Revisiting the Normalized Attenuation Coefficients of Plane P- and SV-Waves in Attenuative VTI Media and Their Effects on Parameter Inversion

Analytical formulae for P- and SV-wave normalized attenuation coefficients play a key role in attenuation anisotropy parameter estimation in dissipative transversely isotropic media with a vertical symmetry axis. We revisit approximate formulae for the P- and SV-wave normalized attenuation coefficients. We use perturbation theory to derive accurate formulae for P- and SV-waves in such media. The proposed formulae can reduce to simple expressions for attenuative elliptical anisotropic media and isotropic media. From the perturbation-based formulae, we obtain the linearized formulae, the second-order formulae and the fractional formulae. We use numerical examples to test the accuracy of the proposed formulae and implement the perturbation-based formulae and the second-order formulae in an inversion scheme to estimate the attenuation anisotropy parameters. From the numerical examples, we analyse the validity of the approximate formulae in computing the normalized attenuation coefficients and attenuation anisotropy parameter estimation.