Abstract: The ratio of compressional to shear wave velocities(hereafter referred to as the P-to-S-wave velocity ratio) is an essential parameter for lithology discrimination,reservoir characterization,and gas reservoir identification.Direct inversion of PP-wave seismic data to derive the P- and S-wave velocities has been a well-established technique.However,calculating the P-to-S-wave velocity ratio using the P- and S-wave velocities obtained through individual inversion may lead to cumulative errors.In contrast,since PS-wave data inherently contain S-wave velocity information,the joint inversion of PS-wave data can significantly improve the accuracy of the P-to-S-wave velocity ratio.This study employed the L_1-2 norm to enhance the resolution of inversion results.Compared to the L₁ and L₂ norms,the L_1-2 norm yielded sparser solutions with higher resolution.First,this study derived and assessed the accuracy of linearized forward modeling approximate formulas for PP- and PS-waves.Second,based on Bayesian theory,this study incorporated the L_1-2 norm to construct an objective function for the direct inversion of the P-to-S-wave velocity ratio.Third,the objective function was solved to obtain the inversion result for the P-to-S-wave velocity ratio.The quantitative comparison of the correlation coefficients demonstrates that the inversion results based on the L_1-2 norm outperform those based on the L₁ or L₂ norm,direct inversion is superior to indirect inversion,and joint inversion provides better results than individual inversion.Finally, the effectiveness and feasibility of the proposed method in this study were validated through inversions of synthetic and field data.