Physics of auroral phenomena : proceedings of the 37th Annual seminar, Apatity, 25 - 28 February, 2014 / [ed. board: A. G. Yahnin, N. V. Semenova]. - Апатиты : Изд-во Кольского научного центра РАН, 2014. - 125 с. : ил., табл.

Application o f mathematical morphology to data o fground-based auroral observations 4. Comparison with traditional methods The same data set (4) has been analysed on periodicity by more known methods traditionally included in numerical libraries. Fig. 4 presents spectra obtained by three methods: i) windowed Fast Fourier Transformation (winFFT), ii) Maximum Entropy Method (MEM), and iii) MM method described in previous section. One can see that all three methods perfectly found the short period o f 16 points. The main difference of the methods is observed in separation of large period (80 points). The winFFT method gives a wide maximum in spectrum near correct period (80±20), but the data set is too short to locate the 5. Example of data analysis The methods decsribed above have been applied to analise data of optical observations of aurora by system MAIN [4]. Fig. 5-a presents a typical North-South keogram obtained by images observed by Guppy-C camera in Apatity with time resolution 1 frame per second. Angular resolution of this camera is ~0.14 degree per pixel. The aurora intensity is shown by grayscale. One can see auroral pulsation in different locations on zenith angle with different intervals between pulses. To obtain a statistic of the intervals we position by this method with good precision. The MEM method indicates that the maximum at 80-90 points exists, but position o f the maximum depends on number of degrees of freedom assumed in the method. Larger number of degrees o f freedom usually allows us to obtain better located steeper maximum (see dashed line in the panel ‘b ’), however it is known that this way sometimes can lead to artifacts. The MM method shows the best results: both main periods are perfectly located. Other peaks observed in the MM spectrum are also understandable: one can see at least first harmonic (~8 points) and subharmonic (~32 points) of the short period. entropy applied the MM formalism described above. Each line for given zenith angle in the keogram has been considered as numerical set like in described in previous section example, and the corresponded MM spectrum has been obtained. As a result we have the MM spectra as a function of zenith angle presented in Fig. 5-b by rainbow color coding. One can see that: i) there are two separated band of pilsations of periods 2-3 seconds and 8-9 seconds; ii) the shorter periods are more often observed at poleward boundary of the aurora region. Moximum Entropy Method Mat. Morphology Spectrum 40 60 period 0 20 40 60 80 100 0 20 40 50 period period , Figure 4. Extracting periodicity in the test set by different methods: a) windowed FFT, b) maximum method, c) mathematical morphology spectrum. 2011-10-31 Guppy-C camera keogram N 23:28 23:30 23:32 23:34 UT Figure 5. Application of the MM to aurora observations: a - N-S keogram of spectrum of pulsations as a function of zenith angle. Spectrum 5 1Q , 15 period, s pulsing multiplet arc; b - MM 44