Application Of The Hilbert-Huang Transform To The Data Analysis Of Transient Time Series In Space Physics

In the solar-terrestrial system,whether from the space or the ground,the observed data usually reflect some complex nonlinear dynamic processes in space physics,with the multi-scale and non-stationary temporal variation.So in order to understand the nonlinear characteristics of such non-stationary system,it is important to obtain the waveforms and vibration energy distribution of key parameters in time-frequency space,by an appropriate time-frequency analysis.In this article,we focus on the instantaneous disturbances and continuous time evo-lution of parameters in solar wind and geomagnetic field.The Hilbert-Huang Transform(HHT)is applied to analyze the typical non-stationary time series,such as Geomagnet-ically Induced Currents(GICs)and Alfvén fluctuations in solar wind.As an adaptive time-frequency analysis technology,HHT can be used to decompose the signals and obtain the instantaneous energy distribution in time-frequency domain.In recent years,HHT has been widely applied for the data analysis of nonlinear non-stationary time changes in various fields.In the research on GIC effect at middle-or low-latitudes,in view of the scarce and weak GIC monitoring data,we proposes a recognition method of GIC weak signals,which is based on the GIC data monitored in local power grids,the local geomagnetic field components and the solar wind energy input parameters.After the disturbance sig-nals are decomposed and reconstructed by HHT,the instantaneous energy distribution of GIC signals and the total energy during each time phase of geomagnetic storm are analyzed comprehensively,in order to identify the GIC responses to a magnetic storm.Then,the power spectrum and time-frequency energy spectrogram of ground-based data during a super magnetic storm are analyzed by different time-frequency technology,such as the Short-Time Fourier Transform(STFT),the Wavelet Transform(WT)and HHT.A pair of GIC geomagnetic amplitude index within dual-frequency band is con-structed by using horizontal components of geomagnetic field.The corresponding re-lationship between the index and absolute amplitude of GIC signals is further analyzed in terms of waveform and energy spectrogram.The results show that GIC signals observed in the local power grid at medium-or low-latitudes are very weak and can easily be concealed by other periodic signals or noises during the period of medium-strong geomagnetic storms.However,after proper processing,GIC signals can still be used to analyze the potential risks of GIC in space weather.For extreme events of space weather,there are concentrated energy distri-bution of GIC monitoring signals in two frequency bands,corresponding to the low-frequency band of geomagnetic horizontal component and the high-frequency band of geomagnetic difference signals,respectively.In addition,according to the analysis of above two aspects and previous relevant studies,several factors affecting GIC effect of local power grid are analyzed and summarized,including the spatial driving source of GIC,deep earth electrical structure and intrinsic factors of power grid system.The above results provide important reference for the statistical analysis of space weather events,the assessment of GIC potential risks of local power grid and the construction of GIC prediction model.Alfvén waves exist commonly plasma flow in solar wind,as a kind of MHD elec-tromagnetic wave,with observational characteristics that the fluctuations of plasma ve-locity and magnetic field are highly correlated and proportional.Therefore,based on the single-satellite observation,the Alfvén waves in solar wind can be identified through the Walen relation between plasma velocity and magnetic field in a De Hoffmann-Teller(HT)frame.In the observation of Alfvén waves in solar wind,the HT frame defined by the traditional method is determined based on the approximation of stabilization,in which the non-stationary temporal variation of plasma background structures in so-lar wind are neglected.Moreover,other factors are not taken into account,for exam-ple,the fluctuations or mixed interference of non-propagating magnetic structure in the observed data.Therefore,in view of the limitation and uncertainty of the traditional methods,we propose a new method based on the Ensemble Empirical Mode Decompo-sition(EEMD)technology for analyzing Alfvén fluctuations,which is compared with validated methods in two ways.In the Walen test based on a HT frame,the HT velocity is extracted directly from the EEMD residual of differences between plasma and Alfvén velocity.The test results are compared with two traditional methods:the minimum residual electric field anal-ysis(MVAE)method and the mean deviation method.In the modified Walen test,the Alfvén and plasma velocity fluctuations are decomposed and reconstructed by EEMD,which is compared with the velocity time difference method.After considering various Alfvénic parameters,the results indicate that the proposed EEMD method can signifi-cantly optimize the effect of Walen test in comparison with the traditional methods.By the EEMD method,we can not only obtain a time-varying HT frame adaptively,but also provide a flexible scheme to reconstruct the Alfvénic fluctuations.It is helpful to remove the high/low-frequency components irrelevant to Alfvénicity,being more suit-able for complex cases with non-stationary plasma background motions and magnetic field structures.Thus,we suggest that the EEMD method can be used as an effective approach to identify large-amplitude Alfvén waves in solar wind streams with single-satellite data.