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Teng Jiwen Zhang Zhongjie Wang Aiwu WeiJichun Ji Lianxian(Institute of Geophysical, CAS, Beijing 100101)  
The study of seismic waves propagation in anisotropic medium is one of frontier problems in seismology. It is also one of the difficulty problems. As the anisotropy of the underground rocks mainly manifests that: seismic waves velocities vary with propagating direction, different type body waves couple each other, the dispersions of surface waves Velocities depend on propagating direction, shear waves split, etc., furthermore, thin-layered medium and preferred cracked distribution are induced to apparent anisotropy. So it has great potentiality and bright future in significal applications for oil and gas seismic exploration, earthquake prediction and the study of lithosphere physics and dynamics, and lots of attention were focused on. For that, we discuss the evolution of the study on the seismic waves in elastic anisotropic medium in detail, and review the main achivements obtained home and abroad up to date, propose some main problems which appear in the study and are expected to be solved. In the last, we make some suggestion about the study of seismic wave motion, detection and it's application in anisotropic medium.
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