The First Break Traveltime Tomographic Inversion Based On The Eikonal Equation For The VTI Medium

In the traditional method of traveltime tomography,the earth medium usually has been seen isotropic media,and many studies have confirmed that anisotropy exists in the earth medium.There are obvious differences of isotropic and anisotropic.The traditional traveltime tomography method has obviously theory of constraints in retrieving speed,static correction,migration and seismic interpretation etc.With the improvement of the precision of seismic exploration,the anisotropic information becomes more and more important.The traditional method of isotropic traveltime tomography based on the theory has not reached the modern seismic data processing requirements,so the traveltime tomography inversion method of two dimensional anisotropic medium has very important research significance.VTI medium is one of the most common medium in anisotropic medium.On the basis of previous studies,this paper first introduce the constitutive equation,then the basic concept of VTI media,and the corresponding expressions for group velocity.And derivated the process of non elliptic approximation coefficient formula.through the numerical simulation of wave field snapshot,this paper discussed the influence of VTI medium on the wave field compared with the isotropic medium,further proves the necessity of anisotropic media research.The first-arrival wave travel time tomography of two dimensional VTI medium is an effective method for inversion of the anisotropic parameters near the surface.Compared with isotropic travel time chromatography,its difficulty is the calculation of the first-arrival wave travel time and the joint inversion of the anisotropic parameters.In this paper,three parameters of vertical velocity,NMO velocity andnon-ellipse coefficient and Thomsen parameters are used to characterize the anisotropic parameters of medium.the VTIFMM(VTI Fast Marching Method)algorithm is introduced by the solution of function equation.It is proved that the algorithm has the characteristics of high precision,stable algorithm and fast calculation speed by numerical simulation.The ray tracing based on Runge-Kutta algorithm is used to calculate the ray length,and according to the corresponding group slowness approximate formula proposed two parametric method: vertical velocity,dynamic correction velocity and non elliptic coefficient parametric method(first parametric method)and Thomsen parametric method(second parameter method),and the expression of sensitive nuclear function the derivation of anisotropic parameters.Then analyzing the problems about magnitudes among the parameters.We briefly summarizes the selection principle based on the effect of various parameters on the kernel function,and theoretically proved that the ray trace is not only suitable for VTI medium but also other anisotropic media by and analyzing two kinds of parametric method.Finally,the joint inversion of two parameterized methods is realized by using the LSQR algorithm.The first arrival wave traveltime tomography of three dimensional is widely applied to real data processing which can provide a precision initial velocity model for followed migration and static correction.However,there are only a few studies on the first arrival wave traveltime tomography in three dimensional VTI media.The main difficulty lies in the joint inversion of 3D VTI medium anisotropy parameters and the processing of large-scale 3D data.Two parametric method is extended to 3D based on the first arrival wave traveltime tomography inversion of two-dimensional VTI medium.In order to solve the problem of three-dimensional operation efficiency of big data,the MPI parallel algorithm is applied to 3D VTIFMM which effectively improve the speed of operation.And the updated Tikhonov regularized by the introduction of anisotropic parameters improve the accuracy of inversion.Finally,the joint inversion of two parameterized methods is realized in 3D VTI media.Two parameterized methods are used to three dimensional theoretical models and real datatest.The results show that the two parameter methods can inverse the variety of trend of near surface anisotropy parameters.the inversed accuracy of first parameter method is higher compared with the first parameter method.Finally,this paper summarized the first arrival wave traveltime tomography inversion in VTI media,and introduced its shortcomings.