Approximate mode conversion coefficients in the Earth-ionosphere waveguide

Constant impedance boundary conditions have been used by many authors to obtain mode reflection and transmission coefficients for propagation across a land-sea discontinuity. The impedance boundary conditions are here replaced by exact boundary conditions and similar formulae are obtained for propagation between a diffuse inhomogeneous isotropic ionosphere and a homogeneous isotropic earth. These formulae permit the use of any ionospheric model with vertical inhomogeneity although some simplification results if impedance boundary conditions are used at the ground. A numerical example is given to illustrate the significance of the formulae.