Theory And Application Research Of Time-frequency Analysis Of Non-stationary Signals Based On The Fractional Wigner-ville Distribution

Seismic signal is a typical non-stational signal and it plays a dominant role in the oil and gas exploration field. It is an important way to solve the current energy crisis with the efficient and accurate method in oil and gas exploration. The complexity and concealment feature of the exploration target undoubtedly increased the difficulty of the exploration. In the meantime, it also put forward higher requirements to the exploration precision and oil and gas identification method.The time-frequency analysis method is the core issue of the spectral decomposition and the explanation of the single-frequency profile of the the seismic signal. Undoubtedly it also occupies an important position in the field of oil and gas identification. But the inherent problems of the time-frequency analysis method have greatly limited its application in the detection of oil and gas reservoirs. Therefore, improve the prediction accuracy of the reservoir through choosing the appropriate method and improving the resolution of the time-frequency results has become an urgent problem.The classical Wigner-Ville distribution was extended to the fractional Wigner-Ville distribution based on the review to precious work. On this basis, the fractional Wigner-Ville distribution was introduced into the technique of time-frequency analysis and spectrum decomposition of the complex seismic signal. The optimal fractional pseudo Wigner-Ville distribution method was proposed. This method could suit well for the complex seismic signal processing. The specific work and achievements are as follows:(1) The basic Wigner-Ville distribution theory and the common methods to remove the cross terms were researched. The advantages and disadvantages of the many methods were also summarized in this dissertation. All these work lay a very good foundation for the removal of the cross terms of the fractional Wigner-Ville distribution.(2) The fractional Fourier transform theory was researched. Its definition forms, properties and two kinds of calculation methods were also summarized in this dissertation and some relevant simulations were also carried out. All this was benefical to making the choice of which definition form should be used to combine with the Wigner-Ville distribution to form the fractional Wigner-Ville distribution.(3) The three different definition forms of the fractional Wigner-Ville distribution were researched and their respective advantages and disadvantages were also summarized. On this basis, the reasonable definition form was chosen and it was used for the time-frequency analysis of the complex seismic signal.(4) The relationship between the fractional short time fourier transform and the fractional Wigner-Ville distribution was researched. Based on this, the optimal fractional pseudo Wigner-Ville distribution method was proposed. In this dissertation the derivation process was given based on the process of obtaining the optimal window of the fractional short time fourier transform.At last, the optimal fractional pseudo Wigner-Ville distribution method was tested in some theoretical signals and the corresponding analysis was given after the simulation.(5) The optimal fractional pseudo Wigner-Ville distribution method was successfully used in the spectral decomposition of the seismic signal and the recognition of oil and gas reservoir. As the commonly used methods of removing the cross terms, the Choi-Williams time-frequency distribution and the smoothed pseudo Wigner-Ville distribution were used to compare with the optimal fractional pseudo Wigner-Ville distribution method.Theoretical model and the real data processing showed that this algorithm could solve the cross terms problem much better with much higher accuracy than the conventional methods.