Exact solution of a model problem of subsurface sensing

Abstract

An inverse electromagnetic wave radiation problem simulating subsurface radio sensing is considered. It is assumed that synchronous external currents with unknown spatial density emerge in the subsurface medium. It is shown that their distribution can be found from the pulsed radiation waveformes measured along the border of the examined half-space. In a model formulation, the problem is reduced to the reconstruction of a 2D function from its integrals over a set of semicircles. An explicit solution of that tomographic problem is found by means of the Darboux equation. Numerical examples are given. Bibliography: 13 titles. Using the method of “exploding” sources, we give the exact solution of an idealized inverse problem of subsurface sensing, namely, the determination of the spatial density of external currents from the electric field measured on the surface.