We use the improved Parker−Oldenburg's formulas that include a reference depth into the exponential term and employ the Gauss‐FFT method to determine Moho depth beneath the Tibetan Plateau. The synthetic models demonstrate that the improved Parker's formula has high accuracy with the maximum absolute error less than 0.25 mGal compared to the analytical solution. Two inversion parameters, i.e., the reference depth and the density contrast are essential for the Moho estimation based on the gravity field, and they need to be determined in advance to obtain correct results. Therefore, the Moho estimates derived from existing seismic studies are used to reduce the non‐uniqueness of the gravity inversion and to determine these parameters by searching for the maximum correlation between the gravity‐inverted and seismic‐derived Moho depths. Another critical issue is to remove beforehand the gravity effects of other factors, which affect the observed gravity field besides Moho variations. In addition to the topography, the gravity effects of the sedimentary layer and crystalline crust are removed based on existing crustal models, while the upper mantle impact is determined based on the seismic tomography model. The inversion results show that the Moho structure under the Tibetan plateau is very complex with the depths varying from about 30 ~ 40 km in the surrounding basins (e.g., Ganges basin, Sichuan basin, and Tarim basin) to 60 ~ 80 km within the plateau. This considerable difference up to 40 km on the Moho depth reveals the substantial uplift and thickening of the crust in the Tibetan Plateau. Furthermore, two visible “Moho depression belts” are observed within the plateau with the maximum Moho deepening along the Indus‐Tsangpo Suture and along the northern margin of Tibet bounding the Tarim basin with the relatively shallow Moho in central Tibet between them. The southern “belt” is likely formed in compressional environment, where the Indian plate underthrusts northwards beneath the Tibetan Plateau, while the northern one could be formed by the southward underthrust of the Asian lithosphere beneath Tibet.

An efficient forward modeling algorithm for calculation of gravitational fields in spherical coordinates is developed for 3‐D large‐scale gravity inversion problems. The 3‐D Gauss‐Legendre quadrature (GLQ) is used to calculate the gravitational fields of mass distributions discretized into tesseroids. Equivalence relations in the kernel matrix of the forward modeling are exploited to decrease storage and computation time. The numerical tests demonstrate that the computation time of the proposed algorithm is reduced by approximately 2 orders of magnitude, and the memory requirement is reduced by N′_λ times compared with the traditional GLQ method, where N′_λ is the number of the model elements in the longitudinal direction. These significant improvements in computational efficiency and storage make it possible to calculate and store the dense Jacobian matrix in 3‐D large‐scale gravity inversions. The equivalence relations can be applied to the Taylor series method or combined with the adaptive discretization to ensure high accuracy. To further illustrate the capability of the algorithm, we present a regional synthetic example. The inverted results show density distributions consistent with the actual model. The computation took about 6.3 hr and 0.88 GB of memory compared with about a dozen days and 245.86 GB for the traditional 3‐D GLQ method. Finally, the proposed algorithm is applied to the gravity field derived from the latest lunar gravity model GL1500E. Three‐dimensional density distributions of the Imbrium and Serenitatis basins are obtained, and high‐density bodies are found at the depths 10–60 km, likely indicating a significant uplift of the high‐density mantle beneath the two mascon basins.

The lunar mascon basins are characterized by high gravity anomalies and thin crust. Study of the density structure beneath the mascon basins can help to understand the origin of these gravity anomalies and infer their formation and evolution. We propose an efficient forward gravity method based on the 3‐D Gauss‐Legendre quadrature (GLQ) and Fast Fourier Transforms combined with the adaptive discretization strategy to ensure high accuracy. The numerical example demonstrates that computational efficiency is increased by about three orders of magnitude compared to the traditional 3D GLQ method. We employ this forward method in a 3‐D inversion of the gravity data derived from the lunar gravity model GL1500E. The inverted results show prominent high‐density structures (namely, mascons) representing significant mantle uplift and thinned crust beneath most impact basins. Marked low‐density rings surround the mascons. Most of the corresponding low‐density anomalies extend from the near‐surface to the Moho, indicating a thick, low‐density crust. Our density model is consistent with the formation processes of mascons that an impact causes collapse of the transient crater and then the shocked mantle drives mantle flow. The low‐density rings surrounding the mascons may stem from the crust thickening following an impact and extensive fracturing of the crustal column.

Three-dimensional gravity inversion has been widely used to infer density structures and tectonic movements of the earth and Moon. However, two problems (the nonuniqueness and low depth resolution) of current gravity inversion methods still exist and are not completely resolved, which affect the reliability of the inversion results and the corresponding geologic interpretation. To improve the depth resolution of the 3D gravity inversion, we propose an efficient inversion method in spherical coordinates based on a mixed smooth and focused regularization with depth-weighting functions. In the inversion, we also use the kernel matrix equivalence strategy and the fast kernel-vector multiplication method based on a fast Fourier transform in each iteration to increase computational efficiency. Two synthetic inversion examples indicate that the proposed method can recover more complex density structures compared with the often used smooth-constraint inversion approach. Finally, the proposed inversion approach is applied to the latest lunar gravitational field model GL1500E to study the 3D density structures of the Moscoviense Basin. The inverted results indicate that the density structure with high-positive anomalies is principally distributed at depths ranging from 5 to 70 km, forming a giant asymmetrical high-density structure inclining from the southwest to the northeast. We may conclude that the Moscoviense Basin was formed by the double impact, where the second collision occurred in the southwest of the basin center of the first collision.

In geophysical research, gravity-based inversion is essential for identifying geologic anomalies, mapping rock structures, and extracting resources such as oil and minerals. However, traditional gravity inversion methods face challenges, such as the volumetric effects of gravity fields and the management of large complex matrices. Unsupervised learning techniques often struggle with overfitting and interpreting gravity data. This study explores the application of various U-Net-based network architectures in gravity inversion, each offering distinct challenges and advantages. Nested U-Net, although effective, requires a high parameter count, leading to extended training periods. The recurrent residual U-Net’s implicit attention mechanism restricts its dynamic adaptability, whereas the attention U-Net’s lack of residual connections raises concerns about gradient issues. This research comprehensively analyzes the training processes, core functionalities, and module distribution of these networks, including the residual U-Net++. Our synthetic studies compare these networks with traditional focused regularized gravity inversion for reconstructing density anomalies. The results demonstrate that the nested U-Net closely approximates the actual model despite some redundancy. The recurrent residual U-Net indicates an improved alignment with minimal redundancies, and the attention U-Net is effective in density prediction but encounters difficulties in areas of low density. Notably, the residual U-Net++ excels in inversion modeling, achieving the lowest misfit percentage and accurately replicating density values. In practical applications, the residual U-Net++ impressively reconstructs the F2 salt diapir in the Nordkapp Basin with well-defined boundaries that closely match seismic data interpretations. These results underscore the capabilities of the residual U-Net++ in geophysical data analysis, structural reconstruction, and inversion, demonstrating its effectiveness in simulated settings and real-world scenarios.