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Criterion for Event Selection

For the purpose of studying pulsations, a criterion for selecting pulsation events from the entire data set is needed. When continuous pulsations are observed on the ground, they usually have a clear enhancement at a particular frequency. An enhancement in the spectrum can be identified by comparing the wave power in the neighboring frequency bands, but before this comparison is made, the ``trend'' in the spectrum should be removed. The trend can be represented by the six median values shown in Figure 2, except for the sixth (highest) frequency band because of its strong noise component. Figure 4 shows the details of the Q-Q plot for $\log(P_6)$, where the wave component and the noise component are fitted linearly. The median of P6 is located in the noise component, and it would have been a smaller value if the noise component were absent. If we assume that the wave component has a linear structure in the Q-Q plot, the median of the wave power data can be estimated by the small square in Figure 4. In the following, this estimation is used as the median wave power for the sixth frequency band.

Figure 4. Q-Q plot of log P6. The two straight lines are the linear fits of the ``wave'' component and the ``noise'' component. Small square shows the estimation of the median of wave power if noise is absent.

If $\bar{P_{i}}$ is the median power of the ith frequency band, the ``detrended'' wave power is defined as
\begin{displaymath}
p_{i} \equiv \log P_{i} - \log \bar{P_{i}} \;\;\;\;\;\; i = 1, \ldots , 6.\end{displaymath} (1)
A pulsation event in the ith frequency band is identified if the following condition is satisfied:
\begin{displaymath}
p_{i} \leq p_{i \pm 1} \;\;\;\;\;\; i = 2,3,4,5.\end{displaymath} (2)
This means that the local maxima in the detrended power spectrum are taken as pulsation events. By using the above criterion, we may avoid including some strong wave power which is, in fact, the leakage from wave activity in neighboring frequency bands. However, we need to sacrifice the analysis for the lowest frequency (2-4 mHz) and the highest frequency band (64-128 mHz). Nevertheless, the four middle frequency bands (4-64 mHz) still cover most frequencies of interest for the dayside continuous pulsations.

The strong noise component in P6 can certainly affect the selection of the P5 events. According to (1), we expect that $\{p_i\}$ generally have an equal number of positive values and negative values. However, it can be visualized in Figure 4 that almost all the p6 values are positive due to the different way choosing the median wave power for P6. This will exclude many P5 events unless they are very strong. Notice that although the selection of events is based on the wave power data, it is expected that selecting wave events at high frequencies from time series data is also difficult since the instrument noise becomes a significant portion of wave power. The number of events for each frequency band is listed in Table 2, where it is shown that the number of P5 events is significantly smaller than those of other frequency bands.


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