Time Frequency Analysis Based On Generalized S Transform And Its Application

Aiming at seismic signal’s non-stationary and time-varying characteristics, this paper starts from the traditional Fourier transform of signal, to illustrate the necessity of development from frequency analysis to time-frequency analysis. Several time-frequency analysis methods are classified and discussed briefly and some models are made to verify the different methods of applicability and defects. In theory, in view of the commonly used linear time-frequency analysis method, based on the theory of function spaces of the inner product, short time Fourier transform (STFT), continuous wavelet transform (CWT), S transform (ST), generalized S transform (GST) unified into a same form. Then, combining with the concept of window and base function, describe the internal relations between the methods above-mentioned and explain their resolution.Among three kinds of time-frequency analysis methods, the methods of linear and bilinear both can’t avoid the application of the window in the process that the signal is projected to the number field, the former use the window to realize the time localization of signal, and the latter take the use of window to suppress the cross terms, one of them follows the Heisenberg uncertainty principle and another is inhibited in a conflict between the suppression of cross terms and as far as possible to maintain the frequency resolution of the initial. In the adaptive synchronous development of time-frequency analysis methods, adaptive kernel time-frequency analysis methods are still have window problem, i.e. the kernel function problem resulted by suppressing the cross terms in fuzzy domain. In addition, the time-frequency based on the matching pursuit and the Hilbert-Huang transform (HHT) make the signal decomposition self-adaption, from a novel point of view, which is different from the Fourier transform, get rid of phenomenon that the time resolution and frequency resolution bound to each other. However, their algorithm is relatively complex, what’s more, have corresponding defects.This paper focuses on the common linear time-frequency analysis methods, respectively, actualize and compare the short time Fourier transform (STFT), continuous wavelet transform (CWT), Wigner-Ville distribution (WVD) and generalized S transform (GST) and so on, from theory and model tria. Then a conclusion is made that under the window, the meaning of time-frequency resolution is not a single time resolution or frequency resolution but window’s flexibility adapt to the local characteristics of signal i.e. the flexibility to realize the reasonable allocation of time resolution and frequency resolution that reflects in the window..Finally, the generalized S transform is used for the feature extraction, whose ultimate goal is seismic data interpretation. Firstly, make a brief description of common time-frequency attributes, then through building the geological model, obtain the corresponding between the time-frequency attribution and the geological attribution, lastly, the conclusion of the model test are used in the actual seismic data interpretation.