The Study On Propagation Feature And Forward Modeling Of Seismic Wave In TI Media

Earth media is characterized by its anisotropy. Seismic anisotropy is mainly manifested in the following aspects: seismic wave propagation velocity differs with the change of the propagation direction, body-wave couples mutually and S-wave splits, etc. As one of the leading-edge topics in seismology study, seismic anisotropy study is of theoretical and practical significance for the cognition of earth structure, the exploration and development of complex oil and gas reservoirs, and the forecasting of geological hazards as well.Anisotropy is common in sedimentary rocks. Anisotropy in sedimentary rocks presents the feature of isotropy in the transverse direction and inhomogeneity in the vertical direction, known as transversely isotropic media (TI media). Some strata caused by folds and uprush may tilt, TI media will turn to so-called tilted transversely isotropic media (TTI media), for the symmetry axis of TI media is no longer horizontal or vertical. Since TI media in sedimentary rocks is common, this paper discusses the elastic wave propagation feature in TTI media, reflection coefficient and transmission coefficient, AVO characteristics in TTI media, the methods of qP-wave one-way wave forward modeling and elastic wave forward modeling in TI media.Phase velocity, group velocity and polarization direction are essential characteristics of seismic wave propagation. In this paper, elastic wave phase velocity and group velocity formulas of TTI media are derived with the application of Bond transform, Christoffel equation and Crampin formula. Thomsen parameters help to realize the weak anisotropy approximation of phase velocity formula. Polarization direction of elastic wave in TTI media is worked out by putting phase velocity substitute into the Christoffel equation. Using the weak anisotropy approximation, the approximate formulas in xoz plane and three-dimensional polarization direction are obtained. Numerical calculations indicate that the approximate formula of weak anisotropy well matches with the accurate values in a certain precision range.Reflection coefficient and transmission coefficient are the basis of AVO study. In this paper, the elastic wave phase velocity and polarization direction in TTI media derived are used to establish displacement wave functions of incident wave, reflection wave and transmission wave. Then, under the conditions of stress and displacement continuity on the media interface, quasi Zoeppritz equation for qP-wave incident in TTI media interface is set up. The solution of the equation is just the exact reflection and transmission coefficients, which can be obtained by numerical methods. The approximate solutions of reflection coefficient and transmission coefficient are deduced by using similar methods of dealing with isotropy, on the basis of weak anisotropy approximation and similar media approximation of elastic interface. This paper mainly studies the approximation of reflection coefficient, and gives three-term approximation and two-term approximation under the condition of small-angle approximation of the reflection coefficient. Based on the exact and approximate reflection coefficients, this paper performs the study of four types of AVO responses of different TTI media, and the analysis of the impact of anisotropic parameters on AVO.One-way wave propagator is the foundation of one-way wave forward modeling and migration. This paper sets up one-way propagator in TTI media, including generalized-screen approximate qP-wave one-way propagator of VTI media, HTI media, elliptical TTI media, and phase-shift propagator of TTI media, in generalized-screen series expansion method, under the premise of homogeneous TI media, depending on media decomposition principle. The qP-wave one-way wave propagator of TTI media derived is used to set up qP-wave one-way wave forward modeling algorithm, based on positioning principle, mathematical geophone principle and equal-time stacking principle, etc. The method of depth migration in TTI media is carried out by one-way wave propagator of TTI media and imaging condition. The result of forward algorithm shows that the reflected wave of TI media is different from the isotropic waves in some aspects, such as time of receipt, energy distribution, which makes surface data more complicate, due to the anisotropy of TI media which leads to the difference of seismic wave propagation velocity with the change of direction. The migration result shows the effect of anisotropy is taken into account for acquisition data in anisotropic media.With respect to TI media elastic wave forward modeling, first of all, media is decomposed into homogeneous isotropic background media and perturbations, with anisotropy parameters as the disturbance of isotropic background media, according to media decomposition principle. On the basis of TI media elastic wave equation, using elastic thin-slab approximation, and separated Green function, this paper obtains elastic wave field propagator of TI media and derives reflection wave field integral solution of TI media. Elastic wave forward modeling of TI media is carried out eventually by the integral solution.