A Research On The Seismic Inversion Imaging Based On Point Spread Function

Based on point spread function(PSF),this paper studies seismic inversion imaging method in model domain.PSF is the mathematical expression of fuzziness in the observation process of an imaging point underground by seismic observation system.The inverse problem solving in model domain is more efficient than that in traditional data domain.In this paper,the least squares migration imaging in model domain is proposed as a problem of image degradation and restoration,an efficient and fast PSF solution strategy is proposed.The PSF is applied to image restoration,and the reasonable inversion results are obtained,which greatly improves the calculation efficiency of least squares migration.Chapter 1 is the introduction.Based on the analysis of the history and current research of the traditional seismic migration imaging method and inversion imaging method,the inversion method of model domain is proposed.Based on the definition of PSF,the relationship between Hessian operator in seismic inversion imaging and PSF in traditional optical imaging is analyzed.Taking PSF as a bridge,the methods of image restoration in optical data processing are summarized.Finally,it introduces the content and innovation of this paper.Chapter 2,the principle of seismic inversion imaging method.In inversion theory,it can be proved that the conventional migration imaging method is equivalent to solving the conjugate of the positive operator,not the inverse one.In this chapter,based on the finite difference forward modeling of wave equation in two-dimensional acoustic medium,PML boundary conditions,cross-correlation imaging conditions and Laplace filtering are used to deal with several key technical points in reverse time migration,and an effective reverse time migration method is obtained as the input of model domain inversion.Then,the mathematical expression of traditional inversion imaging method in data domain is derived,and the workflow of least square migration in data domain based on conjugate gradient method is given.Through the analysis,it is considered that the traditional data domain inversion imaging method has the problems of large amount of calculation and strong dependence on the initial model,and it is proved mathematically that the model domain inversion imaging method with higher efficiency can also achieve good inversion effect in theory.Chapter 3,model domain seismic inversion imaging and image restoration,which is the core content of this paper.The inversion imaging problem in model domain is proposed as an image deblurring problem of the imaging result,and the imaging result is "blurred result" of the real reflection coefficient by the blurry operator,which is called Hessian operator.Firstly,based on the mathematical physics of point PSF and Hessian operator,it is proved that the degradation of Hessian operator on migration profile can be transformed into the degradation of a series of space variant PSF on local profile.Compared with the huge Hessian matrix,PSF is more flexible in calculation,storage and subsequent operation.In this paper,a fast algorithm of full space PSF is proposed based on "forward+migration+interpolation" of scattering point model.The results of numerical experiments show that the obtained PSF can effectively construct the degenerate operator.The key of image restoration is to eliminate the convolution effect caused by PSF.Combined with theoretical analysis,three kinds of model domain inversion methods are introduced in the field of image processing,including wavenumber domain filtering,energy compensation and regularization.The model test results show that the proposed method has higher computational efficiency than the traditional least square migration while obtaining reasonable inversion results.By constructing an appropriate PSF operator,this strategy can be easily extended to other migration imaging methods.Chapter 4 is the conclusion and prospect.By summarizing the research contents and experimental results,the understanding of seismic inversion imaging in model domain is formed.The data processing method proposed in this paper can avoid the huge amount of computation generated by the traditional data domain method,and has the advantages of amplitude preservation and high accuracy compared with the conventional migration imaging method.Finally,combined with seismic wave propagation operator and artificial intelligence data processing means,the next development direction of this work is analyzed.