The surface impedance concept and the structure of radio waves over real earth

The paper is concerned with the concept of surface impedance as applied to the theory of radio-wave propagation over a real, i.e. inhomogeneous and irregular, earth; some of the conclusions may also be of value in the theory of waveguides, cavity resonators and certain types of aerial. The advantages and limitations of the surface-impedance concept are shown in connection with a very general integral equation for the field strength. The approximations and physical phenomena underlying the surface-impedance concept are first discussed in the simplest case of a homogeneous and flat earth. The analysis is then extended to a horizontally stratified earth; it is then possible to characterize the earth by certain effective parameters depending on frequency and the geometric structure of the soil. The same is also true in the cases of a spherical or not too excessively irregular earth. The discussion is then generalized to the case of an arbitrarily inhomogeneous earth. The height/gain function and the shape of the ellipse of polarization are discussed. Approximate boundary conditions for the Hertzian vector and Hertzian scalar function are related to the concept of surface impedance. Practical conclusions are drawn with regard to the existence and measurement of the effective earth constants and to some aspects of geological prospecting by radio methods.