A novel approximate formula on AVAZ of reflection and transmission qP in TTI media

Abstract

This paper introduces a relational formula about crack density, crack-fill and stiffness tensor of the TI medium, and offers the relationship between anisotropic parameters and the weaknesses. We then deduce the approximate formula for the phase velocity in weakly anisotropic media on the basis of the phase velocity solved by the Christoffel equation. According to the polarization in VTI media, we establish the polarization in TTI media. Assuming that qP, SH and qS waves occur simultaneously at the anisotropic interface, simplify the 6-order Zoeppritz and deduce the explicit AVAZ formula. According to the deduced AVO formula, we analyze the anisotropic characterization of qP waves and discover that if we want to accomplish the inversion of anisotropic parameters, the incidence angle should be over 150. Also comparing the approximate curve of qP wave with the exact curve of qP wave, we discuss the effects of the azimuthal and dip angles on the approximate curve and conclude that if the azimuthal angle is around 450 or/and the dip angle is approaching 900, the error between the approximate and exact curves is becoming large. Additionally, we offer the formula of the crack parameters and the weaknesses, which indirectly shows the effects of the crack parameters on the AVAZ formula.