A further note on terrestrial extremely low-frequency propagation in the presence of an isotropic ionosphere with an exponential conductivity-height profile

Abstract

The mode theory of ELF waves has been extended by Galejs to isotropic ionosphere models of an exponential conductivity‐height profile, where the refractive index may be near unity at the lower boundary of the ionosphere. Recent experimental data of Bowhill on the lower nighttime ionosphere differ significantly from earlier estimates. The exponential ionosphere model is re‐examined in view of these data. The calculated daytime attenuation rates were shown to agree with measurements of Jean, Murphy, Wait, and Wasmundt. The calculated nighttime attenuation rates are slightly higher than those measured by Chapman and Macario. The earth‐to‐ionosphere cavity resonance frequencies are computed using the average of day and night ionosphere parameters. They differ by less than ½ cps from the resonance frequencies measured by Balser and Wagner. The calculated Q factors of the cavity are approximately 4.5 in the frequency range between 10 and 30 cps. The computed terrestrial ELF noise spectrum exhibits a more rapid decay at higher frequencies than the measured spectrum. The wave form that results after passing the calculated noise spectrum through a bandpass filter exhibits an average frequency consistent with measurements of König.

Schumann resonances

“…The exponential ionosphere model [Galejs, 1961b[Galejs, , 1962a[Galejs, , 1964a] produces a better agreement with measurements as seen in figures 9 and 10. In this work propagation is assumed to be uniform around the surface of the earth and the propagation parameters represe nt the average of day and night conditions.…”

“…Calculations are based on daytime or day and nighttime ionosphere models. The Q factors considered also the effects of cosmic ray ionization [Bourdeau et aI., 1959] that give a nearly exponential conductivity versus height variation as indicated by Galejs [1962a]' Cosmic ray ionization decreases the effective Q figures , in particu· lar for the lower frequencies. The calculated Q values are still somewhat higher than those estimated from experimental data.…”

“…The isotropic exponential model gives a reasonable approximation to the ionospheric conductivity versus height profile through the lower ionosphere layers, and the propagation parameters of the model can be deter· mined from closed form expressions of the surface impedance [Galejs, 1961a[Galejs, , 1962a[Galejs, , b, 1964a]_ Calcu· lated resonance frequencies and Q factors that are based on (3), (4), and available values of 5 [Galejs, 1962a] are listed in tables I and II. Calculations are based on daytime or day and nighttime ionosphere models.…”

“…This parameter S is determined from solving the appropriate boundary value problem of the earth, the air space and the chosen ionosphere model [Wait, 1962;Galejs, 1964aJ. The resonance frequencies of the nth mode are determined from the minima of sin V1T in (1) [Galejs, 1962a[Galejs, , 1964a which gives f, = 7.5 v'n(n+ 1).…”

The Schumann resonances

“…Theore ti cal cal· c ulation s have bee n pe rformed under various si mplifying assumptions [e.g. , see Schumann, 1952;Wait, 1964;Galejs, 1961a, b, and1962;Chapman and Jon es, 1964;J ones, 1964]; many of th ese give reaso nabl e overall agreement with expe rim e nt, but none is e ntirely satisfactory. The mos t successful models te nd to be somewhat artifi cial and to show great se nsitivity to artificially introdu ced parame ters.…”