ONE-DIMENSIONAL PROFILE INVERSION OF A HALF-SPACE BOUNDED BY A 3-PARTIMPEDANCE GROUND

A method which permits one to reveal the one-dimensional electromagnet ic profile of a half-space over a three-part impedance ground is estab lished. The method reduces the problem to the solution of two function al equations. By using a special representation of functions from the space L(1)(-infinity, infinity), one of these equations is first reduc ed to a modified Riemann-Hilbert problem and then solved asymptoticall y. The asymptotic solution is valid when the central part of the bound ary is sufficiently large as compared to the wavelength of the wave us ed for measurements. The second functional equation is reduced under t he Born approximation to a Fredholm equation of the first kind whose k ernel involves the solution to the first equation. Since this latter c onstitutes an ill-posed problem, its regularized solution in the sense of Tikhonov is given. The accuracy of the asymptotic solution to the first equation requires the use of waves of high frequencies while the Born approximation in the second equation is accurate for lower frequ encies. A criterion to fix appropriate frequencies meeting these contr adictory requirements is also given. An illustrative application shows the applicability and the accuracy of the theory. The results may hav e applications in profiling the atmosphere over non-homogeneous terrai ns.