ON THE GINZBURG-FEINBERG PROBLEM OF FREQUENCY ELECTROMAGNETIC SOUNDING FOR UNAMBIGUOUS DETERMINATION OF THE ELECTRON DENSITY IN THE IONOSPHERE

Abstract

In the present work, we investigate an inverse problem of frequency electromagnetic sounding for unambiguous determination of the electron density in the ionosphere. Direct statement of this problem is known as the Ginzburg-Feinberg problem that has, in general case, an essential nonlinearity. Inverse statement of the Ginzburg-Feinberg problem has the boundary-value formulation relative to two functions: the sought-for electric-field strength and the distribution of the electron density (or rather two-argument function appearing in the additive decomposition formula for distribution of the electron density) in the ionosphere. In the present work, we prove the existence and uniqueness of the solution of the Ginzburg-Feinberg problem as well as we propose the analytical method, permitting: first, to reduce it to the problem of integral geometry, and, thereupon, having applied the adjusted variant of the Lavrentiev's theorem, to reduce the obtained problem of integral geometry to the first kind matrix integral equation of Volterra type with a weak singularity