Schumann Resonances
Davis D. Sentman
Geophysical Institute and Physics Department
University of Alaska
Fairbanks, Alaska 99775-0800, USA
[Excerpts from Sentman, D.D., "Schumann Resonances," in CRC Handbook of Atmospheric Electrodynamics, (Hans Volland, ed.), CRC Press, Boca Raton, 1985. The principal reason for posting this limited version of the paper is to give a rough overview and expose the extensive bibliography that exists on this subject. None of the Figures referred to here are available on this web version. For these, please consult the published text.]
I. Introduction
The space separating the earth and the ionosphere forms a cavity which can support electromagnetic standing waves with wavelengths that are comparable to the planetary dimensions. Within the lower atmosphere to a height of ~60-70 km above the earth's surface the finite electrical conductivity of the atmosphere is maintained primarily by cosmic rays. Near the ground the conductivity is a scalar quantity with a value of approximately 10-14 S-m-1, making the atmosphere in this region a very good insulator. The conductivity increases approximately exponentially with altitude, with a characteristic scale height of 3-6 km, the value of which depends on local time and altitude, from the ground to the lower edge of the E-region at altitudes of 75-90 km. Above these altitudes the ratio of the electron gyrofrequency to the electron-neutral collision frequency is no longer negligible, and the conductivity becomes a tensor quantity. Within the upper D-region and lower E-region the component of the conductivity parallel to the magnetic field is ~10-4-10-2 S-m-1, comparable to that of the terrestrial land surface and fresh water. For waves in the extremely low frequency (ELF) range of frequencies 3-300 Hz, the transition between the insulating lower atmosphere, where electric displacement effects dominate, and the ionosphere where conduction effects dominate occurs at altitudes of 45-50 km.
The combination of the nearly perfectly conducting terrestrial surface boundary and the highly conducting, but dissipative, ionospheric outer boundary separated by an insulating layer of non conducting air creates an approximately spherically concentric cavity, the "earth-ionosphere cavity" with electrically conducting walls, shown in highly idealized form in Figure 1. Large electrical transients, such as lightning, radiate broadband electromagnetic impulses that spread radially away from the source into the cavity. The lowest frequency components of the impulse can circumnavigate the globe several times before suffering serious degradation, and the phase addition and cancellation of waves that have traversed the global circumference several times along multiple paths produce a resonant line spectrum. The principal properties of the spectrum may be accurately described in terms of quasi-transverse electromagnetic (quasi-TEM) normal modes of the earth-ionosphere cavity. The total resonant spectrum is the incoherent superposition of the effects from the totality of global lightning.
These resonances, called Schumann resonances, have been observed at many different locations and can, in principle, be detected from any place on the planet. They are very weak and are easily obscured by nearby lightning and numerous other unrelated sources of man-made noise. However, away from thunderstorms and artificial electromagnetic noise sources, the Schumann resonances constitute the principal component of the natural background of the electromagnetic spectrum over the frequency range 6-50 Hz.
In this paper we describe the basic observational characteristics of the Schumann resonances and outline their theoretical description. Key references to the primary literature are given for readers interested in detailed discussions of various aspects of Schumann resonance research.
II. Background
Resonance properties of the earth-ionosphere cavity were first predicted and discussed theoretically by W.O. Schumann in a series of papers of progressive refinement in the manner in which the ionospheric boundary is treated (Schumann 1952a,b,c, 1954, 1957). The earliest experimental detection of the resonances was made by Schumann and König (1954), König (1959), and the first spectral representation showing the resonance "lines" was presented by Balser and Wagner (1960). During the five years following these initial results, experimental measurements of increasing sophistication were reported by Raemer (1961), Polk and Fitchen (1962), Balser and Wagner (1962a,b, 1963), Pierce (1963), Stefant (1963), Chapman and Jones (1964), and Rycroft (1965). Theoretical descriptions of the resonances to take into account realistic properties of the ionosphere were advanced by Wait (1960a,b), Galejs (1961a,b, 1962, 1964), Row (1962), Johler and Berry (1962), Jones (1964), Galejs (1965a,b) and Wait (1965a,b). In a special issue of IEEE Transactions (Wait, 1963) early work is summarized. An insightful review of early research was given by Madden and Thompson (1965).
Following these initial reports there occurred about two decades of active research in Schumann resonances, and more generally in the entire subject of ELF propagation. This research was stimulated in part by the U.S. Navy's interest in investigating the ELF band for possible use in submarine communications. Although study of the Schumann resonances formed a part of this ELF research, the primary emphasis in these studies was on frequencies above 45 Hz. Good reviews of ELF research directed to communications issues may be found in Wait (1974), the "Special Issue on Long Range Communication at ELF" in the IEEE Journal of Oceanic Engineering, Vol OE-9, 1984, and Jones (1985).
