Application of state-space method to scattering from plane-stratified media

An explicit expression is derived for the surface impedance of a half-space composed of two layers. The upper layer is assumed to be arbitrarily inhomogeneous. The bottom layer, which is of infinite thickness, is assumed to be homogeneous. The expression contains the state-transition matrix elements associated with the upper layer. This matrix is determined numerically and analytically for rapidly and slowly varying media, respectively. The formulation is confined to vertical polarization. The method is applied to reflection from a sinusoidal edge of an opaque sporadic
E
layer in the ionosphere. The results assist some previous calculations.