The Study On Propagation Feature Of Seismic Wave In Anisotropic Media

The medium of Earth is anisotropic.In the anisotropic media,the propagation velocity of elastic waves varies with direction.Studying these characteristics of velocity variations is a key issue in seismic exploration.By studying the seismic anisotropy,we can not only understand the Earth's internal structure more accurately,but also explore and develop more valuable reservoirs.The study of the elastic wave propagation in the Earth's medium is usually based on numerical simulation.In order to study the problem of elastic wave propagation in anisotropic media,the differential equations and the wavefield simulation of elastic wave equations in isotropic media are first carried out.A 2D media model design program is written.Moreover,in order to eliminate the problem of artificial reflection caused by artificial boundary,PML boundary conditions are added.At present,the main targets of oil and gas exploration are concentrated in sedimentary rocks.Anisotropy in sedimentary rocks generally shows isotropy in the transverse direction and non-uniform in the longitudinal direction.In order to reveal the anisotropy of shale,this paper studies the propagation characteristics,stiffness matrix characteristics and reflection-transmission coefficient of elastic wave in TTI media.In theoretical studies,TTI media are generally obtained by rotating the axis of symmetry of the VTI / HTI media by an angle,but their stiffness matrix becomes more complex than the stiffness matrix of the VTI / HTI media,giving some difficults to practical applications.In this paper,the stiffness matrix of the TTI media is simplified by the trigonometric methods,and the stiffness matrix of the initial(VTI / HTI)media is separated from TTI media.The stiffness matrix of the TTI media is then decomposed into the stiffness matrix of the VTI / HTI media and a 'perturbation' matrix.Moreover,this method of separation is applied to wavefield simulation and obtained the wavefield of TTI media by superimposing the wave field of VTI medium on the 'perturbation' medium.The propagation velocity of elastic waves in the medium has always been the key to the seismic exploration work,including the inversion problem.Unlike with isotropic media,the expression of elastic wave propagation velocity in anisotropic media is complex.According to Thomsen's weak anisotropy hypothesis,a simplified anisotropic medium propagation velocity formula can be obtained.However,the anisotropy of shale exceeds this weak anisotropy assumption and a more general approximation formula needs to be found.In this paper,we use the Thomsen parameter to express the phase velocity expression of TTI media and make a general approximation to it.The simplified formula can be applied to a wider range of anisotropic parameters.