Variations of the first mode Schumann resonance frequency in the Kola Peninsula and of the first and second mode frequencies in Kamchatka during seven days of March–April 2001, when the intensive solar X-ray bursts occurred, are studied with 5 min averaging. All X-ray bursts were accompanied by ∼0.2 Hz increase in the first mode frequency, at least in one of the magnetic components. Duration of the increases coincided with that of the bursts. For the second mode the increase (in average by ∼0.3 Hz) was registered in most events, when the ELF noise level was not very high.
 One of the first experimental studies of the Schumann resonance (SR) revealed variation of the SR frequency [Balser and Wagner, 1962]. The reasons of the frequency variability can be thunderstorm dynamics (source position and size) and/or variation in the electric conductivity of the ionosphere. The ionospheric conductivity variations are related to variations in the electron density at altitudes of the D and E regions. Large-scale perturbations of the electric density can be produced, in particular, by variations of the solar X-ray radiation.
Sao et al.  compared the first mode frequency at Tottory observatory (35° latitude) and 1–8 Å solar X-ray intensity during the December 1971–February 1972 period, when the solar activity was sufficiently high. A good similarity between day-to-day variations of both parameters was found. Price and Mushtak  observed emission in 1–50 Hz during the extremely intense γ-ray flare at 27 August 1998, but they did not find any noticeable changes in the amplitude and frequency of SR signals.
 Strong enhancement of the solar X-ray radiation lasting less than 1 hour is called a burst. The solar bursts cause sudden ionospheric disturbances (SID) accompanied by fluctuations in the SR frequency [Cannon and Rycroft, 1982].
 The solar X-ray bursts are usually followed by solar proton events (SPE). Schlegel and Füllekrug  examined changes of the daily averaged first SR frequency at Arrival Heights, Antarctica, for nine strong SPEs and found that the frequency increased by about 0.04–0.14 Hz for the SPE days. The authors related this increase with proton precipitation and not with X-ray bursts.
 The X-ray activity and SPEs are commonly observed in time of maximum of solar cycle. Kulak et al.  examined the changes of the characteristic frequencies of the first resonance during the minimum and maximum of the solar cycle 23, based of the measurements held in the East Carpatian mountains, and found that the frequency grew up clearly during the active phase of solar cycle.
 Variations in the first mode SR frequency during SPEs were studied by Roldugin et al. [1999, 2001, 2003] who compared the SR frequency averaged over 5 min with the 5 min data on the proton fluxes and X-ray intensity measured onboard the GOES satellite. The first mode SR frequency appeared to decrease by about 0.2–0.4 Hz during the main phase of the energetic proton precipitation lasting for several hours. It was noted that the SR frequency increases during X-ray bursts preceding the solar protons by 0.5–1 hour. In this paper we examine variation of the resonance frequencies for several X-ray events of 2001.
2. Lovozero Data
 According to GOES-10 data the solar X-ray activity was high since the end of March through April 2001. We have chosen 7 days when the X-ray bursts were intense: 29 March, 2 April, 6 April, 9 April, 10 April, 12 April, and 15 April.
 The ELF measurements at the Russian observatories of Lovozero (Kola peninsula, geographic coordinates φ = 68.0°, λ = 35.1°) and Karimshino (Kamchatka peninsula, φ = 52.9°, λ = 158.25°) are used. The specification of a two-component inductive magnetometer in Lovozero is given in the work of Roldugin et al. .
Figure 1 shows the variations of the first mode resonance frequencies in H and D components in Lovozero during 2 April 2001. The solid lines give the frequencies, the dotted lines display the X-ray intensity in logarithmic scale, and the dashed lines give the smoothed diurnal variations, averaged for several days when X-ray bursts are absent. According to GOES-10 data, at 2150 UT the X-ray intensity in spectral window of 0.05–0.4 nm reaches 5 × 10−4 W/m2, and in the 0.1–0.8 nm spectral window it culminates to 2 × 10−3 W/m2, i.e., to very high values. Typical undisturbed intensities in these windows are 10−8 W/m2 and 10−6 W/m2, respectively. A frequency increase of about 0.2 Hz is clearly seen in both components. This effect coincides exactly with the X-ray burst duration and ceases after its attenuation. Note that the time resolution for the frequency and for the X-ray intensity is equal to 5 min.
