The Theory Of Fractional Spcetral Estimation For Complex Sismaic Signal And Its Application

Spectral analysis is an important techonology of signal prosssing. For signals of gauss distribution, power spectral is a very effective method. For signals of non-gauss distribution, high order spectral analysis can perform more information. Seismic signals are very common non-stationary signals, people used to analysis them with time frequency analysis method, which can transform the singals to time-frequency plane and will be convenient to observe the signals characteristics.These characteristics may be important evidence of oil and gass forcasting for petroleum professionals.Fractional Fourier Transform is a new signal processing method which occurs in 1990s, and have been developing rapidly in recent years. It is a generalized form of Fourier Transform, and has show some advantages compared with Fourier Transform.When Fractional Fourier Transform and time frequency method are combined, The window of time frequency analysis is more flexible. Thus, the fractional time-frequency analysis has higher resolution than the conventional time-frequency analysis method. It could be speculated that fractional spectral estimation theory has unique advantages than the conventional spectral in seismic signal analysis. Based on the traditional spectral estimation theory, the dissertation proposed the method of fractional local power spectrum estimation and sliced fractional Wigner high order spectrum estimation method, and studied the application of the methods in complex seismic signals. The main research contents of this paper are as follows.(1) Studied spectrum estimation theory. For power spectral estimation method, we studied classic spectral estimation, AR spectral estimation, Burg spectal estimation etc. For high order spectral estimation, we studied Wigner Bispecrum, Wigner Trispectrum.(2) Studied Fractional Fourier Transform theory, especially the fractional time frequency method, the optimal fractional spectrum theory, which makes the foundation for the combination of conventional spectral estimation and Fractional Fourier Transform.(3) The method of fractional local power spectrum estimation is proposed, the direct method and the AR model method are given, and the corresponding simulations are given.(4) The method of fractional Wigner high order spectrum estimation is proposed, and the corresponding simulations are given.(5) Studied the application of the fractional local power spectrum estimation in actual seismic signals reservoir prediction. By extracting the frequency properties of seismic signals in the simulation analysis, we conclude that fractional spectral estimation is superior to conventional time-frequency analysis methods.