Earth–ionosphere waveguide

The Earth–ionosphere waveguide[1] is the phenomenon in which certain radio waves can propagate in the space between the ground and the boundary of the ionosphere.

The earth operates as a ground plane, and the resulting cavity behaves as a large waveguide.

For instance, lightning strikes launch a signal called radio atmospherics, which can travel many thousands of kilometers, because they are confined between the Earth and the ionosphere.

Radio propagation within the ionosphere depends on frequency, angle of incidence, time of day, season, Earth's magnetic field, and solar activity.

An exception is whistler propagation of lightning signals along the geomagnetic field lines.

The region between Earth's surface and the ionospheric D-layer behaves thus like a waveguide for VLF- and ELF-waves.

In the presence of the ionospheric plasma and the geomagnetic field, electromagnetic waves exist for frequencies which are larger than the gyrofrequency of the ions (about 1 Hz).

Its radiation of electromagnetic waves within the Earth-ionospheric waveguide can be described by a transfer function T(ρ,ω): where Ez is the vertical component of the electric field at the receiver in a distance ρ from the transmitter, Eo is the electric field of a Hertzian dipole in free space, and

For the real Earth's surface, the ground wave becomes dissipated and depends on the orography along the ray path.

[5] For VLF waves at shorter distances, this effect is, however, of minor importance, and the reflection factor of the Earth is

) with a fixed boundary at a virtual height h, which means a phase jump of 180° at the reflection point.

[2][5] In reality, the electron density of the D-layer increases with altitude, and the wave is bounded as shown in Figure 2.

3) indicating the equivalence of both theories[7] As seen in Figure 3, the spacing between the mode interference minima is constant and about 1000 km in this example.

The effect of the Earth's curvature is, that near the antipode the field strength slightly increases.

[5] Due to the influence of the Earth' magnetic field, the medium becomes anisotropic so that the ionospheric reflection factor in reality is a matrix.

Waves propagating from east to west are more strongly attenuated than vice versa.

There appears a phase slipping near the distance of the deep interference minimum of Eq.

During the times of sunrise and/or sunset, there is sometimes a phase gain or loss of 360° because of the irreversible behavior of the first sky wave.

The dispersion characteristics of the Earth-ionospheric waveguide can be used for locating thunderstorm activity by measurements of the difference of the group time delay of lightning signals (sferics) at adjacent frequencies up to distances of 10000 km.

Figure 1. Geometry of ray propagation within the Earth–ionosphere waveguide. The ground wave and two sky waves are displayed
Figure 2. Real and virtual reflection height
Figure 3. Normalized vertical field strength E z vs. distance ρ in magnitude (solid line, left ordinate) and phase (dashed line, right ordinate). [ note 1 ]
Figure 4. Magnitude of transfer functions of the zeroth mode and the first mode versus frequency at distances 1000, 3000, and 10000 km using day time conditions.