A Study Of Elastic Wave Gaussian Beam Tomography Inversion

With the rapid development of computer technology,methods and techniques in the field of exploration geophysics have been developed and applied accordingly.Prestack depth migration imaging technology,as an important imaging technology in the field of exploration geophysics,can image complex tectonic areas.The accuracy of velocity is an important factor affecting the imaging results of pre-stake depth migration.A velocity field can be obtained by velocity analysis method as the initial input of migration.There are many methods for velocity analysis,among which tomography inversion method is widely used.In this paper,under the theoretical framework of tomography inversion,a set of elastic wave Gaussian beam tomography inversion equations is constructed,the derivation of sensitive kernels for Gaussian beam tomography is introduced in details,and the method of elastic wave Gaussian beam tomography inversion is studied.The basis of this paper is the basic theory of elastic wave Gaussian beam.Under the paraxial approximation,the solution method and expression form of elastic wave Gaussian beams in the ray center coordinate system are given,and the basic properties of elastic wave Gaussian beams are studied.In traditional ray tomography,the tomographic sensitive kernel function is constructed by a single ray,which will lead to the instability of tomographic inversion.In order to solve this problem,based on Born approximation and Rytov approximation,this paper deduces the theoretical formula of the elastic Gaussian beam tomographic sensitive kernel function,constructs the elastic Gaussian beam tomographic sensitive kernel function,and applies it to the tomographic inversion equations.Although the sensitive kernel function of Gaussian beam tomography covers a wider range of velocity fields,the sparsity of the tomographic matrix will inevitably exist if the observation angle of the observation system is small.In order to reduce the zero value of the tomographic matrix and make the solution of the equations more stable,regularization is added to constrain the matrix in solving tomographic inversion equations by LSQR method.Finally,the results of model test show the feasibility and applicability of the elastic wave Gaussian beam tomography inversion method studied in this paper.