Comparison of the Schumann resonance parameters in horizontal magnetic and electric fields according to observations on the Kola Peninsula



[1] The measurements of horizontal electric components at extremely low frequencies (0.1–20 Hz) have been started in the high-latitude observatory of Lovozero in the Kola Peninsula. It is found that the electric components are not less informative than the horizontal magnetic ones for Schumann resonance study. The diurnal variations in amplitude, frequency, and bandwidth of the first Schumann resonance mode in the electric W-E and N-S components are similar to the variations in the magnetic H and D components, respectively. The same correspondence of the components keeps for Q bursts. The frequencies in electric and magnetic components are not always equal: In summer, the frequency of the electric N-S component in the diurnal variation exceeds the frequency of the magnetic D component by 0.1 Hz. The parameters of both magnetic and electric components have seasonal variations. Three maxima of thunderstorm activity are observed in daily variations of the amplitudes of electric components: the Asian and American ones in the W-S component and the African one in the N-S component. The width of resonance bands in the electric components is somewhat larger than in the magnetic ones. The calculations of ELF wave components near poorly conducting surface are made, the results being in accordance with the observations.

1. Introduction

[2] The initial model for investigation of Schumann resonances (SR) [Schumann, 1952] represented two perfectly conducting concentric spheres, the outer sphere corresponding to the ionosphere, and the inner one referring to the Earth's surface. Yet the first measurements of Balser and Wagner [1962], which confirmed SR existence experimentally, revealed an appreciable difference between the observed frequency of 7.8 Hz and theoretically predicted value (10.6 Hz). The reason for the discrepancy, as was soon found out, is nonperfect conductivity of the ionosphere. The consistence can be achieved by accounting for appropriate conductivity profiles. A theoretical study of Greifinger and Greifinger [1978] proves that exponential conductivity profile, adopted in the model of SR, results not only in reasonable frequency values but provides a simple analytical solution for the altitude dependence of SR electromagnetic field. A spatial structure of SR field has been studied in numerous papers [cf. Bliokh et al., 1980; Tran and Polk, 1979; Sentman, 1983, 1990; Mushtak and Williams, 2002; Grimalsky et al., 2005].

[3] In the theoretical paper by Morente et al. [2004], the altitude dependence of SR frequency has been treated. It was shown that in a model with a lossy resonator cavity, one should discriminate between the global resonance frequency and the local one, which is measured experimentally. The difference appears to be proportional to the local dissipation of energy. The difference was calculated at ionospheric heights. In their earlier work, Morente et al. [2003] considered nonperfectly conductive ground. It was found that with the average conductivity of the Earth's surface of 10−3 S/m and frequency of 30 Hz, the tangential component of the electric field should arise throughout the entire ionosphere, with amounting to 4% of the vertical one at the ground level.

[4] Under the assumption of perfectly conductive Earth's surface, the SR electric component on the ground should have only vertical component, with the magnetic one being purely horizontal. In spite of performing ELF measurements at balloons, the data on the altitude distribution of SR field are scarce. Ogawa et al. [1979] reported about the measurements of SR vertical electric component at 20 km and 26 km altitudes. They found that the Ez component decreases weakly with height. Roldugin et al. [2004] presented the measurements of SR vertical magnetic component at Karymshino observatory (ϕ = 52.8°N, λ = 158.3°) in Kamchatka. The signal turned out to be strong enough to determine the frequency and provide its examination. The cause of Hz component presence there seems to be the closeness of measurement points to a mountain; however, the effect of nonperfectly conductive soil or subsurface geological peculiarity near the stations not being excluded.

2. Data

[5] The inductive magnetometer in Lovozero observatory (68.0°N, 35.1°E) is described in Roldugin et al. [2003]. From autumn 2004, the measurements of two horizontal components of ELF electric field, simultaneously with the magnetic ones started at this station. To register the electric component, symmetric, mutually orthogonal earthed lines composed of downleads and grounding electrodes are used. The length of each line is 200 m. The coils, which are magnetic detecting elements, are oriented along the Earth's magnetic field, so we measure H (along magnetic meridian) and D component (along magnetic parallel). The electric antenna axes are directed along the geographic parallel and meridian (the declination in Lovozero is 12°E). Using the conventional notations, we measure X (along geographic meridian) and Y (geographic W-E direction) components of the electric field.

