A Numerical Investigation of Classical Approximations Used in VLF Propagation

Abstract

With some interest, I have read that Pappert, Gossard, ;1nd Roth· muller have developed a comprehensive computer program to obtain numerical results for the propagation . constants of an earth-ionosphere waveguide with an arbitrary electron-density profile. The overall agreement between their approach based on Budden's (1961) work and our method (e.g., Wait and Spies, 1960;Wait, 1960) is quite reassuring. If nothing else, it should lay to rest the contro· versies which have arisen in connection with the importance of accounting properly for earth curvature in calculating the charac· teristics of the least attenuated modes.In their paper, Pappert, Gossard, and Rothmuller (1967) show good agreement with some of our numerical results for the firstorder mode in daytime but they get only partial agreement for the second-order mode in daytime. Actually, the differences are not to be unexpected. As we explained in our technical note (Wait and Spies, 1964): · "In summary, the calculations given in this technical note are strictly correct for an earth-ionosphere waveguide which is bounded by a homogeneous smooth earth and a reflecting layer at height h with a normalized surface impedance ~-'The applicability of the results to an actual diffusely bounded ionosphere requires a number of approximations which are justified mainly an physical grounds. The principal assumption is that ~ is assumed at the outset and then the mode· equation is solved to yield the propagation characteristics. A fundamental question may arise in that the angle of incidence is complex for modes in a lossy waveguide. However, it is fortunate that the cosine C' of the angle of incidence at the ionosphere is approximately equal to (2h/a+{7JI/2 where Cis related to the parameter t, in (13), by

A Numerical Study of VLF Mode Structure and Polarization Below an Anisotropic Ionosphere

“…In a recent paper (Pappert, Gossard, and Rothmuller, 1967), subsequently referred to as paper I, results of a computer program for VLF propagation in the earth-ionosphere waveguide were presented. The appendix of that paper was devoted to the problem of allowing simultaneously for earth curvature and ionospheric effects in regions where both effects may be comparable.…”

Error analysis for a long‐range lightning monitoring network of ground‐based receivers in Europe

“…For further discussion on the VLF propagation theory, the interested reader is referred to Wait [1970]. Additional studies on long‐range VLF propagation and their interaction with the lower (D‐layer) ionosphere layer, directional effects (easterly westerly propagation) as well as the ground conductivity role have been carried out by Papert et al [1967], Pappert and Hitney [1988], Ries [1967], Taylor [1960a, 1960b], Challinor [1967] and Ferguson [1992] accounting both for day and nighttime propagation regimes.…”

Ionospheric model validation at VLF and LF

“…Propagation of radio waves in the very low frequency (VLF) regime (10 to 30 kHz) and the lower end of the low frequency (LF) regime (30 to 60 kHz) is modeled using a waveguide defined by the Earth's surface and the ionosphere. This waveguide model has been detailed in a series of documents which describe the initial model and its subsequent development [Gessard et al, 1966;Pappert et al, 1967Pappert et al, , 1970Sheddy et al, 1968a, b;Pappert and Smith, 1971;Sheckey, 1972, 1974;Merritt and Shellman, 1976;Pappert and Ferguson, 1986;Shellman, 1986;Ferguson and Snyder, 1987;Pappert and Hitney, 1988]. Although the model can use profiles of particle density and collision frequency specified as arbitrary functions of height, in practice, exponential profiles of ionospheric electron conductivity (which is essentially the scaled ratio of electron density to collision frequency) are used with positive ions assumed for charge neutrality [Bickel et al, 1970;Merritt, 1977;Ferguson, 1980;Ferguson et al, 1985;Merritt et al, 1981; In the past we have found data collected aboard in-flight aircraft to be most useful for selecting ionospheric profiles.…”