вейвлетный анализ

Topic. Based on the assumption that short-term climatic variations are nonchaotic, and, therefore, the paradigm of the limited predictability of weather formulated by E.N. Lorenz is not applicable to these variations, a question is posed about the unlimited predictability of the short-term climatic variations.

The presented paper is an analytical review of the methods and examples of applications of the continuous and discrete wavelet transform in geophysical study. The possibility of the extension of application of the wavelet­based methods in geophysics is also considered.

A comparation of wavelets and empirical modes concepts is performed that represent the most perspective tools to study the structure of nonstationary multimode processes. Their advantages over the classical methods for time series analysis and restrictions of both approaches are discussed that needs to be known for correct interpretation of the obtained results. New possibilities in the study of signals structure at the presence of noise are illuctrated for digital single­channel experimental data of prospecting seismology.

The article discusses the method of analysis and automatic diagnostics of the characteristics of various components of complex signals on digital data on the basis of continuous wavelet transformation. The results of processing of experimental data are exposed. The article shows that the offered method of single­channel continuous wavelet transformation with the subsequent analysis of instantaneous transformation energy in a certain frequency band allows tracing a zone of the registered high­intensity waves of sound and superficial type in an automatic mode.

In the article we present an overview of a number of continuous wavelet transform­based techniques for analysis and diagnostic of oscillatory neuronal network activity of brain in experimentally obtained  electroencephalographic data. We describe a technique for automatic detection of characteristic patterns for paroxysmal activity (spike­wave discharges) in epileptic electroencephalogram (EEG) based on wavelet spectrum power analysis, obtained with continuous wavelet transform with complex mother wavelet (Morlet) in specific frequency ranges.

In the Pliocene (about five – two million years before present) global climate fluctuated with a period corresponding well 41-thousand-year cycle of changes in the Earth’s axis inclination to the ecliptic plane. Then, this period has disappeared, despite the fact that the 41-thousand-year cycle even slightly increased its scope and, therefore, the response to it would have only strengthened. By analyzing paleoclimatic series covering the Pliocene and subsequent Pleistocene, we show that the response of the climate system simply became unstable and therefore unobservable.