Propagation of ELF (Extremely Low Frequencies) Waves in the Spherical Earth-Ionosphere Waveguide with Transverse and Longitudinal Variation of Properties

摘要

A formulation is described for finding the vertical E-field in the spherical earth-ionosphere waveguide at extremely low frequencies (elf). A very general model of propagation parameters is allowed since values of the eigenangles and of the excitation factors are specified at elements of a mesh point array that may extend throughout the lateral extent of the spherical-shell guide the solution is based on the condition that the vertical E-field must satisfy the two-dimensional wave equation in the vicinity of each mesh point. Eigensolutions are found for ranges from the transmitter for which there is no transverse variation of properties, and these are combined with the more general solution which applies to the region of transverse inhomogeneity. Two examples are given to illustrate both a symmetrical and nonsymmetrical case. It is expected that use of the formulation will make it possible to describe the effects of inhomogeneities such as the auroral zone, land-sea boundaries, the day-night terminator and man-made disturbances to the ionosphere on the amplitude and phase of the vertical E-field. (Author)