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 Quasiperiodic (QP) diffraction pattern in scintillation patches has been known to highly correlate with the edge structures of a plasma bubble (Franke et al., 1984). A new time-frequency analysis method of Hilbert-Huang transform (HHT) has been applied to analyze the scintillation data taken at Ascension Island to understand the characteristics of corresponding ionosphere irregularities. The HHT method enables us to extract the quasiperiodic diffraction signals embedded inside the scintillation data and to obtain the characteristics of such diffraction signals. The cross correlation of the two sets of diffraction signals received by two stations at each end of Ascension Island indicates that the density irregularity pattern that causes the diffraction pattern should have an eastward drift velocity of ∼130 m/s. The HHT analysis of the instantaneous frequency in the QP diffraction patterns also reveals some frequency shifts in their peak frequencies. For the QP diffraction pattern caused by the leading edge of the large density gradient at the east wall of a structured bubble, an ascending note in the peak frequency is observed, and for the trailing edge a descending note is observed. The linear change in the transient of the peak frequency in the QP diffraction pattern is consistent with the theory and the simulation result of Franke et al. Estimate of the slope in the transient frequency provides us the information that allows us to identify the locations of plasma walls, and the east-west scale of the irregularity can be estimated. In our case we obtain about 24 km in the east-west scale. Furthermore, the height location of density irregularities that cause the diffraction pattern is estimated to be between 310 and 330 km, that is, around the F peak during observation.
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 Quasiperiodic (QP) diffraction pattern in the scintillation patches have been observed and discussed by a number of researchers since 1965 [Turnbull and Forsyth, 1965; Ireland and Preddey, 1967; Kelleher and Martin, 1975; Heron, 1979; Davies and Whitehead, 1977; Hajkowicz et al., 1981]. Franke et al.  performed a model simulation based on the diffraction theory of Titheridge  with a specially structured boundary. They showed a good interpretation of the quasiperiodic diffraction pattern observed in an equatorial VHF scintillation from plasma bubbles. They have shown that the pattern occurs most often at the beginning or the end of a scintillation patch that are associated with the structured walls (edges) of the plasma bubbles. The pattern is consistent with irregularities having east-west scale sizes of a few hundred meters. By adjusting the parameters in their modeling procedure, they have shown that by matching the modeled QP with the observation, it is possible to estimate some irregularity parameters, such as location, the scale size and the drift velocity of the irregularity.
 In this paper, we applied a newly developed time-frequency analysis technique, the Hilbert-Huang transform (HHT) to study the QP pattern embedded in the scintillation signal. The new technique allows us to extract relevant information about the irregularities causing the scintillation directly from the data without relying on any modeling efforts. Hilbert-Huang transform (HHT) developed by Huang et al.  allows the nonlinear and the nonstationary data to be decomposed into a finite number of “intrinsic mode functions” (IMFs) via empirical mode decomposition (EMD) method. Instantaneous oscillation frequency can be achieved by applying Hilbert transform to each IMF component. Unlike the traditional analysis by fast Fourier transform (FFT) or wavelet transform (WT), HHT does not need a priori frequency bases; it adopts a posterior basis (the IMFs) that comes from the input data itself and are adjusted automatically according to the nonstationary and nonlinear features of the input data. The resulting HHT spectrum has the advantage that it eliminates the need for spurious harmonics to represent nonstationary and nonlinear signals, no additional assumptions on the bases need to be introduced and therefore can represent the spectrum faithfully [Huang et al., 1998].
 Scintillation data often show nonstationary characteristics in its fluctuation pattern. Therefore HHT is very suitable for analyzing such data. The data we studied in this paper are the VHF (244 MHz) scintillation data taken at Ascension Island (7°58′S, 14°25′W, 39°S DIP) from a geostationary satellite FLEETSAT (23 W), recorded by two receiving antenna separated 216 m from each other in a east-west baseline. Studying the scintillation data on 25 March 2000, we noticed certain regular oscillation pattern in a period of a few seconds that appeared before midnight. The ion data taken by ROCSAT-1 at 600 km altitude also show a strong bubble occurred above Ascension Island half an hour early. Although the ROCSAT-1 data do not comprise a coincident observation over the Ascension Island, they implied that plasma bubbles could have occurred somewhere around the area over Ascension Island. In the following, we will first use EMD to separate the quasiperiodic diffraction patterns from the scintillation data. Instantaneous frequencies are computed to construct the time-frequency spectrum. Correlation studies are carried out for the IMF components derived from data recorded at the two receivers. Results of these studies are used to estimate several parameters for the irregularities associated with the bubble.
