Joint PP–PS multi-objective inversion based on exact reflection coefficients in VTI media

With the rapid progress of unconventional oil and gas exploration, detailed characterization of reservoir anisotropy has emerged as a key focus in seismic inversion studies. Traditional pre-stack inversion approaches that rely on approximate reflection coefficient equations often yield biased results at wide incidence angles, limiting their ability to provide high-precision parameter estimates for complex reservoirs. In this work, we develop a joint PP–PS multi-objective inversion strategy based on the exact reflection coefficient formulation for vertical transverse isotropy (VTI) media. To overcome the heavy reliance on weighting factors in joint inversion, we adopt improved Strength Pareto Evolutionary Algorithm (SPEA-Ⅱ) into multi-objective evolutionary optimization algorithm. This allows simultaneous optimization of PP and PS objective functions without predefined weights, significantly mitigating solution non-uniqueness. Synthetic experiments confirm that the method reliably recovers model parameters under both noise-free and low signal-to-noise ratio (SNR) conditions. The inclusion of PS-wave data greatly enhances inversion accuracy, with notable improvements in thin-bed scenarios and structurally complex models. Tests on the 2D Marmousi-VTI model further validate the method's superiority in preserving lateral continuity and improving resolution. Application to field data shows that the proposed approach yields more accurate estimates of both elastic and anisotropic parameters compared with approximate-equation-based methods. The proposed PP–PS joint inversion method, grounded in the exact reflection coefficient formulation for VTI media, exhibits both theoretical rigor and practical applicability, providing a promising pathway for high-resolution exploration of unconventional reservoirs.