中文摘要：

地球介质相对于地震波波长尺度的定向非均匀性会导致波速的各向异性，进而影响地震波场的运动学与动力学特征．各向异性弹性波动方程是描述该类介质波场传播的基本工具，在正演模拟、偏移成像与参数反演中起着关键作用．为了面向实际应用构建灵活、简便的各向异性波场传播算子，人们一直在寻求简化的各向异性波动方程．本文借鉴各向异性弹性波波型分离思想，通过对平面波形式的弹性波方程（即Christoffel方程）实施一种代表向波矢量方向投影的相似变换，推导出了一种适应任意各向异性介质、运动学上与原始弹性波方程完全等价，在动力学上突出qP波的新方程，即qP波伪纯模式波动方程．文中以横向各向同性（TI）介质为例，给出了相应的qP波伪纯模式波动方程及其声学与各向同性近似，并在此基础上开展了正演模拟和逆时偏移试验，展示了这种描述各向异性波场传播的新方程的特点与优势．

英文摘要：

The ordered heterogeneity much smaller than the wavelength will results in velocity anisotropy and thus affects the kinematic and dynamic properties of the seismic waves. As the tools to describe the wave propagation in earth＇s media, anisotropic elastic wave equations play key roles in seismic modeling, migration and inversion. To generate flexible and efficient wave propagators in anisotropic media for practical usage, people never give up to construct simplified anisotropic wave equations in the past years. In this paper, based on wave-mode separation theory, we propose so called pseudo-pure P-wave equations which are equivalent to the original elastic wave equation in kinematics but highlight the P-wave energy. We derive the pseudo-pure P-wave equations in TI media and their further simplified forms. The examples of synthesized wavefront snapshots and reverse time migration prove that, the pseudo-pure-mode wave equation is accurate anisotropic wave propagator with distinguishing features, and has great potential in seismic modeling, imaging and parameter inversion.