2. Analysis of Ascension Island Scintillation Patches
 A segment of scintillation data on 25 March 2000 is plotted in Figure 1 where the quasiperiodic (QP) diffraction patterns are identified. The upper panel shows the VHF data recorded in channel 1 (the west antenna), and the middle one in channel 2 (the east antenna, located 216 m magnetic east of the west antenna). L band data are plotted in Figure 1c where a strong signal appears around the time tic 19 min and around 21.5 min (after 2210:34 UT). An abrupt stop of scintillation is then noticed in the L band data just before 20 min time mark that is close to the diffraction center indicated by a solid arrow. After the L band scintillation signal stops at time mark 20 min, a QP diffraction pattern (boxed by the solid lines) occurs in the VHF band just after an intensive scintillation patch. Later, another QP diffraction pattern (framed by the dotted box) occurs, which is followed by an intensive scintillation patch located around 23 min time mark.
Franke et al.  has considered a special scintillation effect of highly structured walls in a plasma bubble. They pointed out that if a diffraction pattern is caused by the west or the trailing edge of a plasma bubble, the periodic fluctuations at VHF/UHF frequencies will occur on the western side of the diffraction pattern such that a QP pattern appears first and is followed by an intensive scintillation patch. This is exactly seen in the scintillation data boxed by the dotted lines in Figure 1, then the intensive scintillation patch occurred later around time 23 min. Figure 2 is the expansion of the data boxed in Figure 1 by the dotted lines. An obvious quasiperiodic diffraction pattern occurs around time label between 21.8 and 22 min, and a random fluctuation appears after 22.5 min. This can be recognized as an indication of the west wall (the tail) of a plasma bubble that has appeared over Ascension Island. On the other hand, a diffraction pattern symmetric to Figure 2 is boxed in Figure 1 by the solid line indicating that the quasiperiodic diffraction patterns that occur at the end of intense scintillation patch can be recognized as an east wall of the plasma bubble. When plasma bubble moves eastward at night, the QP pattern corresponding to the east wall of a plasma bubble will be observed earlier than the west one. It is interesting to note that the IPEI data do indicate a strong bubble observed around 2155:00 UT, half an hour before the scintillation diffraction patterns are recorded on Ascension Island. This plasma bubble is observed at the west side of Ascension Island. Therefore it is very likely that plasma bubbles could have occurred around Ascension Island at the time of scintillation.
 Using the EMD method the embedded QP diffraction pattern can be separated from the data. Figures 3a and 3b show the decomposed VHF data in channel 1 and 2, respectively. The QP diffraction pattern between time mark 21.83 and 22.17 min is reconstructed by summing the IMF component C2 and C3 for channel 1 and C2 to C4 for channel 2. Adding one additional component C4 in channel 2 is to ensure the optimal correlation between channel 1 and 2. The diffraction patterns from channel 1 for the west station (solid line) and channel 2 for the east station (dotted line) are plotted in Figure 4 for comparison. The patterns resemble each other but a time shift led by channel 1, the west one, is noted. To find the relation between the two patterns, a cross-correlation analysis is performed in which the east one is shifted step by step with respect to the west one. The correlation function shows that the maxima time lag occurs at a left shift of 81 data points which is equivalent to a time lag of 1.62 s for the data sampled at 50 Hz. The diffraction patterns moves with an eastward apparent velocity of about 133 m/s that is very close to the expected horizontal plasma drift velocity at night. This eastward drift is also consistent with the ROCSAT-1 measurement of the background velocity.
