The Schumann resonances (SR) are a set of spectral peaks in the extremely low frequency portion of the Earth's electromagnetic field spectrum. They are global electromagnetic resonances generated and excited by lightning discharges in the cavity formed by the Earth's surface and the ionosphere.
Description The global electromagnetic resonance phenomenon is named after physicist Winfried Otto Schumann, who predicted it mathematically in 1952. Schumann resonances are the principal background in the part of the electromagnetic spectrum from 3 Hz through 60 Hz and appear as distinct peaks at extremely low frequencies around 7.83 Hz (fundamental), 14.1, 20.3, 26.3, and 32.5 Hz. These correspond to wavelengths of 38000, 21000, 14000, 11000 and 9000 km. Schumann resonances occur because the space between the surface of the Earth and the conductive ionosphere acts as a closed, although variable-sized, waveguide. The limited dimensions of the Earth cause this waveguide to act as a resonant cavity for electromagnetic waves in the extremely low frequency band. The cavity is naturally excited by electric currents in lightning. In the normal mode descriptions of Schumann resonances, the fundamental mode is a standing wave in the Earth–ionosphere cavity with a wavelength equal to the circumference of the Earth. The lowest-frequency mode has the highest intensity, and the frequency of all modes can vary slightly owing to solar-induced perturbations to the ionosphere (which compress the upper wall of the closed cavity) amongst other factors. The higher resonance modes are spaced at approximately 6.5 Hz intervals (as may be seen by feeding numbers into the formula), a characteristic attributed to the atmosphere's spherical geometry. The peaks exhibit a spectral width of approximately 20% due to the damping of the respective modes in the dissipative cavity. Observations of Schumann resonances have been used to track global lightning activity. Owing to the connection between lightning activity and the Earth's climate it has been suggested that they may be used to monitor global temperature variations and variations of water vapor in the upper troposphere. Schumann resonances have been used to study the lower ionosphere on Earth and it has been suggested as one way to explore the lower ionosphere on celestial bodies. Some have proposed that lightning on other planets might be detectable and studied by means of Schumann resonance signatures of those planets. Interest in Schumann resonances renewed in 1993 when E.R. Williams showed a correlation between the resonance frequency and tropical air temperatures, suggesting the resonance could be used to monitor global warming. In geophysical survey, Schumann resonances are used to locate offshore hydrocarbon deposits.
History
In 1893, George Francis FitzGerald noted that the upper layers of the atmosphere must be fairly good conductors. Assuming that the height of these layers is about 100 km above ground, he estimated that oscillations (in this case the lowest mode of the Schumann resonances) would have a period of 0.1 second. Because of this contribution, it has been suggested to rename these resonances "Schumann–FitzGerald resonances". However, FitzGerald's findings were not widely known, as they were only presented at a meeting of the British Association for the Advancement of Science, followed by a brief mention in a column in Nature. The first suggestion that an ionosphere existed, capable of trapping electromagnetic waves, is attributed to Heaviside and Kennelly (1902). It took another twenty years before Edward Appleton and Barnett in 1925 were able to prove experimentally the existence of the ionosphere. Although some of the most important mathematical tools for dealing with spherical waveguides were developed by G. N. Watson in 1918, it was Winfried Otto Schumann who first studied the theoretical aspects of the global resonances of the earth–ionosphere waveguide system, known today as the Schumann resonances. In 1952–1954 Schumann, together with H. L. König, attempted to measure the resonant frequencies. However, it was not until measurements made by Balser and Wagner in 1960–1963 that adequate analysis techniques were available to extract the resonance information from the background noise. Since then there has been an increasing interest in Schumann resonances in a wide variety of fields.
Basic theory Lightning discharges are considered to be the primary natural source of Schumann resonance excitation; lightning channels behave like huge antennas that radiate electromagnetic energy at frequencies below about 100 kHz. These signals are very weak at large distances from the lightning source, but the Earth–ionosphere waveguide behaves like a resonator at extremely low resonance frequencies. In an ideal cavity, the resonant frequency of the n {\displaystyle n} -th mode f n {\displaystyle f_{n}} is determined by the Earth radius a {\displaystyle a} and the speed of light c {\displaystyle c} .
f n = c 2 π a n ( n + 1 ) {\displaystyle f_{n}={\frac {c}{2\pi a}}{\sqrt {n(n+1)}}}
The real Earth–ionosphere waveguide is not a perfect electromagnetic resonant cavity. Losses due to finite ionosphere electrical conductivity lower the propagation speed of electromagnetic signals in the cavity, resulting in a resonance frequency that is lower than would be expected in an ideal case, and the observed peaks are wide. In addition, there are a number of horizontal asymmetries—day-night difference in the height of the ionosphere, latitudinal changes in the Earth's magnetic field, sudden ionospheric disturbances, polar cap absorption, variation in the Earth radius of ± 11 km from equator to geographic poles, etc. that produce other effects in the Schumann resonance power spectra.
Measurements
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