Low-frequency radio wave propagation in the earth-ionosphere waveguide disturbed by a large-scale three-dimensional irregularity

Abstract

In this paper, we develop further the analytical and numerical method of solving three-dimensional problems in the theory of radio wave propagation, including three-dimensional local inhomogeneities (ionospheric disturbances or Earth’s surface irregularities). To model the Earth-ionosphere waveguide, we use the surface impedance concept, by which the irregularity extending beyond one waveguide wall has an arbitrary smooth shape, and its surface can be described by the impedance. In the scalar approximation, this problem is reduced to a two-dimensional integral equation for the irregularity surface, which, by asymptotic (kr ≫ 1) integration over the coordinate transverse to the propagation path (with allowance for terms of the order of (kr)−1), is reduced to a one-dimensional integral equation, in which the integration contour is the linear contour of the irregularity. The equation is solved numerically, combining the inversion of a Volterra integral operator and successive approximations. By reducing the computer times, this method enables one to study both small-scale and large-scale irregularities. The results of numerical simulation of radio wave propagation in the presence of a powerful three-dimensional ionospheric disturbance are presented as an example.