Kelvin Inversion of PEC and PMC Spheres for Geoelectric Imaging

The classical Kelvin inversions in spherical geometry are revisited in the context of geoelectric imaging. A point source of current is outside a perfect electrically conducting (PEC) sphere or outside perfect magnetically conducting (PMC) sphere. Perfect electric conductor is very good conductor with zero electric resistivity. Perfect magnetic conductor corresponds to very good insulator with infinite resistivity. The sphere is embedded in a homogeneous whole space which has constant electric conductivity. Analytical solutions can be obtained by the method of images. The methods are described and numerical demonstrations based on them are presented.