Introduction to the Theory of VLF Propagation

This paper is a self-contained exposition of the conventional theory of propagation of VLF radio waves. The model is a spherical earth surrounded by a concentric ionosphere. Although the model is highly idealized, the theory is still quite involved. The complexities arise from the long wavelengths inherent in such problems. In Section I the elementary geometrical or hop theory for VLF is considered. This includes a discussion of ionospheric reflection coefficients and the influence of multiple reflections. The validity of the model is established by a comparison with experimental data. In Section II, the diffractive corrections near the caustics of the ray systems are obtained. These provide a means to extend the theory to points near and beyond the horizon point for the individual hops or rays. In Section III, the waveguide mode theory is expounded. A number of approximations and simplifications are introduced in order to illustrate principles. References to more detailed analyses which use higher order approximations are given. Finally, in Section IV, the influence of a stratified ionosphere is treated by using a two-layer model. The material in this paper was included in the Summer (1961) Lecture Course on Radio Propagation given at the Boulder Laboratories of the National Bureau of Standards, and in earlier graduate courses, at the University of Colorado.

[1]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[2]  P. Debye,et al.  Das Verhalten von Lichtwellen in der Nähe eines Brennpunktes oder einer Brennlinie , 1909 .

[3]  G. Watson.  The Transmission of Electric Waves Round the Earth , 1919 .

[4]  E. V. Appleton,et al.  Wireless studies of the ionosphere , 1932 .

[5]  H. Booker.  The Application of the Magneto-Ionic Theory to the Ionosphere , 1935 .

[6]  K. Budden.  LXXXV. The reflection of very low frequency radio waves at the surface of a sharply bounded ionosphere with superimposed magnetic field , 1951 .

[7]  K. G. Budden.  CXVIII. The propagation of a radio atmospheric—II , 1952 .

[8]  R. Bracewell,et al.  The ionospheric propagation of radio waves of frequency 16 kc/s over distances of about 540 km , 1952 .

[9]  R. Macario,et al.  Propagation of Audio-Frequency Radio Waves to Great Distances , 1956, Nature.

[10]  Leonard Liebermann,et al.  Extremely Low‐Frequency Electromagnetic Waves. II. Propagation Properties , 1956 .

[11]  J. Wait,et al.  Multiple reflections between the earth and the ionosphere in V.L.F. propagation , 1956 .

[12]  J. Wait.  The Mode Theory of VLF Ionospheric Propagation for Finite Ground Conductivity , 1957, Proceedings of the IRE.

[13]  J. Wait.  The Attenuation vs Frequency Characteristics of VLF Radio Waves , 1957, Proceedings of the IRE.

[14]  A. D. Watt,et al.  Characteristics of Atmospheric Noise from 1 to 100 KC , 1957, Proceedings of the IRE.

[15]  J. Wait.  On the mode theory of V. L. F. ionospheric propagation , 1957 .

[16]  J. Wait,et al.  Pattern of an antenna on a curved lossy surface , 1958 .

[17]  J. Wait.  Terrestrial propagation of very-low-frequency radio waves, a theoretical investigation , 1960 .

[18]  James R. Wait,et al.  Influence of Earth curvature and the terrestrial magnetic field on VLF propagation , 1960 .

[19]  J. Ralph Johler,et al.  On the analysis of LF Ionospheric radio propagation phenomena , 1961 .

[20]  D. Crombie.  Reflection from a sharply bounded ionosphere for VLF propagation Perpendicular to the magnetic meridian , 1961 .