A Density-Weighted and Cross-Gradient Constrained Joint Inversion Method of Gravity and Vertical Gravity Gradient Data in Spherical Coordinates and Its Application to Lunar Data

The gravity gradient data have higher horizontal resolution and highlight the shallow sources relative to gravity data; therefore, the comprehensive measurement of gravity and its vertical gradient anomalies is commonly used to reveal the density structure of planets. To obtain higher resolution density results by the joint inversion of large-scale gravity and its gradient, we propose a density-weighted and cross-gradient constrained (DWCG) joint inversion method in the sphere coordinate, which improves the inversion accuracy by introducing a density structural constraint provided by the gravity inversion result. Furthermore, the block-Toeplitz Toeplitz-block (BTTB) structure is used to finish the DWCG joint inversion, which effectively accomplishes a high-efficiency calculation and is more practical for performing the inversion of large-scale data. Theoretical modeling experiments show that the DWCG joint inversion method can effectively improve the resolution and identify the distribution of deep and shallow field sources, and the accuracy is improved by nearly 40% compared to the regularization inversion method of gravity data. Simultaneously, the DWCG joint inversion method has certain noise immunity. Finally, we apply the DWCG joint inversion method to the lunar data to obtain the density distribution and further revealed the Moho relief by nonlinear inversion based on the density results. The results show that the high-density structure corresponds to the uplift of the mantle, and a large number of meteorite impacts caused mantle flow, which is shown as a clear impact basin and ring anomaly on the topography and anomaly map.