The use of equivalent secondary sources in the theory of ground-wave propagation over an inhomogeneous earth

The paper deals with the propagation of a vertically polarized ground-wave over an inhomogeneous spherical earth. On the basis of approximate boundary conditions and a specially chosen auxiliary function in Green´s theorem, the integral equation for the attenuation function is derived. A general method of solving this integral equation by numerical techniques for paths composed of a number of homogeneous sections is discussed. It is proved that the result is in agreement with the reciprocity theorem. The actual field is shown to be the superposition of the fields generated by the primary source and by secondary sources distributed along the path. It is demonstrated that the distributed secondary sources may be approximately replaced by a number of suitably chosen equivalent secondary sources. An approximate method of calculation based on this property is introduced. The method is discussed in some detail in two cases: when the paths may be regarded plane and when they extend into the diffraction zone. The proposed method makes possible a simple and rapid calculation of field strength in many practical cases. It may be used for any phase characteristic of the complex permittivity of the soil. The paper confirms the important conclusion that placing the transmitting or receiving antenna over a well-conducting soil may considerably improve the reception. It is shown further that the electrical properties of the earth in the neighbourhood of the transmitter also have an influence on the phase of the field.