 Other two bursts with maximums at 1010 and 1130 UT are seen in the same figure, they are more than 10 times weaker than the main one. Apparently, both of them are accompanied by the frequency increase. The effect is more distinctive in H than in D component.
 It is also seen that the variation in the D component matches well the undisturbed diurnal curve, whereas the H component variation differs noticeably from its diurnal one. There are some spikes in either component, which are not associated with X-ray bursts. They are most likely caused by noise disturbances of the ELF signal and by smallness of time interval for spectrum calculation.
 In Figure 2 the variations of SR frequency in H and D components and of the X-ray intensity are shown for other 6 days with the solar burst events. We have removed a diurnal variation from the frequency data. The diurnal course for each component is found here as an approximation of the average of these six daily curves by two first harmonics. One burst per day only occurred for these events. The corresponding frequency scales are the same for all six panels, but the X-ray intensity scales are different. It is seen that in H component all the X-ray bursts with no exception are accompanied by an increase of the first mode Schumann resonance frequency. In D component the correspondence takes place also with one exception for the 12 April event. As to the 2 April event, the complete temporal coincidence of both phenomena is observed. The frequency increase is equal to the same 0.2 Hz. No amplitude proportionality between frequency change and burst intensity is observed: the most intensive burst with the amplitude of 4 × 10−4 W/m2 occurring on 15 April enhances the frequency in D component by 0.1 Hz only, whereas the weakest one with 2 × 10−5 W/m2 intensity on 9 April results into the enhancement by 0.25 Hz. The X-ray rigidity (the ratio of X-ray intensities in 0.05–0.4 and 0.1–0.8 nm spectral intervals) is slightly lower in this case than for the 15 April burst.
3. Karimshino Data
 The ELF observations are also carried out in Karimshino observatory in Kamchatka. The data for the same dates were processed with one exception of the 2 April event, when very strong noise disturbances occurred. The processing technique was the same: approximation of 5 min spectra by a Lorentzian with four free parameters. In contrast to Lovozero, in Karimshino the sampling frequency is equal to 200 Hz, but in this investigation we use data with 50 Hz sampling frequency. Furthermore, the two horizontal magnetic coils in Karimshino are supplemented by a vertical one.
Figure 3 shows variations of the first mode SR frequency in H, D and Z components in Karimshino for the same 6 days as in Figure 2. The diurnal variations are eliminated, as earlier, by subtraction of the two-harmonic approximation of the curve averaged for six events. The vertical lines show peak moments of the X-ray bursts. The influence of the X-ray bursts is also visible here in most cases. Oppositely to Lovozero, the frequency increase effect in Karimshino is seen better in D than in H component. However, in Z component the increase is more pronounced than in the horizontal components; it is seen well in all six events and is equal to 0.2 Hz as before. Besides, the diurnal frequency variation in Z component is utterly similar to that one in H component, but it is shifted towards higher frequencies by 0.1 Hz.
 The amplitude proportionality between frequency changes and X-ray intensity is absent in Karimshino as in Lovozero. Again, a prominent effect is observed on 9 April for the weakest burst, and the most intensive X-ray emission on 15 April is accompanied by small frequency increase. The local time shift between the stations is 8 hours. Both bursts occurred nearly at the same time: 1530 and 1400 UT. So we conclude that the local position of the Sun is not responsible for this lack of correspondence between the frequency and X-ray intensity changes.
