Conductivity and resistivity tensor rotation for surface impedance modeling of an anisotropic half-space

The electromagnetic surface impedance of a half-space with inclined conductivity anisotropy can be derived from the isotropic half-space solution provided the conductivity term used in the expressions is the effective horizontal conductivity. For a TM-mode plane wave incidence, the effective horizontal conductivity must be derived from the tensor rotation of the resistivity tensor and not from the tensor rotation of the conductivity tensor. For a TE-mode incident with the same geometry as the TM-mode, the surface impedance is independent upon the inclined anisotropy. This same formulation can then be extended to a multiple layered half-space where each layer has an inclined anisotropy. For an anisotropic half-space with coefficient of anisotropy of 4, with a horizontal conductivity of 0.001 S/m inclined at 45° with respect to the horizontal plane, the magnitude of the surface impedance calculated using the resistivity tensor rotation is approximately 53% larger than the magnitude of the surface impedance calculated using the conductivity tensor rotation.