Monitoring the migration and potential leakage of carbon dioxide (CO₂) is a critical part of carbon capture and storage (CCS). The most widely used monitoring technique is 4D seismic imaging, which involves examining subsurface formations at varying burial depths based on seismic waves, conducting seismic inversion of the acquired data, and then identifying alterations in subsurface structures. Therefore, a thorough understanding of the seismic responses to CO₂ injection and migration is essential, necessitating detailed analysis. In this study, the porosity and saturation parameters related to CCS are transformed into seismic parameters using the Hertz-Mindlin (HM) contact model initially. Then, an elastic wave equation is derived based on the porosity and saturation. To distinctly characterize seismic responses to variations in porosity and saturation, novel decoupled elastic wave equations are introduced. Using these equations, the wavefields and equations associated with porosity and saturation are separated into distinct terms. Through numerical simulation based on a portion of the Marmousi model, this study demonstrates that the proposed decoupled elastic wave equations can effectively identify seismic wavefields and data discrepancies induced by CO₂ migration, thereby enabling their applicability in subsequent inversion processes.