VLF mode conversion at terminator taking into account earth's curvature

As an extension of earlier work in which VLF mode conversion at the solar terminator has been treated with a plane model of the earth-ionosphere waveguide, here a spherical model is used. This is done with some simplifications. First, the real three-layer problem (ionosphere-atmosphere-earth) is reduced to a boundary value problem involving fictitious surface impedances along the interfaces to the ionosphere and to the ground, chosen such that they describe in an asymptotically equivalent way the influence of these layers. Second, the thin shell approximation is employed, which permits one to reduce the problem to a quasi-plane model still containing the spherical characteristics, as, for example, the characteristic values of the spherical modes. A system of coupled integral equations is obtained which is solved rigorously by an iterative procedure.