中文摘要：

地下岩石的速度各向异性影响地震波的传播与成像.横向各向同性（TI）介质为最普遍的等效各向异性模型.引入TI介质拟声波方程可以避免复杂的弹性波方程求解以及各向异性介质波场分离,以满足对纵波成像的实际需要.本文从垂直横向各向同性（VTI）介质弹性波方程出发,推导出正应力表达的拟声波方程以及相应的纵波分量的表达式,进而分析从频散关系得到的拟声波方程的物理意义,而后将拟声波方程扩展到更一般的倾斜横向各向同性（TTI）介质中.波前快照与群速度平面的对比验证了拟声波方程可以很好地近似描述qP波的运动学特征.在此基础上,将拟声波方程应用在逆时偏移中并与其特例声波近似方程进行对比,讨论了计算效率、稳定性等实际问题.数值试验表明VTI介质情况下采用声波近似方程可以提高计算效率,而TTI介质qP-qSV波方程则在效率相当的情况下可以保证稳定性.SEG/HESS模型和逆冲模型逆时偏移试验验证了本文TI介质拟声波方程的实用性.

英文摘要：

Neglecting anisotropy in seismic imaging may result in remarkable positional errors and focusing problem,especially for long-offset,wide azimuth seismic data.A transversely isotropic（TI） medium related to shale formations and periodic thin layers is one of the simplest and most practical approximations for anisotropic media in seismic imaging.For P-wave imaging,we introduce pseudo-acoustic wave equations to avoid solving elastic equations and wavefiled separation in TI media.In this paper,starting from elastic wave equations in VTI media,we present new pseudo-acoustic wave equations and the corresponding expression for qP wave.The equations expressed by wavefield and expressed by stress indicate the physical meaning of second-order coupled equations derived from the dispersion relationship.Then we extend the pseudo-acoustic wave equations to TTI media by tilting the coordinate system.The consistency between snapshots and group velocity surfaces shows their good kinematic approximation for qP wave.We use the pseudo-acoustic wave equations as the basis for TI reverse-time migration and compare qP-qSV wave equation with acoustic approximation equation.Then we also discuss the computational efficiency and stability issue.We show numerical examples to demonstrate that acoustic approximation equations save much computational cost in VTI media;but qP-qSV wave equations involving no acoustic approximation can guarantee the stability.Testing result of reverse-time migration with the SEG/HESS model and overthrust model validated these equations.