# Potential fields

In earth science related fields, geophysics deals with surveying potential, diffusive and wave fields in order to obtain structural information of the subsurface to characterize earth's layers in terms of its physical and geological properties. Examples of potential methods are: gravimetry, magnetometry and electric resistivity methods.

Potential fields are assumed to be time independent, at least during the acquisition time, and their scalar potential field equations satisfy Poisson type equations:

${\displaystyle \sigma (\partial _{x}^{2}+\partial _{y}^{2}+\partial _{z}^{2})G^{3D}(x,y,z)=-\delta (x,y,z)}$,

where σ is the medium parameter controlling the distribution of the fields, e.g. electric conductivity for Electric resistivity surveys, and their Green's functions in a homgeneous medium are given by:

${\displaystyle G^{3D}(x,y,z)={\frac {-1}{4\Pi \sigma R}}}$,

where ${\displaystyle R={\sqrt {x^{2}+y^{2}+z^{2}}}}$ is the three dimensional distance between source and receiver.

Among these potential fields, gravity and Magnetic surveys are routinely carried out over vast stretches of land or sea, thus are characterized by wide coverage but poor resolution, being the least expensive and the most commonly used in mineral and oil exploration. Magnetic surveys are often carried out by means of high technology aeroplanes, helicopters, UAVs or high technology remote satellite sensing whereas Gravity surveys are often land-based or ship-borne. On the other hand, with regard to Electric resistivity surveys, these are acquired in order to characterize the subsurface based on its electrical properties.