[6] The digitization of all electric and magnetic channels is carried out with 12 bit ADC timed through GPS. The sampling frequency is 40 Hz. The frequency response function is the same for all four channels. It is equal to 0.5 at 0.5 Hz, 0.7 at 1 Hz and 1 from 4 to 20 Hz.

[7] It is found that the electric constituent is not less informative than the magnetic one, its intensity being quite sufficient for consistent reception of SR signal. As an example, the frequency-time spectrograms for magnetic D (top) and electric X component (bottom) for 13 July 2004 are shown in Figure 1. The first band of SR is seen near 8 Hz in the electric component, as well as in the magnetic one. In both components, the low-frequency pulsations Pi1, induced by substorm activity, are presented in morning and evening hours as seen at the bottoms of the spectrograms, and they seem very similar. The line at 5 Hz is a persistent calibration signal. The vertical bars are of different origin: the static noise is at 0756 and 2232 UT, the near lightnings are at 0947, 1202, 1924 and 2103, and the trains from the remote lightnings are at 0338 and 0720 UT. The increase in ELF activity between 0800 and 1800 UT, probably due to anthropogenic disturbance, is seen in both channels.

Figure 1.

Frequency-time spectrograms of the (top) magnetic D component and (bottom) electric X component in Lovozero during 13 July 2004.

[8] The data of all four channels are processed with the same technique: the amplitude spectrum of 5 min interval is found by fast Fourier transform, and the first Schumann band within the 5.8–9.8 Hz is approximated by a Lorentzian with five unknown parameters: the frequency of the maximum fmax, amplitude B, half width Δf, and two parameters c1 and c2, approximating the linear decrease of noise intensity with frequency:

equation image

[9] Further we investigate frequencies fmax, amplitudes B and widths Δf, obtained in this way.

3. Frequency Diurnal Variations

[10] As an example, Figure 2 shows the frequency curves for all four channels on 31 July 2004. Their diurnal variations, double-humped shape, antiphase of H and D, also of X and Y components are clearly seen. It is also seen that the frequency in the electric channels is slightly higher than in the magnetic ones. The frequency course in the electric X component is similar to that in the magnetic D component, the same correspondence takes place for the electric Y component and magnetic H component.

Figure 2.

Courses of frequencies in (top) two magnetic components and (bottom) two horizontal electric components during 31 July 2004 at the Lovozero observatory.

[11] The diurnal variations of the frequencies are found for all four channels for the summer period from 9 July to 5 August 2004. They are shown in Figure 3 by the thin dashed lines, the thick solid lines indicating their approximations by first five harmonics. The peculiarities mentioned above are seen here more distinctly: the presence of two maxima, antiphase of N-S and W-E components both in magnetic and electric components. Also, the resemblance between the magnetic H and electric Y components, as well as between magnetic D and electric X components, is evident. The excess of the frequency of the electric Y over magnetic H component is within the limit of accuracy but for the corresponding X and D components it is much larger and reaches 0.1 Hz near the maxima of the components. The minimal discrepancy is observed at minimal frequency.

Figure 3.

Diurnal variations of the first SR frequency (left) in the magnetic H component and the electric W-E component and (right) in the magnetic D component and the electric N-S component for the interval from 9 July to 5 August 2004 in Lovozero.

[12] The average diurnal variation has also been calculated for the winter period combined of the two intervals: 18–31 December 2004 and 13–22 January 2005 (see Figure 4). When comparing Figures 3 and 4, one can notice a seasonal variation in the frequencies: In winter, the frequency of the H component increases remarkably, by 0.2 Hz, and the frequency of the D component somewhat decreases; similar peculiarities are displayed in the corresponding electric components. Now the shape of the diurnal variation in the magnetic D component is different: It is practically one humped, the maximum near Greenwich midnight has almost vanished. The difference between the frequencies of the magnetic D and electric X components exceeds the accuracy level.

Figure 4.

Same as in Figure 3 but for common time interval of 18–31 December 2004 and 13–22 January 2005.

4. Diurnal Variations of Amplitude and Width

[13] For the same time intervals, the diurnal variations in the amplitude of first-mode SR, i.e., the parameter B from equation (1), are found. They are shown in Figure 5 for summer and in Figure 6 for winter conditions. The two maxima in the diurnal curve are well seen for the magnetic H and electric Y components both in summer and in winter. The first maximum is at 0900–1000 UT, the second one at 2100–2200 UT, i.e., 2 hours later. The shapes of the amplitude curves for these components are very similar for both seasons, as it takes place for the diurnal variations of frequency. There is a similarity between the curves for magnetic D and electric X components, but the curves differ significantly from those for H and Y components. In summer, the scope of the diurnal variations of D and X amplitudes is not big, with one maximum at 1400 UT prevailing in winter.

