Static image principle for anisotropic conducting half-space problems; impedance boundary

The image principle developed for static problems involving an anisotropic half-space and bounded by either a perfect electric or magnetic conductor is extended to problems with an anisotropic surface impedance boundary. Such a boundary can be applied to approximate a thin layer of anisotropic conducting material above the anisotropic half-space. The problem is limited by requiring similar anisotropy for the surface impedance and the transverse part of the resistivity dyadic of the half-space. It is seen that, instead of a point image for a point source, the image consists of a combination of a point image and a line image obeying an exponential law. The effect of the impedance surface on the potential field of a point source is considered in terms of a numerical example.