TTI介质qP波入射精确和近似反射透射系数

Exact and approximate reflection and transmission coefficient for incident qP wave in TTI media

介质各向异性是影响振幅随炮检距变化(AVO)的重要因素之一.本文将Aki和Richards以及Rüger的方法进行推广,推导出两个弹性倾斜横向各向同性(TTI)介质密接条件下平面波反射和透射系数及其近似式.从位移波函数出发,利用位移连续和应力连续边界条件,建立了TTI介质qP波入射的拟Zoeppritz方程,求解得到精确反射透射系数.在此基础上,利用弱各向异性近似和介质分解理论,推导了TTI介质qP波入射近似的反射透射系数.近似式的物理意义明确,而且精度较高.PP反射系数近似式表明,垂直横向各向同性(VTI)不影响P-P波反射系数的截距(入射角为0时的反射系数),只对梯度有直接影响;而TTI既影响截距,又影响梯度.对于VTI介质,各向异性参数δ控制小角度反射系数,而ε影响大角度入射.但是对于TTI介质,参数ε和δ对小角度反射系数和大角度反射系数都有影响.

Anisotropy of media is one of the key factor of influence on amplitude vs offset （AVO）. This paper derived the exact and approximate reflection and transmission coefficient expressions of plane waves in two elastic transversely-isotropic （TTI） media with tilted symmetry axis under welded contact condition by extending the expressions of Aki and Richards, and Rüger. Based on displacement wave fuction, we establish the quasi Zoeppritz equation for incident qP wave in TTI media using boundary condition of displacement continuation and stress continuation, and obtain the exact solutions. According to weak anisotropy approximation and the theory of media decomposition, we derive the approximate reflection and transmission coefficient for incident qP wave in TTI media. The expressions have definite geophysical meanings and bring higher accuracy than others. The P-P approximate expression indicates that the vertical transversely-isotropic （VTI） has no influence for the intercept of PP reflection coefficient （reflection coeffient when incident angle equals zero）, but has influence for the gradient of PP reflection coefficient. TTI has influence for the intercept and gradient of PP reflection coefficient. For VTI meida the parameter δ controls the small-angle reflection coefficient, while ε becomes influential at larger incidence angle. But for TTI media, the parameter ε and δ are all influential at both small and larger incidence angle reflection coefficient.