High-resolution Time-frequency Analysis Based On The Fractional S Transform Of Seismic Signal And Its Applications

Due to its unique advantages, the Fractional Time-Frequency analysis(FrTFA) brings new ideals to traditional time-frequency analysis and becomes a hot research issue. Fractional Fourier transform(FrFT) can be viewed as a rotating of time-frequency plane. The minimum value of time frequency product exists in traditional time frequency analysis could be broke during the rotating. That contributes to score better results in concentrating energy. Nowadays we have many new methods by combining FrFT with traditional time frequency analysis technology. This makes the new method possess the advantages both of them. Since the FrFT’s characteristic, FrTFA has a unique advantage in seismic signal processing and reveals its application prospect in seismic signal processing. Learning from previous thinking, we proposed the Fractional Generalized S transform(FrGST) based on Generalized S transform(GST) in this paper. After that we also study the FrGST’s application in high resolution seismic signal. Above all, the main contents of this article are:(1)We have studied some time-frequency analysis methods that used commonly, such as Short-Time Fourier transform(STFT), Cohen bilinear time-frequency distribution, S transform(ST), Generalized S transform(GST), FrFT and so on, the advantages and disadvantages of each mehods have been summed up in this paper.(2)Through the study of some kinds of GST and theirs advantages compared to ST, the energy normalized window has been selected, then the GST with a energy normalized window combines with FrFT could we get the FrGST. Then in this paper we get the Fractional Generalized S transform(FrGST).(3)After a detailed analysis of FrGST’s window function, a 3-D comparison simulation map between FrGST window function and a GST window function without been energy normalized given in this paper. From the simulation result we can see that FrGST’s window function has the ability to suppresses the weighing phenomenon in high frequency which happened in the window functions that lack of the energy normalized step. So we can get a more accurate result form FrGST.(4)The sampling theorem of fractional domain and the optimal order theorem have been used in FrGST after we study them in this paper. Through the comparison of simulations on theoretical signal and seismic signal, we can find that FrGST receive better results than both ST and GST.(5)The applications of time-frequency analysis in high-resolution seismic signals processing have been discussed in this paper. We describe some commonly used instances in this paper, like stratigraphic absorption compensation, Rayleigh surface wave dispersion analysis and time frequency wave field separation and denosing. After all, the FrGST’s aaplicaion is the focus issue. mainly about the spectral decomposition and attribute extraction of seismic signal. For the frequency properties that commonly used, like single frequency property, instantaneous frequency property and root mean square frequency property, their algorithms and simulations by FrGST have been showed in this paper.