Approximate PP reflection coefficient in TTI media

Abstract

The transversely‐isotropic (TI) media is the most common anisotropic media in sedimentary rock. When formations rotate, because of folding and thrusting, the symmetry axis of TI media is tilted instead of vertical or horizontal, which yields so‐called transversely‐isotropic (TTI) media with tilted symmetry axis. In this paper, based on plane wave theory, we derived the exact and approximate expressions of reflection coefficient of plane waves in two elastic TTI media under welded contact condition by generalizing the expressions of Aki and Richards, and Rüger. Based on displacement wave function, we established the Zeoppritz equation for incident qP wave in TTI media using boundary conditions of displacement continuity and strain continuity. According to weak anisotropy approximation and the theory of media decomposition, we derived the approximate reflection coefficient for incident qP wave in TTI media. The expressions have definite geophysical meanings and higher accuracy. The approximate expression of PP reflection coefficient indicates that VTI has no influence on its intercept, but has influence on the gradient, while TTI has influence on both the intercept and gradient.