Integral representations for the electromagnetic field generated by an electric or magnetic dipole line source located within the atmosphere of the two-layer configuration atmosphere-ionosphere rendered anisotropic by a uniform static (terrestrial) magnetic field are evaluated by the method of steepest descent to give analytical expressions for the far field along the interface of the two media. These expressions are used to calculate the surface impedance tensor for the lower boundary of the ionosphere. The surface impedance tensor permits one to replace the continuity conditions by approximate boundary conditions along the interface. Results obtained for an arbitrary direction of the static magnetic field (arbitrary geomagnetic latitude) are specialized to polar and equatorial zones. For these cases, dependence of attenuation and phase velocity of the first few modes of the earth-ionosphere waveguide on ionospheric height and on electric properties of the ground (which enter a scalar surface impedance for the ground plane) is shown. TM modes are much more sensitive to electrical properties of the adjoining media than TE modes. Attenuation is lower for propagation from west to east than in the reverse direction. Icy ground causes severe attenuation of TM but not of TE modes. Various other applications of the surface impedance model are reviewed.
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