ONE-DIMENSIONAL PROFILE INVERSION OF A HALF-SPACE OVER A 2-PART IMPEDANCE GROUND

A method which permits one to reveal the one-dimensional (1-D) electro magnetic profile of a half-space bounded by a two-part impedance groun d is established. The method reduces the problem to the solution of tw o functional equations. One of these equations is solved exactly by re ducing it to a Riemann-Hilbert problem while the other is reduced unde r the Born approximation to a Fredholm equation of the first kind whos e kernel involves the solution to the first equation. Since this latte r constitutes an ill-posed problem, its regularized solution, in the s ense of Tikhonov, is given. An illustrative application shows the appl icability and the accuracy of the theory. The functional equations are valid also when the impedance of the ground varies in arbitrary manne r. The theory can he applied to a quick determination of the constitut ive electromagnetic parameters of the atmosphere over a nonhomogeneous impedance ground.