3.2. Events of 29 October TID
 We observed three TID events over North America during the period of 29–30 October. The first two LSTIDs occurred consecutively between 0620 and 0800 UT on 29 October during the local time of midnight, shortly after the onset of the big substorm. The third one started at 1850 UT at noon on 30 October and lasted for about 1 hour. The occurring time for the TIDs is basically concurrent with the time when the two shocks arrived at the Earth.
 Figure 4 presents the sequence of two-dimensional maps of TEC perturbations during the period of 0620–0800 UT on 29 October. Clear band-like structures are seen. A negative TEC perturbation band appeared at 0620 UT in the northeast area of the United States, and a positive band appeared at the same time to the south of the negative region. A phase front can be clearly seen, which was the border between the negative region and the positive region. Twenty minutes later, another phase front formed, which was characterized by the north border of the negative band in the northeast area of the United States at 0640 UT. The phase fronts passed over the United States and traveled southwestward to the distance of ∼2000 km, with the duration of 1 hour and 40 min and the front width of ∼4000 km. The perturbation structures gradually disappeared in the maps after 0800 UT. We plot the change of phase fronts in Figure 5. It can be seen from Figure 5 that the two phase fronts traveled to different orientations, denoting the change of propagating direction for these TID structures.
Figure 4. Time sequence of two-dimensional maps of TEC perturbations over North America during the period from 0620 to 0740 UT on 29 October 2003.
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Figure 5. The change of two main phase fronts deduced from two-dimensional maps of Figure 4. The phase front was characterized as the border between the negative perturbation region and positive perturbation region. Two kinds of phase front were found, which was distinguished by solid and broken lines. The time at which the front emerged was marked nearby.
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 The amplitudes of TEC perturbations have a maximum of 2 TECU (1 TECU = 1016 eletrons/m2). Nicolls et al.  applied mapping technique to the same data set to study TEC perturbations over US during the geomagnetic storm of 1–2 October 2002 and found a TID propagating at 600 m/s with the maximum amplitude of 2 TECU. The amplitude of the TID reported by Nicolls et al.  is similar to ours. Tsugawa et al.  statistically analyzed the TEC perturbations caused by LSTIDs over Japan and found that the amplitudes were in the range of 1.3 ± 0.7 TECU, which is in agreement with our results.
 Figure 6 shows the temporal dependence of TEC perturbations at certain fixed observation points. We set the observation points along the latitude of 40°N and along the meridian of 90°W, respectively. It shows the TEC perturbation series at different observation points are similar in shape and shifted with time. On the basis of these perturbation series, we plotted in Figure 7 the time at which the maxima and minima of the amplitudes appeared. It can be seen that the time delays between the amplitude minimum and the second amplitude maximum nearly remain constant, while the time delays between the first amplitude maximum and the amplitude minimum change obviously. Thus the two kinds of fronts in Figure 5 differ not only in moving direction but also in moving velocity. This indicates that there are two consecutive LSTID events rather than one LSTID event.
Figure 6. Temporal dependence of the amplitudes of TIDs at certain fixed observation points from 0620 to 0800 UT on 29 October. The observation points were set along the latitude of 40°N (the plots on the left) and along the meridian of 90°W (the plots on the right).
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Figure 7. Plots of the time at which the maxima and minima of TIDs' amplitudes appeared in TEC perturbation series. The TEC perturbation series had been plotted in Figure 6. The asterisks and triangles represent the emerging time for the maximum of TIDs' amplitudes. The dots show the emerging time for the amplitudes' minima.
