This paper investigates the combined application of seismic inversion and migration for processing seismic data in the depth domain. Seismic inversion serves as a widely used practical tool allowing the derivation of detailed subsurface models from seismic data. In this study, we implement a constrained total variation inversion algorithm. The inversion input data comprise true-amplitude depth imaging results along with the depth migration velocity model. Furthermore, we develop and examine an iterative algorithm that jointly performs acoustic seismic inversion and depth migration. This approach aims to refine high-frequency and smooth low-frequency components of the depth velocity model. We validate our methods through numerical experiments using both synthetic data and a realistic Marmousi model.