Figure 5.

Daily variations of the first SR amplitude (left) in the magnetic H component and electric W-E component and (right) in the magnetic D component and electric N-S component for the summer period.

Figure 6.

Same as in Figure 5 but for the winter period.

[14] One can see from Figures 5 and 6 that the middle values of the amplitudes of both magnetic components in Lovozero are nearly equal, and their seasonal variations are not too large. For the electric components it is different. The amplitude of the electric Y component is twice larger than that of the X component, with their winter values being noticeably lower than the summer ones.

[15] The diurnal variations in the width of first-SR mode are shown in Figure 7 for summer and in Figure 8 for winter observations. As clearly seen from the frequency and amplitude, the amplitude of width variations hardly exceed the dispersion. There is also a similarity between the width diurnal variations in magnetic H and electric Y components, as well as in magnetic D and electric X component, both for the frequency and amplitude. The widths for H and Y components are nearly coincident, and the width in X is somewhat greater (by 0.1 Hz) than the width in D component. In winter, the diurnal variations in the latter two components have only one maximum, for both the amplitudes and frequency in D component.

Figure 7.

Daily variations of the first SR width (left) in the magnetic H component and the electric W-E component and (right) in the magnetic D component and the electric N-S component for the summer period.

Figure 8.

Same as in Figure 7 but for the winter period.

5. Q Bursts in the Electric Components

[16] The concept of the emissions radiated in the Schumann bands to be resonances is, in a way, an abstraction. In reality, there are lightning discharges, with their radiation taking several revolutions around the planet, being multiply reflected and gradually damping. The system is a dispersive one and the attenuation is a function of the frequency, this damping being smaller at resonance frequencies which retain a greater amplitude. The wave trains after extremely strong strokes exceed the background ELF. For the first time they were distinguished and examined by Ogawa et al. [1966]. To define this phenomenon, the authors coined a new term “Q burst,” which we will also use. From Q burst damping, Ogawa et al. [1966] estimated the distance from the observation point to the source as 2500–5000 km. Sentman [1989] continued the study of these waves. According to Sentman observations, in the south of the United States the Q bursts occur every few minutes. He also found that the frequencies of the wave trains in the N-S and W-E magnetic components can be strongly different (by 1.4–1.8 Hz).

[17] The records of the inductive magnetometer at the high-latitude observatory Lovozero indicate the Q burst occurrence rate of one per hour. It is interesting to study the horizontal electric components of this signal. A typical example is shown in Figure 9. In the top plot the magnetic H and electric Y component are given for the event of 13 January 2005 at 1624:53 UT, and in the bottom plot the magnetic D and electric X component are shown. As in the previous comparisons, the Y component of electric field corresponds to the magnetic H component, and the X conforms to the D component. From Figure 9 it is also seen that in the event considered, the electric Y component passes ahead of the magnetic H component a bit.

Figure 9.

Q burst on 13 January 2005 at 1624:53 UT (top) in the magnetic H component and electric W-E component and (bottom) in the magnetic D component and electric N-S component.

[18] Twenty-five Q bursts have been selected to investigate the time delay, 9 events for a summer day of 30 July 2004, and 16 events for winter days of 18 December 2004 and 13 January 2005. The magnetic H component of a burst is compared with the electric Y component, while the magnetic D with electric Y. The comparison is performed both visually and by cross correlation. An appreciable discrepancy in the times of arrivals of peaks in the electric and magnetic components is nearly always observed. Almost in all cases, the electric Y component passes ahead of the magnetic H by one to three step intervals or 25–75 ms, and the magnetic D component lags behind the electric X.

[19] It is impossible to explain the lagging of Q burst electric and magnetic components by difference in amplitude-frequency responses of the devices. They are nearly equal for all four channels.

[20] In Figure 10, the variations of polarization vector for several first oscillations in the wave train illustrated in Figure 9 are shown for the (top) magnetic and (bottom) electric vectors of the train. It is seen that the polarization of both vectors is nearly linear, with the gyration being clockwise, as is nearly always the case for SR signal in Lovozero. In Figure 9, both the electric and magnetic vectors are shown in geographic coordinates. As is seen, the horizontal components of the magnetic and electric vectors of the Q burst are not orthogonal.

