Physics of auroral phenomena : proceedings of the 36th Annual seminar, Apatity, 26 February – 01 March, 2013 / [ed. board: A. G. Yahnin, A. A. Mochalov]. - Апатиты : Издательство Кольского научного центра РАН, 2013. - 215 с. : ил., табл.

It is well known that the technique of wavelet transform is used in applications that require data compression with minimal losses. The advantage of this approach, in contrast to the Fourier transform that operates infinite harmonic functions provided primarily defined as a finite basis functions being selected for a specific numerical experiment. In addition, wavelet analysis allows to obtain the spectrum at a specific frequency range, which makes it possible to limit the search features of the original signal. Additional specification information by computing the wavelet skeleton spectra may be provided, reflecting the internal dynamics of the processes of various types and scales. In the present study as a basic wavelet in numerical experiments is selected Daubechies function of the fourth order. In discrete data equal to 1 minute scale wavelet transform coefficients addressed in two frequency bands, a high frequency with a maximum period of 300 seconds and a maximum in the low period 1500 sec. The resulting pattern o f the wavelet transformation is further processed to present the results of the calculation in the form of wavelet skeleton spectrum. The resulting matrix skeleton range o f each parameter of each event is a matrix with elements 0 and 1, where 1 corresponds to the local maximum (point on skeleton image) at a particular frequency at a particular time. Then, by plotting each point of skeleton exactly corresponds to one pixel in the image. This feature to further an objective comparison of the spectra of pairs of skeletons will be used. S.E. Revunov et al. ... 1 ■ 1 1 1 e 3 1 2.5 г 0 150 300 450 600 time, min Fig. 1 Example of a graph for wavelet skeleton spectrum for IMF Bz parameter calculated in the high scale with a maximum period of 300 seconds. Enlarged area shows how plotting the skeleton in which each point of skeleton exactly corresponds to one pixel of image 3. The algorithm of objective calculation of the synchronization flow parameters An important advantage of wavelet skeleton technique in tasks that require numerical assessment of the consistency of the spectra obtained is shown. To successfully assess the consistency of the spectral pattern should contain only the key features. This can be achieved by calculating the corresponding skeletons and comparing them. The conclusion that the consistency of any two sets of skeletons obtained for the same time interval is performed by calculating the normalized standard deviation of the registration of the local maxima for spectrum presented in the form of a matrix with elements 0 and 1. The normalized standard deviation using the formula is calculated: n i=i where n - total number of points that make all the skeletons of the first and second set, A and В - the matrix analyzed skeletons patterns, P - the total number of pixels (the number of elements of A or B) create the image for skeleton spectrum. Subtract the sum of the squares of the unit allows you to operate with an intuitive scale: closer to 1 - a high similarity, closer to 0 - highest difference a pair of skeleton spectra. Fig. 2 shows an example of calculation for the parameter pairs [Bz-V] and [N-V] shock registered 22.07.2004. с 5 < Bz E 3 2,5 r о a 0 J___ L A E=0,04 150 с 5 1 V I 2'5 . 150 300 450 1 с 5 1 V 1 1 11' i | ) | I | 2,5 | ...L, 1 o , , I !, I j 600 150 300 450 600 time, min 300 450 600 time, min с 5 I 1 2,5 I a 0 E=0,31 N 150 300 450 time, mm 600 time, min Fig. 2 Example of calculation of the normalized standard deviation for sets of pairs of skeletons corresponding parameters Bz, N, V for scale fluctuations with a period o f 300 seconds 127