Static image principle for two conducting anisotropic half‐spaces with similar transverse anisotropies

Abstract

Direct‐current image principle, previously developed for an anisotropic half space bounded by a perfectly electrically or magnetically conducting plane or an impedance surface, is extended to problems with two anisotropic half‐spaces. The anisotropies of the two spaces are restricted to be similar in the transverse plane, in which case the image expressions can be solved analytically. In fact, only in this case, for a point current source, there exists a point image source for reflected fields and a point image source for transmitted fields. The reflection and transmission image amplitudes are seen to be obey simple expressions similar to those of two isotropic media with effective isotropic conductivities. However, the locations of the images do not coincide with those of the isotropic theory, it is seen that in general the reflection image is shifted laterally and the transmission image both laterally and axially from those of the isotropic case.