Post-Stack Seismic Inversion with Non-Convex Total Generalized Variation Regularization

Post-stack seismic inversion can reconstruct high-resolution acoustic impedance (AI) models from band-limited and noisy seismic reflections, which is crucial for identifying underground structures and characteristics. Traditional regularization methods, including total variation (TV) and total generalized variation (TGV), are prone to oversmoothing and staircase artifacts, thereby limiting their effectiveness in complex geological environments. In this paper, we introduce a novel regularization method based on non-convex TGV (NCTGV), which integrates the classical TGV regularization into a convex non-convex framework. This integration enables the model to simultaneously promote sparsity and preserve higher-order structural continuity. The resulting seismic inversion model was effectively solved using the alternating direction method of multipliers (ADMM), with a provably convergent scheme adapted to the NCTGV structure. Numerical experiments demonstrated the improved performance of the proposed technique. Compared to existing regularization techniques such as TV, NCTV, and TGV, the NCTGV method achieved lower root-mean-square error (RMSE). It also obtained higher peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) scores, together with enhanced vertical resolution. Visual inspection confirmed that the NCTGV-inverted impedance models exhibited clearer stratigraphic boundaries and sharper geological features.