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 The calculations based on equation (6) and (7) reveal that the first TID propagated with the azimuth of 217° and the horizontal phase velocity of 270 m/s, and the second TID propagated with the azimuth of 191° at 500 m/s. The period of the two consecutive TIDs, though it cannot be precisely determined, is close to 1.2 hour, as calculated by doubling the peak-to-trough time intervals shown in Figure 7. As shown in Figure 7, only one or two perturbation peaks can be found during 0620–0800 UT. Hence our observation does not include a whole cycle of the perturbations for both the first and the second TIDs. Similar observation of LSTIDs through TEC mapping technique was conducted by Tsugawa et al. , who also found two consecutive LSTIDs over Japan with the duration of 2 hours and phase velocities of more than 500 m/s during the 23 September 1999 storm. The period of the LSTIDs in the work of Tsugawa et al.  cannot be precisely measured, either. Afraimovich et al. [2000b] believed that the LSTIDs detected by GPS arrays are more likely to correspond to solitary waves than to periodic processes. This was also reported by Hunsucker .
 Long-distance traveling of slow-speed TID over North America was also reported by Afraimovich et al. [2000a], who studied the TIDs over North America and Russia through applying cross-spectral analysis to GPS TEC array data and found TIDs propagating equatorward to the distance of ∼3000 km, with mean velocity of 300 m/s. The north edge of the detected region for both studies of Afraimovich et al. [2000a] and ours is at the geomagnetic latitudes of 61°N. This location is very close to the auroral oval where there exists possible auroral source, especially at the local time of midnight. The observation of slow velocity TID near this region is consistent with the simulation results of transfer function for the excitation of gravity waves [Mayr et al., 1990], which indicate that relatively small-scale TID is likely to be found near the source.
3.3. Event of 30 October TID
 The third TID event was observed to start at 1850 UT (i.e., 1250 LT) on 30 October, as shown in Figure 8. This TID occurred during the expansion phase of the auroral substorm, which occurred 2 hours after the second IMF shock arrived at the Earth. The phase front of the third TID moved more quickly than the first two. The TID propagated from northeast to southwest of America to the distance of ∼3000 km during 1850 and 2000 UT with the front width of ∼1500 km. The horizontal phase velocity, period, and propagation azimuth were measured to be 738 m/s, 1.1 hours, and 224°.
Figure 8. Time sequence of two-dimensional maps of TEC perturbations over North America during the period from 1850 to 1950 UT on 30 October 2003.
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 The maximum of the perturbation amplitudes of the third LSTID attained 3 TECU. The amplitude was obviously larger than those of the first two TIDs. It was also larger than the amplitude of TID obtained by Nicolls et al. . We noticed that both the TID observed by Nicolls et al.  and the first two TIDs in our study occurred during the local time of midnight, while the third TID event in our study was observed at local noon. It seemed that the maximum amplitudes of these TIDs were roughly proportional to the background TEC, since the background TEC was larger at noon during the passage of the third TID and its maximum amplitude was larger than those of the first two.
 Afraimovich and Voeykov  and Afraimovich et al.  first investigated the LSTIDs during the geomagnetic storm on 30 October 2003 through longitudinal chains of GPS receivers. They filtered out the TEC time series with a running time window of 60 min. By comparing the detrended TEC time series observed by GPS receiver chains, they found a solitary LSTID propagated southwestward to the distance of 4500 km over US during 1930–2015 UT on 30 October 2003. The LSTID caused TEC perturbations with the relative amplitude of up to 40% and the absolute amplitude of 5–14 TECU. Using the SADM-GPS method [Afraimovich et al., 1998], they found the LSTID propagated at the phase velocity of 1400 m/s. Afraimovich and Voeykov  estimated the location of the source of the disturbance and found it was between 50°N and 60°N in the northeast region of the United States.
 It is thought that during auroral substorms, auroral sources such as Joule heating, Lorentz forces or intense particle precipitations [Hunsucker, 1982] generated atmospheric gravity waves, which in turn cause LSTIDs at middle and high latitudes. Both the third LSTID in our study and the solitary LSTID in the work of Afraimovich and Voeykov  were found during the expansion phase of the substorm. The substorm occurred with the onset at about 1830 UT on 30 October after the second shock arrived at the Earth. It is possible that during the substorm, the auroral source generated a variety of gravity waves with different velocities, frequencies, and amplitudes. The gravity waves propagated equatorward and subsequently caused a variety of LSTIDs. As different processing method is sensitive to LSTIDs with different amplitudes and velocities, it is reasonable to suggest that both the third LSTID in our study and the solitary LSTID in the work of Afraimovich and Voeykov  were excited almost simultaneously and were observed by Afraimovich and Voeykov  and us, respectively. Sun et al.  and L. F. Sun et al. (manuscript in preparation, 2007) built the three-dimensional transfer function model to study the excitation of gravity waves and their propagation at ionospheric height. Their study revealed that the source in the form of a unit impulse could excite a series of harmonic gravity waves with a certain frequency range rather than one monochromatic wave.
