Research On Theories And Some Issues Of Seismic Spectral Imaging In Fractional Domain

Spectral imaging technique is one of the commonly used methods for seismic exploration and oil and gas reservoir prediction,time-frequency analysis is the core technology of spectral imaging.Conventional time-frequency analysis methods have some drawbacks such as low resolution and cross terms and so on.In recent years,a series of novel signal processing techniques have been proposed to achieve high resolutions of spectral decomposition and imaging.These techniques greatly expended the connotation and extension of traditional spectral decomposition.One direction to improve the time-frequency resolutions is to introduce the fractional Fourier transform(FrFT)into the traditional time-frequency analysis methods.This kind of methods break through the limitations of traditional time-frequency analysis methods processing signals only in time domain,frequency domain and time-frequency domain,and can process signals in time domain,frequency domain,time-frequency domain and time-fractional domain.Comparing with traditional time-frequency transform,the novel methods introducing FrFT to time-frequency analysis methods add a degree of freedom,in other words,adding a rotation angle in time-frequency plane.As the angle increases continuously from 0 to(17)?,the FrFT is able to exhibit all the features of signals from the all the possible features in fractional time-frequency domain.This dissertation mainly solves the problems in two aspects: first,to enrich and develop the theory of time-frequency analysis in fractional domain;second,the fractional time-frequency analysis methods are used for seismic signal analysis and reservoir prediction;frequency attributes based the novel methods proposed in this dissertation are explored.The main research contents of this paper are:(1)This dissertation presents theories of several conventional time-frequency analysis methods,such as short-time Fourier transform,Gabor transform,S transform,Wigner-Ville distribution and so on.(2)The dissertation presents basic theory of the fractional Fourier transform,and discrete calculation methods of fractional Fourier transform,the theories are basic for the combination of traditional time-frequency analysis methods and fractional Fourier transform for fractional domain time-frequency analysis methods.(3)A fast algorithm for searching the optimal order of generalized time bandwidthproduct is proposed;and the method of calculating the optimal order of fractional timefrequency analysis methods proposed by using the main direction of the signal in ambiguity domain,and the influence of different optimal order calculation methods on the time-frequency analysis methods are tested by simulation signal.(4)The fractional Gabor transform is proposed based on kurtosis maximization determining the optimal order of signal.The method uses kurtosis to search the optimal order of fractional Gabor transform.It can suppress the Gaussian noise,and it is capable in analyzing multi-component signals and the transform has high resolutions.(5)The fractional deconvolution Gabor spectrogram is proposed,which is fractional spectral imaging having high resolution.The fractional optimal window function is introduced to fractional Gabor spectrogram.To improve the resolutions of fractional Gabor spectrogram,the Wingner-Ville distribution(WVD)of fractional optimal window function is used as point spread function(PSF),the deconvolution operations between the PSF and the fractional Gabor spectrogram are conducted,and the fractional deconvolution Gabor spectrogram is obtained.(6)This dissertation presents the fractional time-frequency domain attributes are applied in reservoir prediction,the attributes are root mean square frequency,center frequency,frequency attenuation gradient,instantaneous T-K dominant energy attributes.The conventional time-frequency analysis methods are used to verify the superiority of the methods proposed in this paper.To a certain extent,this study improves the ability of interpretation seismic data,and provides technical support for oil and gas exploration,therefore reducing the risk of reservoir exploration.The results have shown that fractional Fourier transform is a potential strategy for improving the resolutions of time-frequency analysis,so it is needed to make further research in this field.