Abstract: Seismic impedance is an important parameter reflecting lithology and can be obtained via post-stack seismic inversion.The regularization method based on the L₁ norm sparse constraint is a typically used post-stack inversion algorithm; nonetheless, the prior information yielded by this method is limited.Two key technologies based on the L_p quasi-norm (0 < p < 1) sparse constraint and an alternating direction multiplier are introduced to mine more prior information and further improve the inversion accuracy.To address the insufficient mining of sparse prior information, the former technology uses the L_p quasi-norm (0 < p < 1), which is sparser than the L₁ norm as a sparse constraint and adds the initial model constraint to form the objective function.As the L_p quasi-norm cannot be solved, the alternating direction multiplier is used to decompose the objective function into multiple sub-objective functions that can be solved directly and then alternately.The proposed inversion method is applied to a theoretical model and actual data.Compared with the conventional basis pursuit inversion algorithm using the L₁ norm sparse constraint, the proposed method yields more accurate inversion results and exhibits anti-noise properties.