摘要
地球介质广泛存在波动各向异性,地震各向异性主要表现为地震波传播速度是传播方向的函数、体波间的相互耦合、横波发生分裂等。地震各向异性研究已经成为地震学研究领域中的前沿课题之一,开展地震各向异性研究对认知地球介质结构、勘探开发复杂油气藏和预报地质灾害均具有理论意义和实用价值。
各向异性是沉积岩石中几乎普遍存在的现象。沉积岩石中各向异性是横向各向同性而在纵向上为非均质性,称为TI介质。在褶皱和上冲作用下,一些地层发生了倾斜,此时TI介质的对称轴不再水平或者垂直,就形成了所谓的TTI介质。针对沉积岩普遍存在的TI介质,本文深入研究了TTI介质弹性波传播特征、TTI介质反射透射系数和AVO特征,TI介质qP波单程波正演模拟和弹性波正演模拟方法。
相速度、群速度和偏振方向是地震波传播的重要特征。本文用Bond变换、Christoffel方程和Crampin公式推导了TTI介质弹性波相速度和群速度公式。利用Thomsen参数,实现了相速度公式的弱各向异性近似化。将推导的相速度带入Christoffel方程,得到TTI介质弹性波偏振方向。再进一步利用弱各向异性近似得到了xoz面内和三维偏振方向的近似公式。数值计算表明弱各向异性近似公式在一定精度范围之内与精确值吻合很好。
反射系数和透射系数是AVO研究的基础。本文利用推导的TTI介质弹性波相速度和偏振方向,建立入射波、反射波和透射波的位移波函数,再利用介质分界面上应力连续和位移连续条件,建立了qP波入射TTI介质弹性分解面的拟Zoeppritz方程。该方程的解就是精确的反射和透射系数,可以通过数值方法进行求解。按照各向同性类似方法,本文根据弱各向异性近似和弹性界面相似介质近似,推导了反射和透射系数的近似解,并重点研究了反射系数的近似,同时给出了反射系数的三项近似式以及小角度近似下的两项近似式,最后根据精确和近似的反射系数,研究了不同TTI介质四种AVO响应,分析了各向异性对AVO的影响。
单程波传播算子是单程波正演模拟和深度偏移的基础。本文基于介质分解原理,以均匀TI介质为背景,利用广义屏级数展开方法,建立了VTI介质广义屏近似qP波单程传播算子,HTI介质广义屏近似qP波单程传播算子,椭圆TTI介质qP波单程传播算子以及TTI介质qP波相移传播算子。利用推导的TI介质qP波单程波传播算子,根据定位原理、数学检波器原理和等时叠加原理,建立TI介质qP波单程波正演模拟算法。同时利用推导的TI介质qP波单程波传播算子,根据成像条件,建立TI介质qP波深度偏移算法。正演模拟结果表明由于TI介质各向异性的存在,使得地震波传播速度随方向变化,因此TI介质岩层的反射波在接收时间、能量分布和相位等方面都不同于各向同性波的特点,增加了地面资料的难度。深度偏移结果表明,各向异性介质采集的地震资料,偏移处理时需要考虑各向异性的影响,否则会存在一定误差。
对于TI介质弹性波正演模拟,首先根据介质分解理论将介质分解为均匀各向同性背景和扰动,将各向异性参数也当作各向同性背景的扰动。在此基础上,从TI介质弹性波波动方程出发,根据弹性薄板近似,利用分离的Green函数得到TI介质弹性波场传播算子,进一步推导得到TI介质反射波场的积分解。通过求解,实现了TI介质弹性波正演模拟。
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.
引文
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