The Study On Seismic Wave Propagation Characteristics And Numerical Simulation In Moderate-strong Anisotropic TTI Media

The transversely isotropic(TI)media model is the most widely used anisotropic model in seismic exploration.The study of the propagation characteristics of seismic waves in TI media play an important role in theoretical and practical significance for the processing and interpretation of practical seismic data and reservoir prediction.By solving the Christoffel equation,we can obtain the exact expression of elastic wave phase velocity for TI media,which is difficult to use.So,we start from the exact expression of elastic wave phase velocity for TI media characterized by Thomsen anisotropy parameters,obtaining the approximate 3-D qPwave and qSV-wave phase velocities and the approximate dispersion relation for TI media by using the approximate method of completing the square.The approximate qP-wave and qSVwave group velocity can be derived by substituting the approximate phase velocity into the Berryman’s group velocity formulas.Then we calculate and analyze the approximate phase and group velocities,and investigating the error distributions of the two under different anisotropy conditions.Eventually,the numerical results show that the approximate phase and group velocities derived by this paper is more accurate than that of the weak anisotropy approximation in the case of moderate and strong anisotropy.The pure qP-wave and qSV-wave equations with the high-order mixed spatial partial derivatives for TI media are derived basing on the approximate qP-wave and qSV-wave dispersion relation equations.However,solving the pure wave equation can be much difficult and inefficient by involving the great linear matrix equation.Therefore,we derived pure qPwave and pure qSV-wave first-order velocity-stress equations for TI media with hybrid scheme by using the hybrid peseudospectral/finite-difference method.By merging equations,we decrease the times of Fourier transform in each time iteration,and increasing computational efficiency.In this paper,the Roteted Staggered Grid(RSG)scheme with optimal finitedifference coefficients is introduced for decreasing the numerical dispersion,and the stability conditions of pure qP-wave and qSV-wave velocity-stress formulations for TI media with RSG scheme are discussed.In order to increase absorption efficiency of boundary,we apply the Multi-axis Convolutional Perfectly Matched Layer(MCPML)boundary condition with improved attenuation function to the pure qP-wave and pure qSV-wave velocity-stress formultions of moderate-strong anisotropic TTI media.By enhancing simulation stability,it also improves the absorption efficiency of artificial boundary reflection.Meanwhile,advantages and disadvantages of Cerjan and MCPML boundary conditions are comapred.The forward can be carried out by introducing the optimal finite-difference coefficients,RSG scheme and MCPML boundary condition into pure qP-wave and pure qSV-wave velocitystress formulations for TI media with hybrid scheme,while the wavefiled charateristics of pure qP-wave and pure qSV-wave and elastic wave are compared in moderate-strong anisotropic homoheneous,layerd and complex TI media models.Then we compare the snapshots and seismic records of pure qP-wave with elastic wave and acoustic wave in complex media models.The results show that the pure qP-wave velocity-stress equation can propagate stably in moderate and strong anisotropic media,and its wave front is almost in the same spatial location as that of the qP wave of conventional elastic wave.The reflection wave has clearer events,and the deep reflection wave information of pure qP wave is more abundant compared with acoustic waves.