 Meanwhile, the residual lower-frequency portions are reconstructed by summing the IMF components from C4 to C8 for data in channel 1, and from C5 to C8 for data in channel 2. The results are plotted in Figure 5. Figure 5 shows the reconstructed low-frequency wave between time mark 21.5 and 22.5 min for the west station (solid line) and the east station (dotted line). Between these two highly correlated patterns, the east one shows a time delay of 83 data points with respect to the west one. This is equivalent to a time lag of 1.66 s. The low-frequency fluctuation patterns moves with an eastward apparent velocity of about 130 m/s. The drift velocity of the diffraction pattern matches very well with that of low-frequency fluctuation pattern. This may imply that there are subkilometer plasma structures associated with walls of plasma bubble over Ascension Island to cause both the QP diffraction and low-frequency scintillation.
 To study the features in the diffraction pattern further, two HHT marginal spectra are plotted in Figure 6, representing the scintillation data in the west station and the east one respectively. There are two spectral peaks that appear at 0.1 and 2 Hz as seen in Figure 6. The high-frequency peak is the dominant frequency of diffraction pattern and the lower one corresponds to the larger fluctuation in the 1.3 km scale. Through the HHT instantaneous frequency analysis, some interesting features of QP diffraction pattern are also revealed in the time-frequency domain. Figure 7 shows the HHT instantaneous spectrum for the scintillation data at the west stations. The frequency around 2 Hz that descends linearly to 1 Hz during the period between time label 21.8 and 22.1 min, corresponds exactly to the time period of the diffraction pattern occurring at the beginning of a scintillation patch as shown in Figure 2. According to Franke et al. , the QP diffraction patterns are caused by the highly structured edge of a plasma bubble. Their results indicate that a diffraction pattern occurs at the beginning of a scintillation patch is associated with a structured wall on the west side of a plasma bubble, the trailing side of the bubble; and the diffraction pattern occurring at the end is associated with the structured wall on the east side. To see what happens on the eastern side of the bubble, we pick up the diffraction pattern that occurs at the end of a scintillation patch between time label 20 and 21 min as shown in Figure 8. The corresponding HHT instantaneous spectrum is shown in Figure 9, where the high-frequency components between 1 Hz and 0.4 Hz show a trend of linear ascent while the low-frequency portion around 0.1 Hz, is stationary.
 Comparing Figure 9 (the east wall case) with Figure 7 (the west wall case), the HHT instantaneous spectrum shows the detailed frequency transients of QP diffraction. A very complicated frequency transient on the east wall (Figure 9) may be related to the fact that the east wall is steeper and more structured than the west one. Furthermore, the diffraction patterns on the different side of the plasma bubble indicate an opposite trend in frequency transient. To interpret this, we refer again to Franke et al. . For a well-developed QP diffraction pattern, an increasing fading frequency appears as the distance increases from the center of the pattern [Titheridge, 1971; Franke et al., 1984]. If Δx is the distance between two adjacent maxima in the QP diffraction pattern and x is the distance from the center of the pattern, then the behavior of QP is described by the following equation:
where λ is wavelength (m) and h is the height location of the irregularity structures above the ground. In the case of the pattern that moves with a velocity Vo and Δτ is the time between successive maxima and τ is the time measured from the center of the patterns, then [Franke et al., 1984]
The term on the right hand side is a constant. Equation (2) can be rewritten as
where τc is the center of the QP pattern, and f = 1/Δτ is the instantaneous fading frequency.
