Case 1 - 8 April 2010
Figure 2 shows the dynamic spectra of H and D components of the magnetic field variations, polarization angle, coherence between different stations, and cross-correlation of Pc1 amplitude envelopes (red lines in Figure 3), for a clear Pc1 geomagnetic pulsation event observed simultaneously at ATH, MGD, and MOS at 10:00 to 12:00 UT on 8 April 2010. We chose the cross-correlation between the ATH H component and the MGD D component, since they show the highest correlation between ATH and MGD. During this event, geomagnetic activity was slightly elevated (K
p
= 1 to 2), with AE indices of approximately 300 to 500 nT. The local time at ATH was 00:00 to 02:00 LT, and the local time at MGD and MOS was 06:00 to 08:00 LT. In Figure 2a,b,c,d,e,f, Pc1 pulsations can be clearly identified at the three stations in the frequency range of 0.4 to 1.2 Hz. The intensity of PSD at MOS is weaker than at the other two stations, probably because of attenuation due to ionospheric duct propagation to lower latitudes (Kawamura et al. [1981]). We can see that the Pc1 pulsations are observed during three separated time intervals: 10:12 to 10:33, 10:41 to 10:53, and 10:55 to 11:49 UT at all stations. At ATH, the first and second Pc1 bursts can be clearly seen in Figure 2a,b, but the third Pc1 burst is much weaker than the others. On the other hand, Pc1 pulsations are clearly identifiable at MGD and MOS for all three intervals.
The polarization angle at ATH, MGD, and MOS is shown in Figure 2g,h,i. For ATH (Figure 2g), it increased from approximately −50° (dark blue) to −20° (light blue) for 0.6 to 1 Hz. At MGD (Figure 2h), the polarization angle varies from approximately −90° (black) to −50° (dark blue) in the same frequency range as ATH. The frequency dependence at MOS (Figure 2i) shows a decrease of the polarization angle from approximately 30° (green) to −50° (dark blue). According to Nomura et al. ([2011]), this polarization angle dependence on frequency indicates that the Pc1 pulsation observed at the three stations at 10:00 to 12:00 UT has a spatially distributed ionospheric source at high latitudes.
In order to distinguish whether the Pc1 pulsations propagated from the same ionospheric source, we show the coherence of Pc1 waveforms between each pair of stations in Figure 2j,k,l. High coherence of Pc1 waveforms was observed between two stations, indicating that the Pc1 pulsations observed at the three different stations were propagated from the same origin in the ionosphere.
Figure 3a,b shows the waveforms of the H and D components of Pc1 pulsations at ATH, MGD, and MOS on 8 April 2010 at 10:24 to 10:26 and 10:43 to 10:45 UT, respectively. In order to remove noise from other frequencies, we show the time series of Pc1 pulsations obtained using a band-pass filter in the frequency range of 0.5 to 1.2 Hz. The amplitude modulation of the pulsations varies with a repetition period of approximately 10 s in both time intervals. The time difference between ATH and MGD (MGD and MOS) is approximately 4 s (0 s) and was confirmed by lag correlation studies (see below). The repetition periods of pearl structure changes in time during this event at all stations, and the ones observed at ATH, MGD, and MOS are generally similar but differ in their details.
Figure 4 shows the PSD of the H and D components of magnetic field variations at ATH and MGD, respectively, on 8 April 2010 and the coherence of Pc1 waveforms between these two components at 10:24:00 to 10:26:08 (Figure 4a,b,c) and 10:43:00 to 10:45:08 UT (Figure 4c,d,e) with a resolution of 0.0078 Hz. The time intervals of Figure 4a,b,c,d,e correspond to those shown in Figure 3a,b. In Figure 4a,b and Figure 4d,e, we can see a continuous high-PSD band at frequencies of 0.6 to 1.0 and 0.7 to 1.0 Hz, respectively. The coherence between the H component at ATH and the D component at MGD is close to one in the latter frequency range.
We investigated the cross-correlation between the H component at ATH and the D component at MGD using the upper envelope of Pc1 pearl structures in the time domain. We used only these components because they have the highest PSD intensity compared with the other components and the background intensity. Figure 5a,b shows the cross-correlation between the H component at ATH and D component at MGD obtained for the upper envelope of the Pc1 pearl structure at 10:24:00 to 10:26:08 and 10:43:00 to 10:45:08 UT, respectively, on 8 April 2010. In Figure 5a, we can see that the correlation is greater than 0.5 with a time difference of approximately 3 s. On the other hand, in Figure 5b, the cross-correlation between ATH and MGD is close to 0.9, indicating that the upper envelope of the Pc1 pearl structures is generally similar, with a time difference of approximately 3 s. In Figure 2m, the cross-correlation between the H component at ATH and the D component at MGD is greater than 0.5 throughout this event. Especially, for the second of the Pc1 bursts, the coherence and correlation are both extremely high (r > 0.8). For the first and third Pc1 burst time intervals, however, the correlation decreases to 0.5, even if the coherence of the Pc1 waveforms is clearly close to one.
