Research On And Application Of The Seismic Inversion Method In The Generalized Sparse Domain

Seismic inversion is a method for deducing physical parameters of underground me-dia by using acquired seismic data and well log data.It has been widely used in many fields of earth exploration,such as oil and gas resources exploration,engineering geolog-ical survey,volcano,earthquake and other geoscientific research.In the field of seismic exploration for oil and gas resources,seismic inversion has become the core technology.Historically,the discovery of many large oil and gas reservoirs is inseparable from the contribution of seismic inversion.With the deepening of exploration and development,there are fewer and fewer oil and gas reservoirs with simple geological conditions and easy to be discovered,and the remaining ones are those with complex structures and diffi-cult to be discovered.To detect them,it is necessary to further develop efficient and high resolution seismic inversion methods.In recent years,the successful application of compressed sensing and sparse recovery theory in applied mathematics,signal processing,radar detection and other fields has pro-vided useful experience for the development of high-efficiency and high-resolution seis-mic inversion methods.Some existing seismic signal processing,imaging and inversion methods based on compressed sensing and sparse recovery theory have obtained better results than conventional methods.They further prove the feasibility of sparse seismic inversion methods.However,the existing seismic inversion methods based on sparse recovery theory have the following problems:for example,spare inversion for seismic acoustic impedance needs to be carried out in two steps?called two-step inversion?.First,the reflection coef-ficient is obtained by sparse recovery method,and then acoustic impedance is calculated according to the relationship between the reflection coefficient and acoustic impedance.The premise of this method is to know the acoustic impedance at time t=0,and the result of reflection coefficient inversion should be as accurate as possible.Otherwise,the accumulate errors will be in the inversion result.The second problem is the existing multi-channel simultaneous inversion methods need Kronecker product operation,which costs a lot of computation.In addition,the existing sparse inversion methods still have some other problems,such as the mining and utilization of the sparsity and other prior information are inadequate.In data preprocessing,the existing seismic data denoising/reconstruction methods only use the sparsity in the transform domain or non-local self-similarity of the data,but lack the joint use of these two kinds of important a prior information.In view of this,this thesis has carried out research on these issues,the main contents are as follows:?1?Seismic denoising method using local sparsity and non-local self-similarity of seismic data is studied.On the one hand,the data-driven sparse transform learning method is used to update the sparse transform dictionary to provide better sparse transform for seismic data sparse coding.On the other hand,the low rank constraint method based on block matching is used to describe the similarity between non-local patches of seismic data.?2?The shortcomings of the existing two-step sparse acoustic impedance inversion methods are studied.Those disadvantages are explained by theoretical model experi-ments.Based on which,a sparse representation model for acoustic impedance is estab-lished,and a direct seismic acoustic impedance sparse inversion method is proposed.?3?The problems of the existing total variation?TV?regularization seismic inver-sion methods,for instance,the staircase artifacts,are studied.To solve these problems,an inversion method based on anisotropic total variation with overlapping group sparsity?OGS_ATV?is proposed.?4?Solutions to seismic inversion problems with various regularization constraints are studied.Aiming at the seismic inversion problem with L₁/L_pnorm constraint,total variation constraint and L₂norm constraint,a method based on split Bregman iteration and soft threshold shrinkage is proposed.For seismic inversion problems with both OGS_ATV and L₂norm constraints,a method based on the alternating direction multiplier method?ADMM?and the Majorization-minimization?MM?method is proposed.?5?A fast method for multi-channel simultaneous inversion is studied.Multi-channel simultaneous inversion involves a large amount of data and large-scale matrix multiplica-tion.The existing methods need Kronecker product operation,which requires very large memory space.To solve this problem,the properties of related matrices are studied.By using the convolution theorem and 2-D fast Fourier transform,the multiplication opera-tion of such large-scale matrices is converted into a point-wise multiplication operation,which avoids Kronecker product operation,thus greatly improves the inversion speed and reduces the demand for memory space.?6?A prestack multi-gather simultaneous inversion method for prestack elastic pa-rameters is studied.In post-stack seismic inversion,multi-channel simultaneous inversion can make use of space-time information of seismic data to enhance the lateral continuity of inversion results.Based on this,the post-stack multi-channel simultaneous inversion is extended to prestack multi-gather simultaneous inversion,and several regularization con-straints are added to the objective function.The effectiveness of this method is verified by a theoretical model and field seismic data.