Fractional Spectrum And High-order Spectrum Estimation Technology And Its Application Research In Seismic Reservoir Prediction

Fourier transform and its inverse transform have built mapping relation between time domain and frequency domain. Even though we can use Fourier transform analyze signal from time and frequency domain separately, we cannot bring them together. For those non-stationary signals, it is of great importance to know the frequency characters of different time. Therefore, we need to describe the signal with time-frequency combination, put one-dimensional time domain signal imaging to two-dimensional time-frequency plane, and fully reflect the joint time-frequency character of seismic signal. On the basis of analyzing and summarizing the advantages and disadvantages of the traditional time-frequency analysis methods, this paper presents fractional spectrum and high-order spectrum analyzing method.As a generalized form of conventional Fourier transform, fractional Fourier transform can be interpreted as a representation method of fractional Fourier domain constructed after signals do arbitrary counterclockwise rotation about coordinate axis on time-frequency plane. Essentially, the representation of signal on fraction domain has integrated with information of time and frequency domain. It is closely related to conventional Fourier transform, but has more advantages. It is a linear time-frequency analysis method with unique characters, and a very good time-frequency analysis tool for analyzing and processing non-stationary signals. Thus, it is generally accepted by the researchers within the field of signal processing.High-order spectrum estimation technology has several advantages over conventional power spectrum estimation, such as follows: first, for Gaussian noise, high-order spectrum has the merits that it is constant and always zero, so it can be used to extract non-Gaussian signal from Gaussian noise; second, high-order spectrum contains phase information, so it can be used to recognize non-minimum phase system; third, high-order spectrum can be used in testing and describing the non-linearity of the system, such as testing Gaussian or non-Gaussian signal, and so on. Therefore, high-order spectrum estimation technology can be used as a new for analyzing and processing non-stationary signal. It plays an important role in seismic exploration.On the basis of analyzing physical meanings of fractional and high-order spectrum and the differences between them and conventional power spectrum, by calculating fraction and high-order spectrum of synthetic seismics of different types of theoretical models, this paper analyzes the characters of fractional and high-order spectrum of gas sand, and explores its application in seismic reservoir prediction. It also aims at the corresponding fractional and high-order spectrum to the actual seismic data calculation, extracts characteristic parameters of seismic signal or petroliferous related information, and provides seismic reservoir prediction with more abundant information. It has great applied value in qualitative gas-oil prediction.First, this paper gives a review of conventional time-frequency analysis methods, such as, short time Fourier transform, wavelet transform, Wigner-Ville distribution, and Cohen's class distribution, and so on. It shows their advantages and disadvantages through analysis and comparison. Second, this paper gives a detailed description about the basic theory of fractional and high-order spectrum estimation technology, and compares fractional and high-order spectrum estimation time-frequency analysis method with those conventional time-frequency analysis in detail. Through the comparison between the calculating results of theoretical formula and theoretical model, we fully realized the superiority of the fractional and high-order spectrum estimation time-frequency analysis method used in non-stationary signal analysis and process. Finally, we apply fractional and high-order spectrum time-frequency analysis method into division of geological sedimentary cycle bodies, folium seismic exploration, detecting carbonates apertures anomalous, and have obtained a good effect. Followings are some meaningful conclusions:(1) Through detailed description of fraction and high-order spectrum estimation, we get a better understanding about fractional and high-order spectrum estimation time-frequency analysis method. It is of some theoretical value.(2) The implementation algorithm of fractional spectrum estimation optimum order calculating, which is derived from the process of applying second-order moment of fractional Fourier transform, is reasonable and effective. Thus, the calculating time of fractional spectrum estimation can be reduced significantly, and it can promote the application of fractional spectrum estimation.(3) Combine the advantages of exponential kernel function and cone-shaped kernel function, which are commonly used in Wigner-Vile bi-spectrum time-frequency analysis process, we put forward joint distribution kernel function, which has a great effect in suppressing cross-terms of Wigner-Vile bi-spectrum time-frequency distribution.(4) We apply fractional spectrum estimation technology into the division of geological sedimentary cycle bodies, and get a good effect. By the fractional spectrum analysis of theoretical model and actual seismic data, we conclude that the frequency of positive cycle decreases gradually along with the increase of seismic signal time but the frequency of negative cycle increases gradually along with the increase of seismic signal time.(5) By applying Wigner-Vile bi-spectrum time-frequency analysis technology into folium seismic exploration, we have improved its resolution, and have obtained a good interpretation result.(6) We apply direct bi-spectrum time-frequency analysis technology into carbonates apertures anomalous testing, and succeed in detecting apertures' existence from theoretical models and actual seismic data. Through theoretical models and noise experiment, we find that this method has very good noise resisting ability.