Figure 10.

(top) Magnetic and (bottom) electric polarization vectors for the beginning of the Q burst in Figure 9.

6. Theory

[21] As we mentioned in the introduction, all simulation models of SR fields assume the Earth's surface to be a perfect conductor. Such an abstraction is not unreasonable. The conductivity at the top (ionospheric) boundary of the resonator is equal to10−4–10−2 S/m, while the conductivity of the seawater is about 4 S/m, i.e., several orders of magnitude higher. Therefore, in the global consideration of the phenomenon or in the analysis of measurements taken near the ocean, this assumption is consistent.

[22] However, it may not be correct for some localities. Let us estimate the thickness of the skin layer

equation image

where μ is magnetic permeability, closed to μ0 = 4π × 10−7 H/m outside magnetic materials. For the angular frequency ω = 50 rad/s and conductivity σ = 10−2 S/m the skin depth is equal to 1800 m. In the Kola Peninsula, the thickness of sedimentary rocks, which conductivity may be close to the specified value, is equal to several tens of meters at most. The conductivity of basement rocks is much lower. The ratio of the penetration depth δ to the wavelength λ is given by

equation image

where ɛ0 = 10−9/36π and ɛrel is the relative permittivity. This ratio is equal to 7 × 10−5 under ɛrel = 5, thus this thin conducting upper layer does not influence the ELF wave propagation. The value of the relative permittivity for the basement rocks is about 5–10. Thus we will study the field configuration of ELF wave near a layer of low conductivity as a more appropriate model for the Kola Peninsula.

[23] To investigate the fields in the cavity between the Earth and the ionosphere we have considered the wave equations. A direct application of the Wentzel-Kramers-Brillouin approximation is invalid for our problem because of partial reflection of ELF waves, and we have to perform a complete wave analysis. Starting from the Maxwell equations and by eliminating Ez and Bz components of the fields, it can be shown [Budden, 1985] that the system of equations for the transverse field components is

equation image

where e = [Ex, Ey, Hx, Hy]τ, k = equation image, ω is the angular frequency of propagating wave, c the light velocity, kx the component of the wave vector k along the x axis. The matrix T is given by

equation image

where Mxy are the components of the susceptibility matrix for the ionosphere, nx = equation image. We consider the wave in the form e = e(z) · exp(−iωt + ikxx).

[24] For the above system of equations we formulate the following boundary conditions. At the lower boundary we impose the impedance conditions

equation image

where ς = (1 − i)equation image, σ is the Earth's conductivity, ns is unit vector of normal. At the upper boundary (above the ionospheric D and E regions), the downward propagation is ruled out, that is, at this height we neglect any reflection from upper layers. The problem is solved numerically by orthogonalizing technique to avoid numerical instabilities.

[25] All six field components are calculated. In Figure 11a, the ratio of horizontal electric component Ehor to the total one Etotal at the ground is shown as a function of conductivity of the medium, which has been varied from 10−9 to 10−5 S/m, for two values of relative dielectric permittivity of 5 and 80. One can see that for conductivity decreasing from 10−6 S/m to lower values, an appreciable horizontal electric component appears. It reaches 30% of the total field (which is quite a measurable value) for the conductivity of ∼10−8 S/m for ɛ = 5. The ratio of the vertical magnetic component Hver to the total field Htotal is given in Figure 11b under the same values of parameters. It is seen that the vertical magnetic component emerges too, but it is twice smaller than the horizontal electric component. In the issue, the vertical component of Poynting vector indicates the presence of energy flux toward the ground.

Figure 11.

(a) Ratio of the horizontal electric component to the total field in the case of a poorly conducting surface. (b) Same for the vertical magnetic component. (c) Real and imaginary parts of the refractive index depending on the conductivity.

[26] This result is consistent with the behavior of the complex refractive index for the ELF wave in this range of conductivity, which is shown in Figure 11c under the same permittivity values. For small conductivity, the imaginary part decreases and dissipative losses diminish.