 The second mode SR frequency also have been analyzed with the Karimshino ELF data for these 6 days. The signal-to-noise merit for the second mode is proved to be less than for the first one, so that sometimes gaps happen because of disturbances. In H component the frequency mean value is equal to 14.4 Hz. The effect is seen in the 9 and 15 April events, and its value is equal to about 0.3 Hz. In D component it occurs in the 29 March, 6, 10, and 15 April events, with the frequency increase being of 0.3–0.4 Hz. The mean frequency is equal to 14.0 Hz, that is noticeably less than for the H component. The frequency increase is seen in Z component best of all, see Figure 4, because this component is less noisy in comparison with the horizontal ones. As in the first mode, the diurnal variations in the Z and H components look rather similar, with the mean frequencies being the same and equal to 14.4 Hz. The frequency increase of about 0.3 Hz is seen in all six cases but the 6 April event. The increase is not so obvious as in the first mode though.
4. SR Amplitude and Width Variations
 In addition to frequency, the amplitude and half-width of the SR band have been calculated for all considered events as well. Both parameters are compared with the solar X-ray bursts. Neither in Lovozero nor in Karimshino any appreciable effect is found in any components and modes. As an example, Figure 5 shows the amplitude variations of H component in Lovozero for the six events. There is a resemblance in shape and value between all the curves, and no burst is accompanied by growth or decrease in amplitude. Similar to this plot, the variations of the SR half-width do not display any changes during the X-ray bursts. The mean half-width value is equal to 1 Hz, its noise level is about of 0.1 Hz, so potential changes of the SR half-width must be less than 5%.
5. Comparison With Theory
Greifinger and Greifinger  proposed the first theoretical model for determining ELF eigenvalues. In this model the ionospheric conductivity profile is assigned as exponential, and in the issue the eigenvalues are determined by two specific altitudes where maximal ohmic dissipation occurs. Sentman  improved this idea by consideration of spherical geometry and two scale-height of ionospheric conductivity. He found that in this model the Joule dissipation of SR energy is confined to two layers at 70–80 km and 40–50 km, where the horizontal and vertical component of the electric field prevails respectively. This formalism was further developed by Mushtak and Williams , who validated the two-scale-height “knee” conductivity profile from physical viewpoint, what permitted them to simulate the dissipation altitude dynamics within the lower layer as a function of ELF frequency. Their model predicts satisfactorily not only modal frequencies but the quality factors and phase velocities as well.
Roldugin et al.  calculated the eigenfrequencies in a simple model of a horizontally homogeneous resonator consisting of two layers: (1) the vacuum layer located between the perfectly conducting Earth and the altitude a, and (2) the upper layer with the electric conductivity exponentially growing with height. The following expression for the resonance frequency was obtained
where c is the light velocity, n is an integer, RE is the Earth radius, ωo2 and νe2 are the plasma and collision frequencies at the height z = a, h is the scale height of the conductivity, γ ≈ 0.577 is the Euler constant.
 The expression (1) was linearized in the vicinities of some typical parameters. As a result the following expressions were obtained for the two first modes (for n = 1 and n = 2):
where the frequency f = ω/2π is expressed in Hz, the electron density N2 = N(a) in cm−3, the altitude a and scale height h in km. To estimate the effect of solar flares to SR frequency we use the results of Rowe et al.  who measured the electron density profiles before and during the solar flare of 21 October 1968 accompanying a strong X-ray enhancement (about a factor of 50 below 8 Å). It was found that the density was enhanced several times at altitudes from 60 to 85 km, with the strongest enhancement (ten times) occurring at 70 km. According to expression (2), the tenfold increase of the electron number density N2 causes the first mode SR frequency increase by ∼0.32 Hz. Since the half of the Earth is sunlit only, the real increase is about twice smaller, i.e., ∼0.16 Hz, which is in agreement with our results. Comparison of expressions (3) and (2) shows that the variation in the second mode frequency exceeds that one in the first mode 1.5–2 times that is also in agreement with the observations.
 The presented results allow us to make conclusion that X-ray bursts cause, as a rule, an increase of the first and second mode SR frequencies. The frequency increase is equal to ∼0.2 Hz for the first mode and 0.3–0.4 Hz for the second one, and its duration coincides with the time interval of the X-ray burst. The increase occurs in both H and D components. Sometimes no increase is observed in one of the components. Occasionally, the second mode frequency reveals no effect in both components. Impossibility to detect the frequency increase seems to be explained by large errors arising when the frequency is determined from 5 min intervals. At Karimshino station the noise level for the second mode frequency is noticeably larger than for the first one, and the lack of the increase effect comes about more frequently for the second mode. For both modes the noise level is lower in the records provided by the vertical magnetic coil in comparison with the horizontal ones, so the increase effect is manifested in Z component more evidently.
