Efficient L1–TV1 Inversion of the Vertical Gravity Gradient With Application to the Vinton Salt Dome

Achieving high depth resolution while accurately recovering sharp structural boundaries presents a significant challenge in gravity gradient inversion. This study addresses this issue by employing an L1–TV1 regularization framework for the interpretation of vertical gravity-gradient data, which combines the L1 norm of the model with the L1 norm of the of the model gradients (TV1). To balance model sparsity and structural smoothness and to improve depth resolution, we introduce four weighting factors. The resulting objective function is solved efficiently using the Alternating Direction Method of Multipliers (ADMM). Model experiments demonstrate that this method successfully delineates causative bodies while preserving sharp structural boundaries. The method is then applied to airborne gravity-gradient data from the Vinton Dome in southern Louisiana, U.S. The inverted density model reveals a dense rock cap at depths of 300–700 m, exhibiting a density contrast of approximately 0.7 g/cm³. Beneath this cap, a large salt dome is imaged, centered at depths of 2300–4900 m, with a density contrast of about -0.2 g/cm³. The recovered density structure provides a more realistic representation of the deep salt body, characterized by geologically plausible geometry and clear boundaries that closely align with known geological constraints. These results highlight the practical utility of the proposed method for detailed subsurface imaging of complex salt structures.