Quantitative estimate of VTI parameters from AVA responses

The influence of the vertical transverse isotropy (VTI) on amplitude versus angle (AVA) responses is first studied on the linearized formula of the PP-reflection coefficient. Up to medium angles of incidence, as in the isotropic case, only two quantities can be retrieved, the second with less accuracy than the first. These quantities are the P-impedance and the S-impedance multiplied by 1? δ/2, where δ is one of the two anisotropic parameters introduced by Thomsen. To extend these results to the exact formulae, the AVA analysis is then formulated as an inverse problem and a least-squares cost function is defined. A study of the eigenvalues and eigenvectors of the Hessian of the least-squares cost function confirms these results. Though these results are dependent on the amount of data and on the maximum angle of incidence available, they are appropriate for small and medium angles of incidence. Thanks to this inverse formulation, this work can be extended to the case of multicomponent AVA responses. The addition of PS-reflection data further constrains the problem, but the S-impedance and δ are still coupled. However, the addition of SS-reflection data gives an estimation of both P- and S-impedances and δ. The last two parameters, the density and the second anisotropic parameter ?, remain difficult to determine, at least with small-to-medium angular apertures.