A method for identification of structures of a complex signal and noise suppression based on nonlinear approximating schemes is proposed. When we do not know the probability distribution of a signal, the problem of identifying its structures can be solved by constructing adaptive approximating schemes in an orthonormal basis. The mapping is constructed by applying threshold functions, the parameters of which for noisy data are estimated to minimize the risk. In the absence of a priori information about the useful signal and the presence of a high noise level, the use of the optimal threshold is ineffective. The paper introduces an adaptive threshold, which is assessed on the basis of the posterior risk. Application of the method to natural data has confirmed its effectiveness.

We present and describe an automated method for analysis of magnetic data and the detection of geomagnetic disturbances based on wavelet transformation. The parameters of the computational algorithms allow us to estimate the characteristics of non-uniformly scaled peculiar properties in the variations of the geomagnetic field that arise during periods of increasing geomagnetic activity. The analysis of geomagnetic data on the eve and during periods of magnetic storms was carried out on the basis of the method according to the network of ground stations. Periods of increasing geomagnetic activity are highlighted which precede and accompany magnetic storms. The dynamic of variation of the geomagnetic field in the auroral zone is considered in detail.

We present and describe an automated method for analysis of magnetic data and for detection of geomagnetic disturbances based on wavelet transformation. The parameters of the computational algorithms allow us to estimate the characteristics of non-uniformly scaled peculiar properties in the variations of geomagnetic field that arise during increasing geomagnetic activity. The analysis of geomagnetic data before and during magnetic storms was carried out on the basis of the method according to ground station network. Periods of increasing geomagnetic activity, which precede and accompany magnetic storms, are highlighted. The dynamic of geomagnetic field variation in the auroral zone is considered in detail.

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A detailed spatio-temporal analysis of magnetic data was performed during the periods of magnetic storms on October 02, 2013 and September 27, 2019 based on measurements of the station network. In this work, we used a method developed by us for the analysis of magnetic data, based on the use of wavelet transform and adaptive thresholds. The method allows us to identify short-period field disturbances and estimate their intensity from the data of the H-component of the geomagnetic field. The features of the occurrence and propagation of geomagnetic disturbances in the auroral zone and at meridionally located stations have been studied. Dynamic spectra of disturbances of different intensity and duration are obtained. The paper confirms the possibility of occurrence of short-period weak geomagnetic disturbances at stations from high latitudes to the equator, preceding magnetic storms and correlating with fluctuations of the southern Bz-component of the interplanetary magnetic field and increases in the auroral indices of geomagnetic activity. Cross-correlation dependences of the intensity of geomagnetic disturbances on the parameters of the interplanetary medium during magnetic storms were obtained from the data of the network of magnetic stations. A statistically significant influence of the magnitude of the scope of the Bz-component of the IMF and the speed of the solar wind on the development of magnetic storms during the initial and main phases of magnetic storms was revealed.