The general electromagnetic theory for VLF and ELF waves in the earth-ionosphere system is contained in the books by Galejs (1972), Wait (1972) and Bliokh et al. (1980, and the paper by Bezrodny et al. (1977). Numerous contributions from research sponsored by the U.S. Navy have been collected together by Bannister (1987a,b,c,d,e). Extensive contributions have been made by Jones (1964, 1967, 1970a,b,c, 1974, 1985) and collaborators (Chapman and Jones, 1964; Jones and Lewis, 1969; Jones and Kemp, 1970, 1971; Kemp and Jones, 1971; Kemp, 1971; Jones and Joyce, 1989; Burke and Jones, 1992a,b), and by Rycroft (1965) and Cannon and Rycroft (1982). Fundamental observations of properties of Schumann resonances have been made by Ogawa et al. (1966a,b, 1967, 1969a,b), Ogawa and Tanaka (1970), Ogawa and Murakami (1973), and Ogawa et al. (1979).
The most recent comprehensive reference works on Schumann resonances are the book by Bliokh et al. (1980) and the review by Polk (1982). The reader is referred to these works and the accompanying exhaustive reference lists for detailed discussion of the large amount of research that was performed between 1965 and 1982 when Schumann resonance research was at its peak. Results of subsequent research, including theory of relevance to Schumann resonances, have been reported by Nickolaenko and Rabinovich (1982), Cannon and Rycroft (1982), Behroozi-Toosi and Booker (1983), Polk (1983), Sentman (1983), Jones (1985), Beamish and Tzanis (1986), Greifinger and Greifinger (1986), Sentman (1987a,b), Tzanis and Beamish (1987a,b), Holtham and McAskill (1988), Bashkuev et al. (1989), Bashkuev et al. (1990), Jones and Joyce (1989), Bashkuev et al. (1990), Jones and Burke (1990), Sentman (1990a,b), Sentman and Fraser (1991), Sakhorukov (1991, 1992), Burke and Jones (1992a,b), Jones and Burke (1990, 1992), and Wait (1992). A novel application of the Schumann resonances in earth system studies has been proposed by Williams (1992).
III. Principal Observational Characteristics of the Schumann Resonance Spectrum
The principal features of the Schumann resonance spectrum were established within the first few years of research in the field following the spectral analysis of Balser and Wagner (1960). Numerous reports of early observations of the Schumann resonances and the diurnal amplitude and frequency variations can be found in Bliokh et al. (1980) and references therein. Advances in computer technology during the 1980's have resulted in the development of real time data acquisition systems that are capable of performing continuous power spectrum calculations in the field to monitor variations in the amplitudes and eigenfrequencies of the Schumann resonances. Here, we shall summarize the principal observational characteristics of the Schumann resonances by referring to a compact frequency-time spectrogram representation of the data generated by such a system. The observations were obtained in 1989 from an instrument located at Table Mountain Observatory in Wrightwood, California, and described by Sentman (1987) and Sentman and Fraser (1991). The theoretical interpretation of the structure of the modes is given in Section V.
Figure 2 shows a dynamic frequency-time spectrogram of the component of the magnetic field parallel to the surface of the earth, corresponding to the magnetic component of the Schumann resonances. The plot covers a period of 5 days during September, 1989. Each vertical strip in the plot is an 18 minute average Fourier power spectrum over the frequency band 0-40 Hz, with power encoded according to the gray scale at the right, at the corresponding Universal Time (UT). The frequency resolution is approximately 0.47 Hz. In this representation up to six of the Schumann resonances are clearly discernible as intensifications in the power at approximately 8, 14, 20, 26, 32, and 38 Hz. There is a quasi periodic diurnal modulation in the modes that reaches a maximum at approximately 2200 UT, as indicated by the arrows along the top of the plot.
Diurnal Intensity Modulations
The Schumann resonance intensities undergo a quasi-periodic diurnal modulation in both the vertical electric field and horizontal magnetic field intensities. This behavior is depicted in Figure 3, where we show two sets of data covering 6 days each, also from 1989, in the frequency-time format. The top panels are the spectrograms from the vertical electric field, and the bottom panels are from the horizontal component of the magnetic field covering the same interval (6 days) at the corresponding electric field data in the top panel. Five or six distinct resonance lines are discernible in these plots, in both the electric and magnetic field components. The electric field and magnetic field spectrums generally exhibit similar frequency resonance structure and diurnal intensity profiles. The similarity of the electric and magnetic diurnal profiles is shown in Figure 4, where the respective power spectrums have been averaged over the lowest few modes for the same intervals as in Figure 3. During the June, 1989 interval the diurnal profiles undergo a fair amount of day-to-day variability, with indications of maximums at ~1600 UT and ~2200 UT. However, over a similar interval in 1989 the diurnal maximums exhibit a strong single maximum near ~2200 UT. These results demonstrate that day-to-day variations in the diurnal profiles may be substantial, and that there is a seasonal effect. The source of these variations between days is unknown, but it is tempting to speculate that they reflect a corresponding variability in the totality of the global lightning source function.
