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ELECTROMAGNETIC PROPAGATION AND SCATTERING IN SPHERICALLY-SYMMETRIC TERRESTRIAL SYSTEM-MODELS (WAVE GUIDE, ZONAL, HARMONICS)
MCKAY, EDWARD G., II
Doctor of Philosophy
A study of the quantitative solutional approaches to boundary-value problems associated with terrestrial electromagnetic propagation is carried out, with particular attention given to spherical-system models and the frequency range below 3 MHz. The field solutions are determined from dyadic Green's functions, the elements of which are infinite Bessel-Legendre (zonal harmonic) series. The three classical approaches to evaluating these solutions--mode theory, wave-hop, and summation of the zonal harmonic series--are surveyed, and techniques to improve the rate of convergence of the latter series are investigated. Provided the field point is not too near the source, the more effective methods prove to be certain Shanks' transformations, an application of the generalized Euler transformation when an asymptotic expansion for the Legendre function is substituted, and a transformation developed using summation by parts that appears to be new. Kummer's transformation, Cesaro summation, and repeated-averaging are also considered. The groundwave (two-media) series solutions are shown to be summable with an order of magnitude fewer terms than the number required by earlier researchers.