 Interesting to note, the amplitude of the signal in Z component is 1.5–2 times less in H and D components only. In the case of a perfect Earth conductivity, the Z component should be absent. It turned out that the diurnal variation of the frequency in the Z component is in line with the H component frequency variation and not with that of the D component. Maybe the reason of the phenomenon is due to geographic location of Karimshino near the seashore line, stretched along the meridian, on account of different conductivity of seawater and of rocks or in peculiarities of geological texture of the region.
 All the nine solar X-ray events examined here occurred at different times and both in dark and light periods of a day at both stations, but no dependence of the effect on local time is found. It should be expected from the global character of the Schumann resonance.
 There are some reports about dependence of the SR frequencies on geophysical activity. Sao et al.  revealed a positive correlation of the frequency variations not only with the solar X-ray intensity but with geomagnetic Ap index as well. We suppose that it would be more fruitful to investigate relationship of the SR frequencies to the ionospheric conductivity height profiles but not to the magnetic indices. The changes of ionosphere conductivity are manifested ambiguously in indices for different types of geophysical disturbances. The results of the frequency analysis with 5 min resolution, given here and in [Roldugin et al., 1999, 2001, 2003], yield somewhat unexpected result: during a solar X-ray burst the SR frequency increases, however after the following energetic proton precipitation it decreases.
 Both agents (proton-precipitation and X-ray) produce an additional ionization in the ionosphere, but in different altitudes: the X-rays do it above of 60–70 km, see Rowe et al.  and Mitra , and protons ionize also the heights below, as low as 40 km [e.g., Mitra, 1974, chapter 11]. Two dissipative layers of Sentman  are situated at altitudes of additional ionization caused by these two sources. The author says that “…modification of the upper dissipation layer… may yield a different system response than a similar modification of the lower dissipation layer.” Indeed, accordingly to his expression (42), growth of energy dissipation in the lower, radial dissipation layer, must give rise to the frequency decrease, and growth of dissipation in the upper, transverse dissipation layer, causes the frequency increase.
 Our formulas (2) and (3) show not only the frequency increase induced by the electron density raising. They reveal also the frequency decrease with lowering of a, altitude of the bottom layer of the ionosphere.
 We can explain this effect also in physical terms: the ionization enhancement in the lower part of D region gives rise to the growth of refractive exponent for an ELF wave that leads to reduction of its velocity, and as a result, to the resonance frequency decrease. The ionization increase in the upper region raises reflection coefficient of a wave, and the wave energy is displaced to lower layers where the velocity is larger that yields the frequency increase.
 The variations of the SR frequencies in two stations Lovozero and Karimshino, spaced several thousand kilometers from each other, were compared with the solar X-ray intensity for seven days when strong X-ray bursts have been observed. For all the cases of the burst observations the frequency of the first SR mode increases by ∼0.2 Hz. Duration of both increases is the same within the 5 min sampling accuracy. The increase is observed in both horizontal components and in the vertical magnetic component in Karimshino. The frequency increase of about 0.3 Hz is also seen in the second SR mode in Karimshino in most cases.
 The effect is in contrast to the decrease of the SR frequency during the solar proton events, although both kinds of precipitation produce an additional ionization in D-region. The distinction in the SR frequency reaction to SPE and X-ray burst can be explained by different responses of the Earth-ionosphere resonator to modification of two dissipation layers, which were considered in some theoretical works. Only energetic solar protons may reach the lower layer, localized within 40–50 km, and the conductivity increase in it stimulates the frequency decrease. The ionization rise in the upper layer at 70–80 km causes the frequency increase. In case of the X-ray bursts the conductivity enhancement takes place in the upper layer only, and the SR frequency increases.
 Arthur Richmond thanks Colin Price and another reviewer for their assistance in evaluating this paper.