Research On Methods Of Data Reconstruction And Denoising For Oil And Gas Seismic Exploration Based On Sparse Representation

The data reconstruction and denoising for oil and gas seismic exploration are the underlying processes to improve the signal-to-noise ratio and resolution,and also are the key problems of seismic data processing.Their common essences are to recover the original seismic data approximately with mathematical means by solving the nonlinear ill posed inverse problems,according to the observed data collected from the blocks.In the study of solving this kind of inverse problems,there are often a case of small number samples in high dimension.Too few training samples usually lead to over fitting problems and reduce the generalization abilities of the model.In recent years,sparse representation technology can remove a large number of redundant variables in seismic data,then only preserve the explanatory variables most related to the response variables,therefore it can simplify the model while preserving the most important information in the data.If the solutions of seismic data processing satisfy the sparsity condition,solving the inverse problems of data reconstruction and denoising turn into solving the nonlinear ill posed problems with sparsity constraint to improve the well-posedness of the problem model,which makes convenience to data processing,and also reduces the amount of computation,transmission and storage.Especially under the influences of theories of compressed sensing and overcomplete dictionary learning,the theories of sparse representation and sparse constraint model have been rapidly improved,which provide new ways to solve the problems of seismic data reconstruction and denoising.Therefore,aiming at the problems of reconstruction and random noise suppression of seismic data,the sparse representation method of multi-scale geometric analysis is used to research the data reconstruction technology under the framework of compressed sensing theory,and the method of overcomplete dictionary learning is applied to study the solution of random noise suppression.Then the theoretical models of seismic data reconstruction and random noise suppression are analyzed,and their inherent regularities are revealed.The main research contents and research achievements of this thesis are focused on the following aspects:(1)In the framework of compressed sensing,seismic data reconstruction methods based on sparse representation of multi-scale geometric analysis are researched,the principles and steps of sparse representation,sampling observation,method of optimization solving are analyzed.The random noise suppression model of seismic data based on overcomplete dictionary is studied to explore the optimal sparse representation method with the local dictionary learning technology.(2)Aiming at the problem that the present seismic data reconstruction methods based on sparse representation in curvelet domain has so far paid little attentions to the dependencies among the coefficients,the data recovery algorithm via Bayesian estimation threshold function based on the curvelet domain is proposed,which improves the efficiency of the sparse representation,and enhances the accuracies and convergences of the solutions of the sparse constrained ill posed inverse problems.Taking advantage of the strong correlations among the curvelet coefficients which are adjacent and inside scales,the respective parent-child curvelet coefficients joint distribution models of fully-sampled seismic data and noise signal caused by missing traces are established in the framework of compressed sensing,then the bivariate shrinkage function according to the Bayesian maximum posterior probability estimation is obtained,and the parameters are determined by the coefficients distribution of the highest scale and the neighborhood window,the Landweber iterative shrinkage algorithm is used in the recovery process.Compared with the soft shrinkage function algorithms,the proposed algorithm could make the events more continuous and obtain higher reconstruction performance.(3)According to the problem that the oscillatory function(simple texture model)can be most sparsely represented in the wave atom domain,and it has more sparse characteristics for texture information in seismic data events than other commonly used sparse representation method of multi-scale geometric analysis,the seismic data reconstruction algorithm based on wave atom domain is proposed,which breaks the limitations of the traditional sparse representation methods in multi-scale geometric analysis for reconstruction of seismic data,and improves the effectiveness of explanatory variables in sparse constraint regularization models.The normalized reconstruction model of seismic data in the compressed sensing framework is established.Then in the process of solving the model,the technology of cycle spinning is adopted to suppress the noise in the reconstructed data,moreover the exponential threshold contraction model is exploited to gradually promote the sparse degree of coding coefficients,and recover the main features of seismic data.Compared with similar reconstruction method,the proposed algorithm can improve the quality of the waveform texture information and overall reconstruction data.(4)In view of the problem that the current global dictionary denoising methods can not provide the optimal sparse representation for the different spatial positions in the seismic data,the algorithm of random noise suppression based on sparse representation of structured clustering dictionary learning is proposed,which enhances the completeness of atoms in dictionary and improves the accuracies and stabilities of the solutions of the sparse constrained regularization denoising models.According to that the strong self-similarities among the seismic data blocks,and the regularities and redundancy existing in the coefficients distribution of global dictionary sparse representation,the seismic data blocks are clustered according to the structural features,and the overcomplete dictionary is obtained for each class of data blocks,and then the seismic data of each class are sparsely represented by the local overcomplete dictionary.So the seismic data blocks are recoded according to each clustering center,and the original seismic data is represented and described more sparsely,then seismic random noise is suppressed.Compared with similar algorithms,it could obtain better quality in waveform complex regions and the denoising effect.(5)In view of the problem that the strong similarities between the local directions along geophones and samplings in seismic data can not be fully represented in the current sparse representation method which used seismic data blocks as the dictionary learning samples,a novel denoising algorithm based on sparse representation model of multi-trace similarity group dictionary is proposed,which improves the accuracies of the atoms in the dictionary,and makes the denoising model with sparse constraint regularization more generalized and robust.Firstly,the strong similarities among the adjacent traces of waveforms are used to construct the multi-trace similarity group which is consist of a group of data blocks highest similarity to the target seismic data block,according to the multi-trace similarity in the training window;Secondly,the adaptively learning algorithm of over-complete dictionary based on multi-trace similarity group is adopted to complete the dictionary construction and sparse coding;Finally,The L1 norm minimization problem is solved through iterative threshold shrinkage algorithm,as the sparse degree of coding coefficients is promoted gradually,the main characteristics of seismic data are retained,and the random noise are suppressed as well.Through the contrast with the existing denoising algorithms,the proposed algorithm yields higher quality of details feature and denoising performance.In this thesis,taking the sparse representation as the main research line,and combining the actual demand for seismic data reconstruction and denoising,with the theories of the multi-scale geometric analysis,sparse representation,compressed sensing,dictionary learning,optimization solution,and machine learning,the new effective methods are researched for seismic data reconstruction and denoising,to enhance the signal-to-noise ratio,resolution and fidelity of seismic data,to improve the accuracy for subsequent seismic data processing,interpretation and judgement of oil and gas reservoir in target areas,and to provide a reference for other aspects of seismic data processing.