P‐wave reflection coefficients for transversely isotropic models with vertical and horizontal axis of symmetry

Abstract

The study of P‐wave reflection coefficients in anisotropic media is important for amplitude variation with offset (AVO) analysis. While numerical evaluation of the reflection coefficient is straightforward, numerical solutions do not provide analytic insight into the influence of anisotropy on the AVO signature. To overcome this difficulty, I present an improved approximation for P‐wave reflection coefficients at a horizontal boundary in transversely isotropic media with vertical axis of symmetry (VTI media). This solution has the same AVO‐gradient term describing the low‐order angular variation of the reflection coefficient as the equations published previously, but is more accurate for large incidence angles. The refined approximation is then extended to transverse isotropy with a horizontal axis of symmetry (HTI), which is caused typically by a system of vertical cracks. Comparison of the approximate reflection coefficients for P‐waves incident in the two vertical symmetry planes of HTI media indicates that the azimuthal variation of the AVO gradient is a function of the shear‐wave splitting parameter γ, and the anisotropy parameter describing P‐wave anisotropy for nearvertical propagation in the vertical plane containing the symmetry axis.