Abstract:The anisotropy of medium is one of the significant factors which disturb amplitude variation with offset(AVO).The reflection and transmission coefficient expressions of plane waves in two elastic transversely-isotropic (TI) media under welded contact condition have been deduced by generalizing the expressions of Aki and Richards,and the approximate expressions of the coefficients in weak elastic TI medium are given in this article.The expressions have definite geophysical meanings and bring higher accuracy than others.The P-P approximate expression indicates that Thomsonsen's anisotropic parameter δdifference between upper and lower layers plays an important role in AVO when incident angle ranges from small degrees to middle degrees,but the difference of P-wave anisotropic parameter εp can have strong influence on AVO when incident angle is above 20 degrees.As far as P-P wave AVO fitting is concerned,TI doesn't affect zero-offset reflection coefficients,but causes direct influence on the "gradient".For three types of isotropic gas sand-stones(high impedance,near zero impedance contrast,and low impedance),we analyse the influence of TI overlying shale on P-P AVO.The research says that TI overlying shale may make a water-bearing sandstone exhibit better AVO phenomenon.