Elastic impedance in weakly anisotropic media

The original formulation for the P-wave elastic impedance (EI) equation ignores seismic anisotropy. Incorporation of anisotropy effects into the El formula requires a suitable approximation for reflection coefficients. In order to derive an anisotropic El equation, this paper uses an approximation for PP-wave reflection (R-PP) coefficients which holds for weak-contrast interfaces separating weakly anisotropic media of arbitrary symmetry. Inserting the chosen R-PP coefficient approximation into the original formalism provides an anisotropic El formula, which is written as a product of two terms: a modified version for the isotropic El equation and a correction because of weak anisotropy. The latter term shows dependence of the anisotropic El formula on the so-called weak anisotropy (WA) parameters, on a reference isotropic medium, and on the azimuthal and incident phase angles. Numerical tests show the performance of the El formula in calculating anisotropic R-PP coefficients and in constructing azimuthal far-offset El logs. Since El allows applying poststack algorithms without modification, an inversion methodology can be designed for investigating anisotropy in sedimentary formations.