Astron. Astrophys. 357, 337-350 (2000)

3. Data sets and analysis procedure

The data sets are single frequency recordings from the multichannel radio-polarimeter of the Trieste Astronomical Observatory, which is operating in the dm-m wavelength range. The investigated data sets are recorded at the frequencies 237, 327, 408 and 610 MHz, with a sampling rate of 50 Hz, i.e. a temporal resolution  ms. We analyzed 30 data sets of type I storms and 27 sets of type IV events, which cover samples with different kind of fine structures, such as pulsations, fast pulsations, sudden reductions and spikes. Some of the events were analyzed at different times and/or frequencies. Therefore, the 30 data sets of type I storms represent 24 different events, the 27 data sets of type IV events 20 different ones. In Table 1 and Table 2 we give a description of the type I and type IV events, respectively. The main criteria for the data selection from the solar radio burst data archive of the Trieste Observatory were:

Table 1. Summary of the analyzed type I storms. The first set of columns gives a description of the events, including the date and start time in UT, the available number of data points, the recording frequency in MHz, and the predominant polarization sense (L for Left, R for Right handed circular polarization). Each event was recorded with a temporal resolution of 20 ms. In the second set of columns, for each event the longest stationary subsection (given in number of points) is listed. The third set contains the results of the pointwise dimension analysis. We list the mutual information  in points, the averaged pointwise dimension  with standard deviation , the percentage of points passing the scaling and convergence test ("ok"), the increase of the averaged pointwise dimension with increasing embedding dimension in percent, , and the outcome of the surrogate data test (pos(itive) means that the null hypothesis can be rejected and nonlinearity is detected).

Table 2. Summary of the analyzed type IV events. The same quantities as in Table 1 are listed. Additionally, if particular fine structures are present in an event, the predominant type of fine structure is listed (pulsations, fast pulsations, sudden reductions, and spikes).

1. The selected data sets were representative for the particular types of events.

2. To ensure a high signal-to-noise ratio only intense events were selected.

3. The related time series were substantially long and fulfilled Eq. 13.

For the analysis, the predominant polarization sense, LCP (Left-handed Circular Polarization) or RCP (Right-handed Circular Polarization) of the burst series was used.

The first step in the correlation dimension analysis was to search for stationary subsections by shifting windows with decreasing length through the time series and applying the stationarity test proposed by Isliker & Kurths (1993). Only those stationary subsections which still fulfilled the minimum length criterion of Eq. 13 were accepted for further analysis, and the correlation dimension was calculated only from such subsections. The analysis was repeated with different values for the delay parameter, located around the first minimum of the mutual information. The relevant quantities were calculated up to embedding dimension . Finally, the algorithm for automatically searching the scaling region, checking its validity and testing the convergence behavior was applied. The convergence was checked for m-intervals containing four successive embedding dimensions, starting with .

The pointwise dimension analysis was basically carried out in the same manner, except that the overall time series was used instead of stationary subsections. Moreover, only for points which passed both scaling and convergence test a local pointwise dimension was accepted. Finally, the pointwise dimension analysis was repeated for 10 different sets of surrogate data to test against the null hypothesis that the results are caused by linearly correlated noise, and to get evidence on nonlinearity in the data.

© European Southern Observatory (ESO) 2000

Online publication: May 3, 2000
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