The Research Of Seismic Signal Analysis Method Based On The Fractional Fourier Transform

The seismic signals are nonstationary by the effect of stratum through which the signals are absorbed and attenuated, So they should be analyzed with the nonstationary signals processing methods. When we analyze the nonstationary signals,what we want to get is how the frequency of signals changes with the time ,but the traditional Fourier transform analysis method can only represent the whole frequency element,not reflect the change . So people improved on the Fourier transform from the two different directions , one of which aim to the time-frequency localization precision and another of which is the Fractional Fourier Transform (FRFT) which is researched in this paper. The FRFT put forwad based on the rotation of coordinate axes is generalized Fourier transform.In the paper, the physics meaning, definition and character of the FRFT are introduced. On the basis of the theory research of FRFT,the discrete FRFT and its inverse transform algorithms are realized by computer, and the relation between the FRFT and Fourier transform is tested with the model and real seismic data.The results approve that the Fourier transform can be regarded as the special condition in the FRFT and the algorithms referred above is correct and available. That is a foundation of the continue research.Because the FRFT equates the rotation of time-frequency plane and can improve the time-frequency distribution, so time-frequency analysis based on FRFT called Generalized Time-Frequency(GTF) analysis method is studied in this paper. TheGTF generalizes some common time-frequency analysis. The two kinds of GTF methods, time-frequency analysis in fractional domains and the time-frequency analysis based on the kernel function of FRFT, are primary discussed. The emphasis of this part is on the formula derivation and numerical algorithms. Through the research of the time-frequency analysis in fractional domains,the algorithm to find the best fractional domain in which signals centralized the best is realized, and the formular that Pseudo Wigner-Ville Distribution(PWVD) is expressed by Short Time Fourier Transform(STFT) is gotten. consequently, the discrete PWVD in fractional domains is gotten on the basis of discrete STFT.Through the research of the time-frequency analysis based on the kernel function of FRFT called fractional time-frequency analysis for short ,the emphases are the discrete formula derivation of fractional Wigner-Ville Distribution and fractional ambiguity function and the study of their inversion . The two GTF methods are compared with the common time-frequency analysis ones by analyzing the seismic signals. The research result of this part show that the algorithms are valid and effective, the GTF shows some different characteristics and can provide more centered time-frequency distributions, and the PWVD in fractional domains not only can centralized the every component of the signal during analyzing ,but also can eliminate and restrain the cross-terms.Since the FRFT is generalized Fourier transform and can transform the signals to any fractional domains, it can replace the Fourier transform in some algorithm where the Fourier transform is used and make the result vary. In this paper, the FRFT is introduced to the spatial predictive techniques to seismic data to find a balance between signal character preservation and noise removal. The FRFT allows transformation to any of a continuous family of spaces intermediate to the time and frequency domains by introducing a fractional parameter , and the SVD technique is uesd to attain the filter during the course of filtering. The cross correlation coefficient curve and relative error energy curve are used as attributes to evaluate the quality of results. The researchful result of this paper prove that we can find a proper fractional domain in which the spatial prediction filtering can keep a balance between noise removal and signal character conservation .This method is more flexible than the classical one.