Research On Non-stationary Signal Time-frequency Analysis And Seismic Spectrum Imaging

To improve the prediction accuracy of oil and gas reservoir,denoising methods and high-resolution time-frequency analysis methods for analyzing and processing non-stationary seismic signal are becoming more and more active nowadays.Thus,non-stationary denoising and non-stationary time-frequency analysis are researched in this dissertation,including the non-stationary signal pre-processing,high-resolution time-frequency analysis methods based on fractional Fourier transform,and sparse time-frequency analysis scheme.The contents are divided into six parts shown as follows.(1)The foundation of time-frequency analysis and data preprocessing methods for non-stationary signal are reviewed.Time frequency analysis and data preprocessing are key technologies for non-stationary signal.Due to the diversity of noise sources,time-frequency analysis and data preprocessing are challenging and active research topics.Thus,this paper first reviewed traditional time-frequency analysis and data preprocessing methods.(2)A signal denoising method using total generalized variation with overlapping group sparsity is proposed.The total generalized variation(TGV)denoising model is the extension of the total variation(TV)model and is capable of avoiding the staircase artifacts of the TV model.However,the TGV model independently disposes the pixels,ignoring the structural similarity prior of the processed image.Thus,the TGV model is not robust to high amplitude noise.The motivation of this paper is to employ the structural similarity and improve the TGV denoising effect.By introducing the overlapping group sparsity(OGS)to the TGV model,a new improved TGV model is then proposed,exploring both the first-order and second-order neighborhood differential gradient information to improve the robust of TGV to heavy noise pollution.To solve the proposed model,we adopted the accelerated alternating direction method of multipliers(ADMM),in which,the multi-constrained problem is divided into several sub-problems.To avoid large-scale matrix computation in the spatial domain,we regard the differential operators as the convolution form,and thus the fast Fourier transform and the convolution theorem are employed to efficiently solve the proposed model.Finally,experiments were conducted on several seismic signals under different types of noise to verify the proposed method.The findings are listed as follows.1)The proposed model is particularly good at removing the heavy noise in smooth area.2)The accelerated ADMM with restart process is capable of solving the proposed model and is much faster than traditional ADMM.3)The group size should be properly chosen to arrive the best performance of the proposed method.(3)A multi-directional window Cohen distribution based on fractional Fourier transform and greedy strategy is proposed to avoid the cross-terms of Wigner-Ville distribution(WVD).WVD is an important time-frequency analysis technology with a high energy distribution in seismic signal processing.However,it is interfered by many cross terms.To suppress the cross terms of the WVD and keep the concentration of its high energy distribution,an adaptive multi-directional filtering window in the ambiguity domain is proposed.This begins with the relationship of the Cohen distribution and the Gabor transform combining the greedy strategy and the rotational invariance property of the fractional Fourier transform in order to propose the multi-directional window,which extends the one-dimensional,one directional,optimal window function of the optimal fractional Gabor transform(OFrGT)to a two-dimensional,multi-directional window in the ambiguity domain.In this way,the multi-directional window matches the main auto terms of the WVD more precisely.Using the greedy strategy,the proposed window takes into account the optimal and other suboptimal directions,which also solves the problem of the OFrGT,called the local concentration phenomenon,when encountering a multi-component signal.Experiments on different types of both the signal models and the real seismic signals reveal that the proposed window can overcome the drawbacks of the WVD and the OFrGT mentioned above.(4)A sparse time-frequency representation based on primal-dual method is proposed.Time-frequency analysis is widely used in many engineering fields.However,the traditional time-frequency analysis methods suffer from issues such as low resolution or the interference of cross terms.To solve the above issues,this paper proposes a sparse time-frequency analysis by using an L1-norm constraint,fitting the sparse prior of a signal's spectrum.This process begins with the relationship between the sparse spectrum and the short-time measurement in order to propose the short-time sparse spectrum inversion model.Then,the first-order primal-dual method is employed to solve the proposed model.In this way,the reconstructed spectrum is constrained to be sparse.On the one hand,the concentration of the proposed algorithm is high due to the adoption of the L1-norm constraint.On the other hand,cross terms are avoided because the proposed method is based on the short-time Fourier transform and convex optimization technology.To show the performance of the proposed method,experiments based on both the theoretical signal and the real seismic signal are then conducted and compared with state-of-the-art time-frequency methods.The results show that the proposed method can obtain more accurate time-frequency distributions than other algorithms.(5)A sparse time-frequency representation based on Lp-quasinorm constraint is proposed.In the proposed method,we regard the short time truncated data as the observation of sparse representation and design a dictionary matrix,which builds up the relationship between the short time measurement and the sparse spectrum.Based on the relationship and the sparsity constraint described by the Lp-quasinorm,the sparse time-frequency representation model is established.The ADMM is adopted to solve the proposed model.Experiments are then conducted on several synthetic signals and applied to a seismic signal and a seismic profile crossing gas reservoir.These examples indicate that the proposed method is able to obtain a time-frequency distribution with higher resolution than state-of-the-art time-frequency methods.Thus,the proposed method is of great importance to seismic exploration.(6)A sparse time-frequency algorithm based on matching pursuit is proposed to avoid the disadvantage of STFT,fitting the sparse prior of the local observed signal.Experiments are then carried out on the seismic signal,comparing with some state-of-the-art time-frequency methods.The results show that the proposed method is able to compete with the state-of-the-art time-frequency methods and is capable of obtaining high-resolution time-frequency distribution,which is of great importance to seismic signal spectrum decomposition.