The spectrums that are shown in Figure 3 and the corresponding averages in Figure 4 are typical of results obtained for an observing site located in California. When a comparison is made of diurnal profiles simultaneously recorded at widely separated locations, striking differences are observed. Figure 5 (top panel) from Sentman and Fraser (1991) illustrates the difference between diurnal profiles recorded in California and Western California (great circle distance ~14,800 km) during an eight day interval in April, 1990. The much greater diurnal variability of the California profiles compared to Australia are distinctly evident. It has been hypothesized that the differences are due to a local modulation related to the local height of the ionosphere at the respective observing sites. This modulation is superimposed on the Schumann resonance spectrum excited by the totality of global lightning.
The local time modulation factor can be determined directly from the two data sets, and the resulting effect removed to obtain a hypothetical "universal source function" as detected at each site. The corrected diurnal profiles at the widely separated sites exhibit remarkable similarity (Figure 5, bottom panel), suggesting that the global lightning function may be determined from the Schumann resonances once the diurnal modulation factor has been removed. By making the crude assumption that Schumann resonance energy is approximately uniformly distributed throughout the earth-ionosphere cavity and invoking conservation of wave energy, the local time modulation factor may be determined directly from the data, as shown in Figure 6 for analysis intervals close to the equinox. The effective height dependence on local time derived in this fashion, with a minimum near local noon, is broadly consistent with the existence of a day-night asymmetry in the height of the D-region induced by solar ultraviolet and x-ray illumination of the day-side hemisphere and the absence of such illumination on the nightside.
Spatial Coherence
Schumann resonances exhibit a very high degree of spatial coherence, as determined from simultaneous measurements across several hundred km, both at high latitudes (Holtham and McAskill, 1988) and at midlatitudes (Sweeney, 1989). In the study of Sweeney (1989), cross spectrums of the resonances were measured across a baseline of 480 km stretching along an east-west line between Mercury, Nevada and Table Mountain, California. Results show temporal coherence at a level of greater than 90 percent over the lowest three resonances covered by the analysis; in the case of the lowest order mode at 8 Hz the coherence was approximately 98 percent. When the extremely long wave length of these waves is taken into account (~40,000 km/n, where n is the mode number), these results indicate that the coherence length of the waves is very much greater than 480 km, consistent with the normal mode description of the Schumann resonances.
Diurnal Frequency Variations
The peak frequencies in both the electric and magnetic Schumann resonance spectrums are observed to undergo a moderate diurnal variation of approximately ±1/2 Hz about their nominal average values of 8, 14, 20, ... Hz. Further, in the case of the magnetic field, the frequency variation depends on the orientation of the antenna, i.e., whether the measurement is made along the north-south or east-west direction.
To interpret this behavior it is important to distinguish between the eigenfrequencies of the cavity, and the frequencies at which the peak power is observed (peak frequencies) in the power spectrum. The eigenfrequencies of the earth-ionosphere cavity are geometric properties of the cavity as a whole, and exist independent of the presence or absence of sources or observers. Shifts or modulations of the cavity eigenfrequencies may occur in response to modulations of the ionospheric boundary by external ionization sources, such as solar x-rays and energetic particle precipitation from the magnetosphere into the high latitude ionosphere. Excitation by lightning of the cavity modes is at the corresponding eigenfrequencies, but in a dissipative system the peak frequencies may be shifted relative to the actual cavity eigenfrequencies. In a dissipative system the finite width of each resonance line bleeds into other lines, principally the adjacent ones. The amount of this leakage depends primarily on the relative amplitude of the contaminating lines, which on account of the nodal structure of the normal modes is strongly dependent on the great circle distant to the excitation source. As the distance to the late afternoon thunderstorm regions of the earth varies with time for an observer fixed to the earth, so also does the amount of this leakage. The effect is to produce a time varying shift in the peak frequencies. It is an artifact of the source-observer geometry unrelated to any change in the underlying geometric properties of the earth-ionosphere cavity. Much of the diurnal frequency variations observed within the electric field power spectrum has been attributed to this source-observer distance effect, although some of it may also be due to the effect of cavity asymmetries on the normal modes.
A more complicated effect occurs in the case of removal of degeneracy among the 2n+1 linearly independent components of the n'th normal mode, as is expected for the case of an asymmetric earth-ionosphere cavity. The removal of degeneracy, or the separation in frequency of nominally orthogonal normal modes in the earth-ionosphere cavity, is accompanied by changes in the phase speeds of the corresponding modes. Attempts to detect the removal of degeneracy of the normal modes by the splitting of the resonance lines in the electric field have not been successful, apparently due to line spreading of the spectrum by amounts greater than the estimated degree of splitting. However, the removal of degeneracy may also be detectable through the accompanying effects on the polarization of the magnetic field. Differences in the diurnal variation of the peak frequencies of the lowest resonances, as measured in the east-west and north-south directions, respectively, may be attributed to this effect.
