One-dimensional profile inversion of a half-space over a two-part impedance ground

A method which permits one to reveal the one-dimensional (1-D) electromagnetic profile of a half-space bounded by a two-part impedance ground is established. The method reduces the problem to the solution of two functional equations. One of these equations is solved exactly by reducing it to a Riemann-Hilbert problem while the other is reduced under the Born approximation to a Fredholm equation of the first kind whose kernel involves the solution to the first equation. Since this latter constitutes an ill-posed problem, its regularized solution, in the sense of Tikhonov, is given. An illustrative application shows the applicability and the accuracy of the theory. The functional equations are valid also when the impedance of the ground varies in an arbitrary manner. The theory can be applied to a quick determination of the constitutive electromagnetic parameters of the atmosphere over a nonhomogeneous impedance ground.