use the capacitive action of the subsurface to detect areas where conductive materials have permeated their host rocks. The phenomenon of induced polarization was first discovered by Schlumberger in 1912. Electrically conductive materials exhibit: 1. delayed voltage response and 2. over-voltage effect. In simple terms, the induced polarization response reflects the extent to which the subsurface is able to store electric charge analogous to a capacitor. Polarization occurs due to the redistribution of ions along the interface (metal-fluid or nonmetal-fluid) after applying an electric current. After the electric field is removed, a residual current arises as the ion relaxes into equilibrium. The induced polarization method indicates the presence of clay material.

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