 This explains why the HHT instantaneous spectrum shows that the QP diffraction frequency varies with time in a linear trend. The slope of the linear variation of the time-frequency spectrum is obtained by least squares fitting of the spectrum between time mark 21.8 and 22 min, the period during which QP occurred. In the fitting, points in the time-frequency spectrum with spectral power lower than one percent of the maximum were discarded. For the case in Figure 7, where the QP pattern is caused by the structured west wall of a plasma bubble, the least squares fitting on the time-frequency distribution between 21.8 and 22 min gives f = −2.5t + 56.86, where f is in Hz and t is in minutes. From equation (3) we find τc, the center of the QP pattern, occurs at 22.7 min time mark. It means that the center is located at the east side of the QP diffraction pattern. The constant in (3) can then be found to be τΔτ = 24 (sec)2. For λ = 1.23 m, and Vo = 130 m/s from the correlation analysis, equation (2) yields the height of irregularity to be 330 km. For the case in Figure 9 where the QP pattern is proposed to be caused by the structured east wall of a plasma bubble, the least squares fitting on the time-frequency distribution between 20 and 20.2 min gives f = 2.65t − 52.1 and the center of the QP pattern is found to be at 19.65 min. It means that the center locates at the west side of the QP diffraction pattern. The height of irregularity is then at 310 km. It seems that the plasma bubble should have appeared at height about 310∼330 km and its horizontal scale is about (22.7–19.65) * 60 sec * 130 m/s = 23.8 km.
 As can be seen from Figure 7, the linear fitting is quite straightforward for the case of the west wall. It became somewhat complicated for the case of the east wall (Figure 9). Apparently the structures corresponding to the east wall are more complicated, causing more complex frequency change behavior of the diffraction pattern. We have chosen for the linear fitting the period where the main trend of the frequency change is clearly increasing. Certainly, there are errors associated with our estimation. Indeed, if we have chosen instead the period from 20 to 20.3 min for our fitting, the estimated height will be 275 km.
 Quasiperiodic diffraction patterns in the scintillation data have been studied and are concluded as a result from the steep irregularity structure located very near the edges or walls of a plasma bubble. The in situ ROCSAT-1 measurement around 600 km indicate that plasma bubbles have happened in the west side of Ascension Island half hour early. Therefore it is very likely that plasma bubbles might occur at some altitude around the area over Ascension Island to cause the observed scintillation.
 We apply the HHT analysis to separate QP diffraction pattern (the high-frequency portion, about 1 Hz) from the ambient scintillation fluctuations (the low-frequency portion, about 0.1 Hz). The cross-correlation analysis from the data at the west and east stations show that both QP diffraction pattern and low-frequency ambient pattern move together with an eastward apparent drift velocity of about 130 m/s. Such eastward drift velocity of 150 ∼ 200 m/sec has been observed by ROCSAT-1 over Ascension at the time of scintillation experiment. Meanwhile, the occurrence of QP diffraction pattern that corresponds to the structured west and east wall of a plasma bubble is consistent with what is proposed by Franke et al. .
 The HHT instantaneous spectrum provides a detailed variation of the QP diffraction and shows a different frequency transient in the west and east edges of a plasma bubble. The very complicated frequency transient on the east wall may be correlated to the feature that the east wall is steeper than the west one. From the HHT analysis the linear frequency modulation of the QP diffraction pattern are revealed. A linear ascent in frequency occurs at the east side of a plasma bubble and a linear descent in frequency occurs at the west wall of a plasma bubble. It is consistent with what Franke et al.  proposed. For a well developed QP diffraction pattern, it will show an increasing fading frequency as the distance from the center of the pattern increases [Titheridge, 1971; Franke et al., 1984]. The center of the QP diffraction pattern estimated from the QP pattern for the east wall of a plasma bubble is located at its western side. For the QP pattern corresponds to the western wall of a plasma bubble, the center is found at the eastern side of the pattern. Therefore the horizontal scale of the plasma bubble is estimated to be about 24 km from the central position of the west wall to the east wall. We note also that the observed QP pattern in VHF band occurs just after an abrupt stop in the L band scintillation. This also confirms the simulation result of Franke et al. . The height of irregularity is estimated to be about 320 km to give some effect on the scintillation signal significantly. For further studies, the comparison between recorded scintillation and simulations making use of the ROCSAT-1 is expected to bring some interesting results, albeit not simultaneous, in situ measurements.
 Completion of this paper was supported in part by a contract from AFOSR project AOARD-03-4010 to the National Central University. K. Y. Chen is supported by NSC grant NSC 92-2111-M-008-027-AP5. The ROCSAT-1/IPEI data process is supported by NSC 91-NSPO(A)PDD-008-STP01. S. Basu was partially supported by AFOSR grant 2311AS.