Research On Seismic Traveltime Tomography Based On Eikonal Equation Of The Factorization Form

Seismic wave traveltime tomography has a wide range of applications in petroleum,coal,and mineral seismic exploration.Forward modeling is the basis of inversion.Therefore,how to improve the calculation accuracy and efficiency of forward modeling is the primary task and key to solving the problem of seismic traveltime tomography.Since the wavefront curvature of the seismic wave field is large at the near source point,the problem of source singularity will occur in the process of solving the Eikonal equation.The error generated by the source point will extend from the source point to the entire model calculation domain as the calculation progresses,so that the calculation accuracy of the seismic wave travel time is greatly affected.In order to obtain more accurate travel time calculation results,the following aspects are studied and improved in this paper.(1)The mathematical background of the travel time calculation method is introduced,including the origin of the equation,the ray equation and the dynamic equation.Taking the time proposed by the method as a clue,the common finite difference travel time calculation method is summarized,and the fast scan method is introduced in detail.(2)In order to solve the source singularity problem,a method of calculating the travel time of the equation based on factorization is proposed.The equation is divided into multiplicative or additive factorization,and the corresponding perturbation term is used to represent the wavefront curvature to reduce the calculation error caused by the source singularity.Based on the common fast scanning algorithm,a fast scanning algorithm based on factorization is implemented.(3)In the numerical simulation stage,the proposed method is compared with the ordinary fast scan algorithm and the travel time algorithm in the PStomo_eq package.Several 2D and 3D velocity models are tested,and the forward and inverse effects of each velocity model are shown respectively.The numerical results show that the accuracy of the fast scanning algorithm based on factorization is better than that of the other two travel-time methods.(4)Combining the field data,the fast scanning algorithm based on factorization and the fdtime3 d.c method are used for seismic travel-time tomography.The former is better than the latter,which proves the superiority of the fast scanning method based on factorization.