V.V. Akhiyarov – Ph.D.(Eng.), Senior Research Scientist, 

Kotel'nikov IRE of RAS (Moscow); 

Leading Engineer, JSC «SPC «SRI of Long-distance Radio Communication» (Moscow)

E-mail: vakhiyarov@gmail.com

The problem of the attenuation function calculation above inhomogeneous surface is considered. Brief historical review of the radio wave propagation theory is introduced, the famous Sommerfeld’s error, connected with surface wave propagation above homogeneous earth, is discussed. This error was due to the fact that the surface wave cannot be separated from the total solution based on normal mode analysis and later Sommerfeld admitted it himself. This error has been the reason for scientific discussions for several decades until it was corrected by Soviet scientists V.A. Fock and E.L. Feinberg. Later J.R. Wait showed that a surface wave is practically not excited above homogeneous earth using physically realized antenna height.

However, above sea surface covered with a layer of ice, a surface wave can propagate under certain conditions. In this case, the surface wave corresponds to the first term of the series in the V.A. Fock’s diffraction formula. However, when moving away from the source, the surface waves quickly decay, so there is the problem of the attenuation function calculation over the sea–ice surface.

The influence of ice thickness and electromagnetic wave frequency on the attenuation function is investigated. A comparison of the attenuation function for a flat and spherical earth model is produced and it is shown that the curvature of the earth does not affect on the surface wave attenuation (if this wave really propagates above the ice–sea surface). The dependences of the absolute value and phase of the normalized surface impedance on the frequency and on the thickness of ice are presented. It is obtained that the nature of the surface impedance can be in both inductive and capacitive. The real part of the relative dielectric permittivity of the underlying surface with impedance corresponding to the input impedance of the sea–ice is calculated. It is shown that the surface wave above the sea–ice effectively propagates only for large negative values of the real part of the relative permittivity of the underlying surface. Positive values correspond to homogeneous earth; therefore, the surface wave is practically not excited in this case.

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