Joint AVAZ Inversion of PP-, PS1-, and PS2-Waves Based on Linearized Reflection Coefficients of HTI Media

Azimuthal reflection coefficients provide essential information for estimating anisotropic parameters in transversely isotropic media with a horizontal symmetry axis (HTI). The joint utilization of azimuthal PP-, PS1-, and PS2-wave reflection coefficients enhances the sensitivity to fracture parameters and increases the computational complexity. To address this issue, we derived analytical linearized azimuthal reflection coefficients for PP, PS1, and PS2 waves, expressed with respect to isotropic background parameters and fracture weaknesses defined by linear-slip theory. For the split P-to-S converted (PS) wave, we first derived the linearized PSV and PSH reflection coefficients under the Born approximation. By applying a polarization correction to rotate the SV and SH waves into the split S-wave basis, we obtained general linearized PS1 and PS2 reflection coefficients, which are applicable for arbitrary observation azimuths and are free from small-angle restrictions. The derived coefficients and Sobol’s global sensitivity analysis confirmed that PS1 and PS2 reflections were considerably more sensitive to fracture parameters than were PP reflections. Accuracy tests using HTI two-layer models showed that our approximations closely matched the exact solutions and outperform Rüger’s linearized equations across incident angles. Furthermore, a joint azimuthal Bayesian inversion method using PP-, PS1-, and PS2-wave data was developed to efficiently estimate the fracture parameters. Synthetic tests demonstrated that the proposed multimode inversion significantly enhanced the reliability and stability of fracture-parameter estimation, reducing uncertainty and improving confidence compared with PP-only inversion. Ocean-bottom node (OBN) field data examples further confirmed the effectiveness of the proposed method.