Abstract
A direct integration of MAXWELL'S equations is performed in the case of microwave propagation beyond the horizon, taking into consideration the atmospheric turbulence. Following the method developed by STRATTON-CHU, the solution is found to be composed of a volume integral term and a surface integral one with the help of BoRN's approximation. The former term coincides with the expression so far given by solving a wave equation for the electric or magnetic vector. However, this does not give a transverse wave at great distances from the so-called scattering region, and, hence, this does not satisfy MAXWELL'S equations. In other words, a solution of a wave equation of the second order is not always a solution of MAXWELL'S equation of the first order.
In order to avoid the above difficulty, a new method is proposed to correct the volume integral term, giving the fundamental expression for the turbulent scattering.
Concerning the suface integral term, there is some correction needed in case of BoRN's approximation and the term corrected is found to agree with J. ORTIISCS theoretical result in which the earth is regarded rather as a black body.
In case elevated layers with discontinuity are present in the atmosphere, STRATTON-CHU'S formalization is also shown to be applicable, giving usual layer-reflection.
Consequently, without enough information on atmospheric structures, the field beyond the horizon is composed of three parts: scattering due to eddies, diffraction due to the earth of a black body type and layerreflection, which are of equal weight from a theoretical point of view at present.
