The data were obtained with the ground magnetometer array of the Institute of Geological Sciences [Stuart, 1982]. On the day of the event shown in this study, the six stations along the British chain, Lerwick (LE), Durness (DU), Loch Laggan (LL), Eskdalemuir (ES), York (YO) and Hartland (HA), have magnetic field records available. Table 1 shows the locations of those stations, lying along approximately the same magnetic meridian. The sampling interval is 2.5 sec and the daytime sensitivities of those magnetometers range from 0.04-0.06 nT.
Broadband Pc 3 power was observed across the IGS array during the daytime on May 9, 1979. Figure 1 plots the power spectrum of the magnetic fields at DU and the cross-phase spectrum for the DU-LL pair during the time interval 0603-0624 UT. The H, D, and Z represent the directions of magnetically north, magnetically east, and downward, respectively. Also plotted in Figure 1 for comparison is the power spectrum of the H component for a time interval, 0002-0023 UT on the same day, where no discernible pulsation activity was present. Enhanced wave power was observed for the frequencies roughly between 30 and 90 mHz. The power spectra for the H and Z components are rather similar but different from that for the D component. The peaks in the power spectra for the H and D components can be identified at 40 and 70 mHz. Located 175 km south from DU, LL observed a very similar power spectrum (not shown). The bottom panel of Figure 1 shows the cross-phase spectrum for the DU-LL pair, , and it indicates that the phase differences are generally found in H and Z components, while in the D component the phase difference is insignificant and it cannot be used to identify eigenfrequencies. In this example, the phase difference in the Z component is the greatest for all the three components, and it even exceeds and appears as a negative phase difference at 55 mHz. The peaks in the cross-phase spectrum are located at 10, 25, 38, and 60 mHz, and they are quite different from the peaks in the power spectrum,
The same cross-phase spectrum is produced for other pairs of adjacent stations, namely LE-DU, LL-ES, ES-YO, and YO-HA. Figure 2 shows the frequencies where the phase difference maximizes, i.e., the eigenfrequencies of the magnetospheric field lines, as a function of latitude. Only the results for the H component are shown, and the results for the Z components are very similar. In the figure the latitude for the field line resonances is taken to be at the center of the station pair. The curves in the Figure represent the best fit of the observed eigenfrequencies by theoretical estimation. The formulae behind the curves assume a simple dipole magnetic field model and a plasma density function that follows , where r is the radial distance to the Earth. The exact computation follows the algorithm given by Schulz . The fit in Figure 2 also implies that and the proton density at the equator of L = 4 (assuming that all ions are .
The cross-phase spectrum can also be applied to the pairs of nonadjacent stations to further compare the theory with our observations. Figure 3 shows the results for the pairs DU-LL, DU-ES, DU-YO, and DU-HA. The north-south separation of stations ranges from 175 km (DU-LL) to 800 km (DU-HA). Again only the results for the H components are presented. All the four pairs indicate local maxima of phase differences at roughly 9, 18, and 36 mHz. The phase difference for these frequencies is general larger when the separation between the two stations of concern is greater. At 18 mHz, the phase difference for the DU-LL pair is approximately , and the phase differences expand as the distance between the pair of stations increases.