Analytical solution for the electric potential due to a point source in an arbitrarily anisotropic half-space

A very large class of important theory and applications in geophysics requires analytical solutions for the determination of the electric potential due to a point source in an arbitrarily anisotropic half-space. In this paper, a very clear and simple solution to the half-space problem has been developed from consideration of an arbitrarily anisotropic whole space. For the first time, the method of images is used to generate the solution for an arbitrarily anisotropic three dimensional half-space. Based on traditional extreme value theory the image source point has been determined and calculated for the half-space case.