Q-Bursts
The average Q-factors of the transverse magnetic normal modes of the earth-ionosphere cavity are in the range 3-6, and correspond to the approximate number of wave periods in the damping interval of each excited mode. For the n=1 mode at 8 Hz, the damping period is approximately 0.5 second, and higher modes decay over correspondingly shorter time periods. Global lightning occurs at a rate of approximately 100 strokes per second, and so within the 0.5 sec damping interval of the 8 Hz mode approximately 50 lightning strokes occur. Lightning flashes, consisting of 3-6 strokes, occur at quasi random times and so their signals add incoherently. Discrete excitations of the earth-ionosphere cavity at 8 Hz by the vast majority of individual lightning strokes are therefore not usually discernible in the Schumann band.
However, the "ringing" of the TM normal modes of the cavity can be directly observed when a sufficiently large transient excites it. Lightning current and charge moments are distributed over a large range of amplitudes, and occasionally include extremely large events. A single pulse from a very large discharge can temporarily excite the cavity to an amplitude greater than the incoherent sum of excitations of the lightning strokes of average amplitude occurring within the damping period of the modes. Such excitations by large lightning transients are believed to be the source of transients called Q-bursts (Ogawa, 1966b). Figure 7 shows several typical examples of Q-bursts recorded in California in 1985 (Sentman, 1987). Very large discrete events such as these are typically observed in both vertical electric and horizontal magnetic signals simultaneously and occur at random intervals at the rate of several to tens of events per hour. They possess a continuous range of amplitudes from background levels to levels that may exceed the background by factors of 10-20 or more. Q-bursts are characterized by a discontinuous onset initiating a quasi-periodic oscillation at one of the Schumann resonance frequencies, usually the lowest frequency near 8 Hz, that subsequently decays exponentially at a rate corresponding to the Q-factor of the cavity. Their power spectra, as determined using maximum entropy spectral techniques suitable for short time series (Sentman, 1989), shows the energy to be concentrated at the Schumann resonances frequencies. The quasi-periodic behavior of the bursts is the direct signature of the electromagnetic wave circumpropagating around the globe several times as it decays to background levels.
The removal of degeneracy in the earth-ionosphere cavity has been detected in the magnetic polarization characteristics of Q-bursts (Sentman, 1989), as well as in the average polarization characteristics of the Schumann resonances described above. By analyzing individual Q-bursts, Jones and Burke (1992; Figure 8) have shown that the attenuation of ELF waves propagating in the earth-ionosphere cavity is a function of direction of arrival of the waves. Since the attenuation constant is equivalent to the imaginary part of the frequency, the directional dependence of the attenuation is further evidence of the removal of degeneracy in the earth-ionosphere cavity. However, in the case of Jones and Burke (1992), most of the effect may be due to wave propagation over the highly magnetized north polar cap.
Although Q-bursts are thought to be cavity excitations from extremely large lightning transients, to date this has not been verified by simultaneous optical observations of specific source discharges. Other possible sources have been suggested as possible excitation sources, including fluctuating polar electrojet currents and leakage of ELF whistlers originating in the cusp and funneled to the earth-ionosphere cavity through the polar cusp.
Magnetic Polarization
In the theoretical description of the Schumann resonances using the normal mode theory, a simplifying assumption often employed is that the earth-ionosphere cavity is spherically symmetric and the ionospheric conductivity is a scalar quantity (see below). In this model the electromagnetic normal modes excited by a vertical electric dipole source are azimuthally symmetric with respect to a radius vector passing through the source, and the horizontal magnetic component is linearly polarized. More realistic ionospheric models include a day-night height variation of the D-region ionosphere axially symmetric about the earth-sun line, magnetization of the night-time ionosphere, and eccentricity of the geomagnetic dipole.
Observations have shown, however, that the polarization of the horizontal magnetic field may be strongly elliptical, with an ellipticity that undergoes a diurnal modulation that can approach values of |e| ~ 0.7 (Sentman, 1987). Similarly, individual Q-bursts often exhibit substantial elliptical polarization (Sentman, 1989). These results provide additional evidence, in addition to that indicated by the diurnal intensity modulations discussed in the previous section, that the earth-ionosphere cavity may either depart significantly from spherical symmetry or that a significant portion of the ionosphere is anisotropic. To date, a satisfactory quantitative description accounting for the substantial elliptical polarization observed in the magnetic component of the Schumann resonances has not been advanced.