Case 2 - 11 April 2010
Figure 6 shows the dynamic spectra of the H and D components of magnetic field variations, polarization angle, coherence between different stations, and cross-correlation of Pc1 amplitude envelopes (red lines in Figure 7) between the ATH H component and the MGD D component, for a clear Pc1 geomagnetic pulsation event observed simultaneously at ATH, MGD, and MOS at 11:00 to 13:00 UT on 11 April 2010. Geomagnetic activity was relatively high during this event, with K
p
= 3 to 4. The average AE index during the 11:00 to 13:00 UT interval was approximately 104 nT. The local time at ATH was 01:00 to 03:00 LT, and 07:00 to 09:00 LT at MGD and MOS. In Figure 6a,b,c,d, Pc1 pulsations were clearly identified at ATH and MGD in the frequency range of 0.2 to 0.8 Hz. However, the Pc1 pulsations observed at MOS were much weaker than those seen at the other two stations (Figure 6e,f). At 11:30 to 12:20 UT at ATH, we can see three different frequency bands of Pc1 pulsations at 0.38 to 0.48, 0.5 to 0.6, and 0.61 to 0.73 Hz. At MGD, the two different frequency bands of Pc1 pulsations at 0.4 to 0.47 and 0.52 to 0.6 Hz can be seen in the D component of magnetic field variation (Figure 6d).
The polarization angles at ATH, MGD, and MOS are shown in Figures 6g-6i. From 0.3 Hz to 0.7 Hz, the polarization angle at ATH (Figure 6g) is almost constant, with values around 0° (light green). In Figure 6h, the polarization angle at MGD barely varies, and remains near −60° (dark blue) in the frequency range of 0.3 to 0.6 Hz. The frequency dependence at MOS, as seen in Figure 6i, is not clear because the intensity of the Pc1 pulsations is very weak. The constant polarization angle observed at ATH and MGD, independent of frequency, suggests that Pc1 pulsations have a localized ionospheric source at high latitudes (Nomura et al. [2011]).
In order to distinguish whether Pc1 pulsations propagated from the same ionospheric source, we show the coherence of Pc1 waveforms between the different stations in Figure 6j,k,l. The coherence between two stations is close to one for all frequencies, even if the Pc1 pulsation at MOS was weak for frequencies near 0.5 Hz. This indicates that the Pc1 pulsations observed at the three different stations propagated from the same origin.
Figure 7a,b shows the waveforms of the H and D components of Pc1 pulsations observed at ATH, MGD, and MOS on 11 April 2010 at 11:57 to 11:59 and 12:02 to 12:04 UT, respectively. We show the time series of Pc1 pulsations obtained using a band-pass filter from 0.3 to 0.7 Hz in order to remove noise from other frequencies. Even if the amplitude modulation of Pc1 pulsations at MOS was weak in both time intervals, we can clearly see Pc1 pearl structures in all three stations. The repetition periods of Pc1 pearl structures vary from 10 to 40 s. We also note that there is a time difference of a few seconds in the pearl structures between ATH and MGD. The Pc1 pearl structures observed at ATH and MGD are similar in the time series of magnetic field variation, even though these two stations are separated by a distance of approximately 4,000 km.
Figure 8 shows the PSD of the H and D component magnetic field variations at ATH and MGD, respectively, and the coherence between these two components at 11:57:00 to 11:59:08 (Figure 8a,b,c) and 12:02:00 to12:04:08 UT (Figure 8c,d,e) on 11 April 2010, with a frequency resolution of 0.0078 Hz. The time intervals in Figure 8a,b correspond to those shown in Figure 7a,b, respectively. In Figure 8a,b and Figure 8d,e, we can see a continuous high-PSD band at frequencies of 0.4 to 0.6 Hz in both time intervals. The coherence between the H component at ATH and the D component at MGD is close to one in the frequency range of 0.4 to 0.6 Hz.
Figure 9a,b shows the cross-correlation between the upper envelopes of ATH H and MGD D components of Pc1 pearl structure at 11:57:00 to 11:59:08 and 12:02:00 to 12:04:08 UT, respectively, on 11 April 2010, in the same format as Figure 5. In Figure 9a,b, we can see that the correlation is greater than 0.8 with a time difference of approximately 4 s during both time intervals. As shown in Figure 6m, we made this cross-correlation analysis of Pc1 envelopes for the whole time interval. The cross-correlation of Pc1 envelopes between the H component at ATH and the D component at MGD is greater than 0.8 throughout this Pc1 event, which also has high coherence (r > 0.8).