To reduce the ill-posedness of seismic full waveform inversion,a common method is to introduce prior information to regularize the inversion problem.Traditional regularization methods still face challenges even when they contain multiple prior information.This study proposed an extended full waveform inversion formula,which includes the convex set constraints on models.Specifically,this study showed how to constrain the total variation of the slowness square while forcing the constraint to keep it within a physical reality range.To verify the applicability of the algorithm proposed in this study,numerical experiments on simple models and international standard geological models were carried out.The results show that the introduction of total variation regularization can improve the reconstruction of high-speed disturbances under smooth background models.