7. Discussion

[27] The measurements of horizontal electric component of ELF in Lovozero demonstrate that it is as informative as the horizontal magnetic one, considering signal-to-noise ratio. The daily variations in the frequency, amplitude and width of the first SR suggest that the variation of the horizontal W-E (Y) electric component is similar to that of the N-S (H) magnetic component, and the N-S electric component behaves as the W-E magnetic one. This feature is not obvious on account of a priori postulated orthogonality of total electric and magnetic vectors of the wave. In case of strictly horizontal Poynting vector, the components of the same direction should be similar; that is, the X(H) component of electric vector should have a similarity to the X(H) component of the magnetic field. Electric and magnetic vectors rotate around the Poynting vector. The presence of a vertical component of the Poynting vector means geometrically an occurrence of a horizontal electric component. If the magnetic vector were horizontal, within the assumption of perfectly conductive Earth, the horizontal electric component would be strictly perpendicular to the horizontal magnetic vector. This is not quite consistent with the observations. As it is seen from Figure 10 for the Q burst, the electric and magnetic vectors are not quite perpendicular. This feature indicates a presence of a small vertical magnetic component, which is reproduced in our calculations (see Figure 11b). The Poynting vector bends down and rotates.

[28] The presence of amplitude diurnal variations in all components is most likely associated with a diurnal variation in the activity of thunderstorm centers. Sentman and Fraser [1991] revealed that the intensity of SR is determined essentially by the local time because of D layer height variations associated with solar illumination. The dependence of the main parameters of SR on solar terminator passing is clearly shown by Melnikov et al. [2004]. However, in the period of polar summer (from 9 July to 5 August), that we have chosen, the ionosphere over Lovozero is sunlit all the time, and in the winter period it is illuminated only for a short time near the local noon of about 0950 UT. Yet, the positions of maxima in the magnetic D and electric Y components at about 1000 and 2200 UT do not change with season, so we may relate them, without any correction for local illumination conditions, to the Southeast Asian and South American maxima of thunderstorm activity, respectively.

[29] The 1400 UT maximum in the magnetic D and electric X component refers to the African maximum. This is in agreement both with seasonal activity—during South African winter the amplitude peak of the D component is small (see Figure 5)—and with the polarization the thunderstorm activity center near South Africa is located at Lovozero longitude; that is, the effect of lightnings from there should be pronounced just in the D component. For this reason, the Asian and American lightnings contribute to the magnetic H component in Lovozero. The positions of maxima in the horizontal electric components are caused by obliquity of the vertical electric field in the plane of wave direction, as mentioned above.

[30] The connection of the 1400 UT maximum in the magnetic D component with the African thunderstorm activity, and of 0900 and 2100 UT maxima in the H component with Asian and American ones has been ascertained in Germany for one November day by Füllekrug [1995] and in Israel from observations for 4 years by Price and Melnikov [2004]. It should be mentioned, however, that the latter authors also observed it in summer, when it is absent in Lovozero. Maybe this difference can be related to poor statistics of our material. We note that Price and Melnikov present in their figures the diurnal variations of power, while we show them for the amplitude, which leads to smoothing out the ratio of maxima.

[31] The big seasonal variations of the amplitude of the W-E and N-S components arose probably not because of physical but because of equipment reasons: In winter time the effective antenna length decreases because of the enlargement of the ground resistance. The diurnal variations in the first SR width for the magnetic components presented here strongly differ, both in shape and in amplitude, from the obtained by Price and Melnikov [2004] curves for Q factor determined as Q = fmax/2Δf. A similar feature is only the presence of two Δf maxima (Q factor minima) at 0600 and 1900 UT in the H component in summer period. In Israel these two minima are also observed in winter. In the D component there is no correspondence in either seasons. The discrepancy may result both from geography and from different manners of approximation by Lorentzian. As distinctly seen from equation (1), Price and Melnikov do not account for the noise constituent of the spectrum.

8. Conclusions

[32] The horizontal component of electric vector of the first SR in Lovozero is intensive enough to be used in studies of SR instead of or along with the horizontal magnetic vector. The diurnal variations of the frequency, amplitude and width of SR (as well as the development of Q burst) in the N-S electric component are similar to those in the D component of the magnetic vector. The W-E component of the electric field resembles the H component of the magnetic vector. This means that the Poynting vector is nonhorizontal.

[33] The frequencies and widths of the electric components are somewhat different from the corresponding magnetic ones. The parameters of electric components, as well as of magnetic ones, have seasonal dependence, both in the shape of daily variations and in their amplitude. The measured values of horizontal electric field indicate that the bottom boundary of the Schumann resonator is most likely a poor conductive layer instead of a perfectly conductive surface.


[34] This work is dedicated in memory of Yuri Maltsev. The work was partly supported by the Presidium of the Russian Academy of Sciences through basic research program 16, part 3, “Solar activity and physical processes in the Sun-Earth system.”