3.4. Discussion of TIDs' Source Region
 All the three TIDs were observed during the auroral substorms at the geomagnetic latitudes of 41°N–61°N. This strongly implies the TIDs are closely related to auroral sources.
 We used the magnetic field data to investigate the possible source region of LSTIDs over North America. The magnetic field data used here were from 12 geomagnetic observatories located in North America, which belongs to Geological Survey of Canada. The geomagnetic data are available on the Web site http://www.intermagnet.org. We also chose one European observatory and one Asian observatory. The locations and codes of all the fourteen geomagnetic observatories were plotted in Figure 9. Also plotted in Figure 9 were the locations of 6 GPS arrays, each of which consists of three GPS receivers, whose data will be used later in next section to study the propagation of TIDs through cross-spectral analysis.
Figure 9. Geodetic locations of geomagnetic observatories (triangles) and locations of the GPS arrays (asterisks) in North America, Europe, and Asia. The code name for each geomagnetic observatory and GPS receiver is marked on the map.
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 Figure 10 presents the temporal variation of magnetic field H component observed by all the 14 geomagnetic observatories during 0500–1000 UT on 29 October (Figure 10a) and during 1800–2200 UT on 30 October (Figure 10b). After the onset of the substorm at 0612 UT on 29 October, the values of magnetic field H component at YKC, FCC, IQA, PBQ, GDH, and NAQ began decreasing during 0612–0620 UT. The decreases of H component values at these observatories exceeded −2000 nT. Four of these observatories, namely YKC, IQA, GDH, and NAQ, are located between the geographic latitude of 60°N and 70°N. The other two, namely FCC (59°N, 94°W) and PBQ (55°N, 78°W), are more close to the north edge of the region where TIDs were observed (50°N). The geomagnetic latitudes of these stations are roughly calculated as the geographic latitudes plus 11 degrees. The variations of H component values at the observatories between the latitudes of 45°N–50°N (namely NEW, OTT, and STJ) are not noticeable. This denotes the south edge of auroral oval at the local time of midnight is between 50°N and 60°N (i.e., between the geomagnetic latitudes of 61°N and 71°N) in North America.
Figure 10. Time dependence of the magnetic H component during 0500–1000 UT on 29 October (Figure 10a) and during 1800–2200 UT on 30 October (Figure 10b) at the geomagnetic observatories. The code name of each geomagnetic observatory was marked nearby.
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 The first TID, which propagated at 270 m/s, was observed about 10 min after the decrease of H component at YKC, FCC, IQA, PBQ, GDH, and NAQ. As the north edge of the region where TID was observed was 50°N, the source region for this slow-velocity TID should be located within 200 km to the north of 50°N (i.e., the geomagnetic latitudes of 61°N). There are two geomagnetic observatories (MEA and PBQ) between 55°N and 50°N. However, the decrease of H component was not obvious at MEA. Thus the source region may lie to the south of PBQ. The region near PBQ is in the northeast of North America. This is consistent with the southwestward propagating direction of the first TID.
 In order to get more information of the location of source region, we estimated the elevation of the gravity waves corresponding to the observed TIDs through
The elevation of a gravity wave refers to the angle between the wave vector and the local horizon, kz and kh are the vertical and horizontal wave number of the gravity wave, ωa and ωb are the Brunt-Väsälä frequency and sound cutoff frequency, respectively, and c is the sound speed. The dispersion equation of gravity waves is used in equation (8) [Ding et al., 2003]. Here, ω is the intrinsic frequency of the gravity waves, which is related to the observed frequency ω′ by
where is the gravity wave vector and is the thermospheric wind vector. The thermospheric wind always exceeds 100 m/s, as calculated by HWM93 wind model. thermospheric wind speed to the direction of thermospheric wind speed to the direction of is in the range of ±100 m/s. We use this unreal wind speed value to estimate the biases that may arise when we include wind in calculating the elevation of gravity waves.
