Inverse problem on the vertical conductivity profile of a plane-layered medium

Mambo et al. (1983, 1985) have made a simulation estimating the electron density profile of the lower ionosphere from knowledge of the VLF reflection coefficients. The fundamental equation used in the estimation is a Fredholm integral equation of the first kind with respect to the variation of the electron density and the variation of the receiving antenna output voltage, derived from Maxwell´s equations. An unknown electron density profile is obtained by an iterative full wave calculation technique solving the integral equation. The method is extended to the VHF case in which the transmitted field strength varies. The vertical conductivity profile of a plane-layered medium is estimated by applying the knowledge of both reflected and transmitted field strengths. Only the case of homogeneous isotropic conductivity and TM-mode plane wave propagation is treated. However, this technique is also applicable for all propagation modes in a general anisotropic complex medium