Abstract: Multi-wave seismic exploration offers distinct advantages in lithology identification, reservoir characterization, and gas-bearing property prediction. However, due to different propagation mechanisms of compressional waves (P-waves) and shear waves (S-waves), the same geological interface often exhibits different kinematic and dynamic characteristics in reflected compressional wave (PP-wave) and converted shear wave (PS-wave) data. This makes high-precision PP-PS data registration challenging, especially when the target formation exhibits weak internal signals. By constructing pseudo-S-waves similar to PS-waves, PP- and PS-data are first matched on a large scale. Dynamic sliding time windows are then employed for local automatic fine matching, ultimately achieving accurate registration of PP- and PS-waves within the target formation. On this basis, relative S-impedance is calculated using the PS-data to construct an initial 3D lithofacies volume, which is then used as a constraint to perform facies-controlled geostatistical inversion on the PS-data, resulting in a high-precision 3D lithofacies volume. This lithofacies volume serves as a constraint for facies-controlled geostatistical inversion on the PP-data to obtain facies-controlled P-impedance volume. Inverted P-impedance is combined with S-impedance to calculate P- to S-velocity ratio, thereby enabling effective reservoir and gas predictions. This progressive, facies-controlled multi-wave joint prediction method enhances the accuracy of reservoir and gas predictions. Verification well results show small errors between predicted and measured values for reservoir thickness and gas-bearing property, demonstrating the effectiveness of the proposed method.