Broadside excitation of ELF by a horizontal dipole beneath a sporadic <i>E</i> environment: Theory

Pappert, R. A.

doi:10.1029/rs021i001p00106

Cited by 2 publications

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“…Paper number 88RS03707. and the lower edge of the E layer [Pappert and Moler Pappert, 1980Pappert, , 1985aPappert, , 1986.…”

Section: For a Number Of Years There Has Been Interest In Long-range mentioning

confidence: 99%

“…Paper number 88RS03707. and the lower edge of the E layer [Pappert and Moler Pappert, 1980Pappert, , 1985aPappert, , 1986.Wait [1964] introduces the use of the reduced two-dimensional wave equation for describing the effects of inhomogeneities in the Earth-ionosphere waveguide on single-mode VLF propagation. He also points out the optical analogy of the approach with propagation of light through a lens of refractive index equal to the sine of the waveguide eigenangle.…”

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A model for propagation of ELF waves throughout the lateral extent of the inhomogeneous Earth‐ionosphere waveguide

Shellman¹

1989

Radio Science

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A formulation is described for finding the surface vertical E field throughout the lateral extent of the spherical Earth-ionosphere waveguide at extremely low frequencies (ELF) below 100 kHz for a completely general model of values of the sine of the waveguide eigenangle. These values are specified at elements of a mesh point array that extends throughout the lateral extent of the spherical shell guide. The solution is based on the condition that the vertical E field at the surface must satisfy the reduced two-dimensional wave equation at every localized group of mesh points. It has been found practical to use a mesh size of 312.5 km halfway to the antipode, which implies a mesh size of $0 km at a distance 1 Mm from the transmitter. oeigensolutions are found for any far range 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. The latter may include the entire waveguide. An example is given for illustration. It is expected that use of the formulation will make it possible to describe the combined effects of inhomogeneities such as land-sea boundaries around continents and large seas and islands, the day-night terminator, and particle precipitation on the amplitude and phase of the vertical E field. INTRODUCTION For a number of years there has been interest in long-range extremely low frequency (ELF) communications [Wait, 1974]. The ELF waves travel within the spherical shell waveguide formed by the Earth as a lower boundary and by a diffuse upper boundary formed principally by the ionosphere E layer. The propagation of ELF waves in a homogeneous spherical shell waveguide has been described by various workers [e.g., Galejs, 1972]. Inhomogeneities in the real Earth-ionosphere waveguide, however, have a pronounced effect on propagation. The difference in the properties of the day and night hemispheres represents a large-scale inhomogeneity in the spherical shell waveguide [Large and Wait, 1968]. Inhomogeneities in the Earth-ionosphere waveguide also include differences in ground conductivity over continents, seawater, and ice caps. Anomalies in ELF propagation are also caused by particle precipitation in the polar regions [lmhof et al., 1978], and can be caused by resonance between a layer of sporadic E This paper is not subject to U.S. copyright. Published in 1989 by the American Geophysical Union. Paper number 88RS03707. and the lower edge of the E layer [Pappert and Moler Pappert, 1980Pappert, , 1985aPappert, , 1986.Wait [1964] introduces the use of the reduced two-dimensional wave equation for describing the effects of inhomogeneities in the Earth-ionosphere waveguide on single-mode VLF propagation. He also points out the optical analogy of the approach with propagation of light through a lens of refractive index equal to the sine of the waveguide eigenangle. This approach is used in the theory that follows. It is assumed that the propagation of ELF waves may be described by ...

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“…Paper number 88RS03707. and the lower edge of the E layer [Pappert and Moler Pappert, 1980Pappert, , 1985aPappert, , 1986.…”

Section: For a Number Of Years There Has Been Interest In Long-range mentioning

confidence: 99%

mentioning

confidence: 99%

A model for propagation of ELF waves throughout the lateral extent of the inhomogeneous Earth‐ionosphere waveguide

Shellman¹

1989

Radio Science

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“…Although a number of researchers have addressed the question of propagation in waveguide environments that vary both along and transverse to the propagation path, no formulation presently exists that can account fully for the Ev, H,, and Ho adverse nocturnal-propagation effects produced by a localized disturbance with simultaneous allowance for vertical inhomogeneity and anisotropy in a spherical geometry. A start in this direction recently has been accomplished by Pappert [1986], who has developed an ELF propagation model that allows for the inclusion of excitation factor and height-gain effects along with allowance for the H o (TE) component.…”

Section: We See That the H• Variation Is Closer To Type A While The mentioning

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Summary of Connecticut 76‐Hz vertical electric, transverse magnetic, and radial magnetic field‐strength comparisons

Bannister¹

1986

Radio Science

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The results of 60 days of vertical electric-field and 136 days of radial horizontal magnetic-field measurements taken in Connecticut are summarized in this article. The main results are (1) the vertical electric field-strength behavior usually is very similar to the transverse horizontal magnetic fieldstrength behavior (in both amplitude and relative phase) during both normal and disturbedpropagation conditions, (2) during normal-propagation conditions, the radial magnetic field-strength amplitude behavior usually is similar to the transverse magnetic field-strength amplitude behavior, while the radial magnetic field-strength relative-phase variation usually is somewhat greater than that for the transverse magnetic field strength, and (3) during disturbed-propagation conditions, the daily radial and transverse magnetic field-strength plots, versus GMT, usually are dissimilar (in both amplitude and relative phase). In particular, the radial magnetic field-strength variations usually are greater than the transverse magnetic field-strength variations.

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Broadside excitation of ELF by a horizontal dipole beneath a sporadic E environment: Theory

Cited by 2 publications

References 16 publications

A model for propagation of ELF waves throughout the lateral extent of the inhomogeneous Earth‐ionosphere waveguide

A model for propagation of ELF waves throughout the lateral extent of the inhomogeneous Earth‐ionosphere waveguide

Summary of Connecticut 76‐Hz vertical electric, transverse magnetic, and radial magnetic field‐strength comparisons

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