Time-lapse seismic monitoring plays a critical role in tracking the evolution of carbon dioxide (CO₂) plumes in geological storage. Most existing studies focus primarily on P-wave velocity and attenuation, while the contribution of S-wave responses is often neglected due to their relatively weak sensitivity to fluid saturation. However, seismic-wave propagation in viscoelastic media involves coupled compressional- and shear-wave responses, suggesting that S-wave–related effects may still influence time-lapse imaging and interpretation. In this study, we developed an integrated framework for CO₂ time-lapse monitoring by combining rock-physics modeling, viscoelastic wavefield simulation, and multicomponent reverse time migration. The framework accounts for both velocity and attenuation effects and enables a systematic investigation of S-wave responses, including S-wave velocity and attenuation (Q_S). To accurately describe wave propagation in such media, we derived a generalized standard linear solid-based viscoelastic wave equation with an explicit representation of the quality factor (Q), and employed reverse time migration to generate time-lapse seismic images. Using synthetic models, we analyzed the sensitivity of seismic attributes to CO₂ saturation and evaluated the impact of different Q_S modeling strategies on time-lapse imaging results. The results show that different Q_S assumptions lead to noticeable variations in amplitude and phase behavior, which can significantly affect the interpretation of CO₂-induced changes. These findings demonstrate that S-wave responses, particularly S-wave attenuation, should not be neglected in viscoelastic time-lapse seismic analysis. The proposed framework provides a physically consistent approach to improving the reliability of CO₂ monitoring.