 The elevations for the atmospheric gravity waves corresponding to the first two TIDs are 76° ± 5° and 70° ± 4°, respectively. As the observation height of GPS TEC is about 350 km, the source region may locate below 300 km height to the distance of a few hundred kilometers north of 50°N. The source region for the second TID are likely to locate between 50°N and 55°N (i.e., the geomagnetic latitudes of 61°N–66°N) near the observatory of PBQ (55°N, 78°W).
 Moreover, the second TID was related to the second decrease of H component at PBQ at 0640 UT. The magnetic H component decreased twice between 0600 and 08:00 UT on 29 October at PBQ with the first decrease at 0612 UT and the second one at 0640 UT. The decrease at 0640 UT was much weaker in other observatories. The phase front of the second TID moved at the velocity of 500 m/s after 0640 UT on 29 October, as shown in Figure 4. If the TID had been caused by the decrease of H component at 0612 UT, it should have taken 28 min for the TID to propagate to the distance of ∼800 km from the source region to 50°N. However, this propagation distance does not agree with the elevation angle of 70°, as mentioned above.
 It is most likely that the westward electrojet, which is always detected near the auroral oval at midnight-dawn sector, is the cause for the TIDs observed on 29 October. We checked the variation of magnetic field X and Y component at the observatory of PBQ and found the significant decrease of H component during 0612–0700 UT was mainly caused by the decrease of X component. As magnetic field X component is northward in Canada, the decrease of the X component indicates the enhancement of westward electric current. This subsequently excited atmospheric gravity waves (AGWs) and LSTIDs through the enhancements of Lorentz force (J × B) or Joule heating (J × E) [Hunsucker, 1982].
 The change of the first and the second TIDs' propagation direction during 0620–0800 UT on 29 October may indicate the movement of auroral source region along auroral oval. Tsugawa et al.  also reported two consecutive TIDs over Japan during the storm of 22 September 1999. However, as the longitudinal range is limited in the work of Tsugawa et al. , and Japan is far away from auroral region, the difference of the azimuths for two TIDs is not as obvious as those shown in Figure 5. Hajkowicz [1991, 1990] suggested “the AGW source is neither a point nor a line but circular or oval… It is generated in the wake of an auroral surge moving with supersonic velocities along the ovals [Hajkowicz, 1991, 1990; Hocke and Schlegel, 1996].” However, in this stage, we have no direct evidence to demonstrate the movement of the source region.
 The third TID was observed at 1850 on 30 October during the expansion phase of the substorm which occurred with the onset at about 1830 UT. The elevation for the atmospheric gravity wave corresponding to the third TID was 60° ± 10°. Because the TID was observed at local noon, the variation of magnetic H component seems not as obvious as that of 29 October. However, we could still find the decrease of H component to the extent of −1000 nT at around 1840 at the observatories of BLC (64°N,96°W), FCC (59°N, 94°W), PBQ (55°N, 78°W), and NAQ (61°N, 45°W). Because of the high elevation angle of the third TID, the source region is within several hundred kilometers north of 50°N in North America.
 The source of the third TID remains unknown. Shiokawa et al.  suggested that the electrodynamic instability in the ionosphere could cause southwestward medium-scale TID. However, there is still no evidence to show that electrodynamic instability can cause large-scale TID. Huang et al.  suggested the midlatitude ionospheric disturbances could be caused by the penetration of magnetic electric fields that were controlled or modulated by the oscillations in the IMF or solar wind pressure. However, quasiperiodic turning of IMF z component was not found during 1850–2000 on 30 October, as shown in Figure 3, and the temporal variation of magnetic H component appeared to be steady during that time at the observatories between 30°N and 50°N.