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.

The three-direction magnetization intensities of a source can be obtained by the magnetization vector inversion (MVI) of magnetic data, and therefore MVI can be well applied to a magnetic anomaly with remanence. However, MVI exhibits poor applicability attributed to its low computational efficiency for a data with large area and undulating terrain. We proposed a discrete function (DF) method to improve the efficiency of MVI, which is suitable for uniform hexahedron mesh and unstructured tetrahedral mesh. In this method, DF was used to fit the magnetization vectors of a given number of cells, and the computation of the physical properties of the cells was replaced by the computation of function coefficients, and the memory and calculation time were reduced, as the number of function coefficients was less than the number of cells. The Gramian constraint item in MVI could be directly computed by function coefficients without increasing the computation process. For uniform hexahedron mesh, the integration of DF with block-Toeplitz-Toeplitz-block-fast Fourier transform (DF–BTTB-FFT) method can further improve the inversion efficiency. The model tests revealed that the DF method could reduce the storage and computation time by approximately five times without precision loss, and DF – BTTB-FFT method could achieve approximately four times improvement compared with DF method. Finally, the proposed DF method was used to accomplish the MVI of real magnetic anomaly and its gradient data in Shaanxi Province to delineate the range of the subsurface burned zone, and the distribution was ascertained by combining the nuclear magnetic water measurements.

The three-dimensional inversion of geophysical data is an effective method for analyzing underground structures. The seismic method is widely used due to its high resolution. However, the uneven distribution of seismic stations, especially in offshore areas, increases the uncertainty of inversion results. Gravity data are easy to obtain and offer high lateral resolution. For the influence of the Earth’s curvature in large-scale inversion, we first developed the joint inversion method of seismic ambient noise and gravity data in the ellipsoidal coordinate system, achieving the acquisition of large-scale and high-precision underground density and velocity structures. Experiments were conducted to address the uneven distribution of seismic stations, which proved the accuracy of the method. The proposed method was applied to the Jiaodong Peninsula (China) to obtain the transcrustal property distribution, further revealing that gold deposits are formed by the upwelling and condensation of hydrothermal materials, which causes the destruction of the North China Craton caused by the subduction of the Western Pacific Plate. Furthermore, we inverted the high-precision gravity anomaly of Sanshan Island, obtaining the structural distribution and predicting the distribution of offshore gold deposits.

The aeromagnetic survey is a common remote sensing tool for detecting iron deposits. The local wavenumber of a magnetic anomaly is used to interpret the edges or positions of the sources, and can involve first- or second-order local wavenumbers. In this paper, we derived a linear equation between the second-order local wavenumber and the source location; therefore, we propose a constraint of first and second-order local wavenumbers. Tests on synthetic data show that the source parameters, computed using a combination of equations that involved different-order local wavenumbers, are closer to the true values and show a smaller spread in estimated values. For gridded data, we proved that the different-order combination allowed us to accurately estimate the source position. When applied to the aeromagnetic data from Hebei province, China, we refined the location of most magnetic features, which we interpreted as possible iron deposits.

Considering the effect of remanence, the magnetization vector inversion method can recover three orthogonal components of the total magnetization vector using the magnetization intensity as a constraint, which makes it a more practical approach for the inversion of magnetic. However, inversion precision is relatively low when the magnetization directions of adjacent geologic bodies differ significantly. Based on the characteristic that the normalized source strength (NSS) is weakly sensitive to the magnetization direction, NSS was adopted instead of magnetization intensity to constrain the three orthogonal components. To address magnetic anomalies arising from the superposition of multiple magnetization directions, a geometric-shape-based partitioning method was further developed to realize high-precision magnetization vector inversion constrained by NSS; this approach is termed the NSS-GSC inversion method. Synthetic tests showed that the NSS-GSC inversion method yielded more accurate inversion results compared with the magnetization intensity method and exhibited good antinoise performance. The NSS-GSC method was applied to the Huanggangliang–Ganzhuermiao metallic ore cluster in China to obtain the distribution of high magnetization bodies located near NE- and NW-trending faults, with top depths ranging from 178 to 384 m. This provided robust evidence for further mineral exploration.

The Antarctic continental margin, a critical transition zone between thin continental and incipient oceanic crust, preserves vital records of lithospheric extension and rupture, crucial for reconstructing Antarctica's ancient configuration. Extensive ice cover and extreme environments restrict the obtainable geological and ground‐based data. Although airborne and satellite gravity‐magnetic data are essential tools for Antarctic studies, their integration with sparse outcrops remains hindered for interpretational ambiguity. Magmatic rifting alters crustal density and magnetization while preserving remanent magnetism, facilitating continent‐ocean boundary (COB) identification. We develop a high‐precision and fast inversion method to obtain density and magnetization structures following subduction and fragmentation. Magma intrusions in the Antarctic Peninsula and Dronning Maud Land exhibit 20° and −120° magnetization directions, respectively, at 10–30 km depths, reveal differential tectonic patterns along the margin. The refined COB highlights how subduction and extension shape continental margins, offering new insights into geodynamics and plate evolution under global climate change.