Gravity inversion using L0 norm for sparse constraints

Gravity surveys constitute an important method for investigating the Earth’s interior based on density contrasts related to Earth material differentials. Because lithology depends on the environment and the period of formation, there are generally clear boundaries between rocks with different lithologies. Inversions with convex functions for approximating the L₀ norm are used to detect boundaries in reconstructed models. Optimizations can easily be found because of the convex transformations; however, the volume of the reconstructed model depends on the weighting parameter and the density constraint rather than the model sparsity. To determine and adapt the modelling size, a novel non-convex framework for gravity inversion is proposed. The proposed optimization aims to directly reduce the L₀ norm of the density matrix. An improved iterative hard thresholding algorithm is developed to linearly reduce the L₀ penalty during the inner iteration. Accordingly, it is possible to determine the modelling scale during the iteration and achieve an expected scale for the reconstructed model. Both simple and complex model experiments demonstrate that the proposed method efficiently reconstructs models. In addition, granites formed during the Yanshanian and Indosinian periods in the Nanling region, China, are reconstructed according to the modelling size evaluated in agreement with the magnetotelluric profile and density statistics of rock samples. The known ores occur at the contact zones between the sedimentary rocks and the reconstructed Yanshanian granites. The ore-forming bodies, periods, and processes are identified, providing guidance for further deep resource exploration in the study area.