Analytical solution for the point source potential in an anisotropic 3-D half-space I: Two-horizontal-layer case

An analytical solution for the electrical potential due to a point source in a two layered anisotropic half-space is obtained using an advanced anisotropic image point source method. The positions of the images of the point source in a two layered half-space, which can be classified as reflection and transmission images, depend on the resistivity tensors of the earth media and the point source position. This solution provides a complete description of the potential in the two-layered anisotropic half-space and the point source may be located in either layer. large class of important theory and applications in geophysics requires this solution. In this paper, for the first time, the method of images is extended by the use of reflection and transmission images to generate the solution for a two-layered anisotropic half-space. Consequently, four principles of the anisotropic point image method (APIM) are advanced. Using these principles a more complex solution is obtained in a companion paper in this series (namely, “Analytical solution for the point source potential in an anisotropic 3-D half-space II: with two-vertical boundary planes”). This solution may be extended to the solution of the N-horizontal layer case.