The cross-gradient joint inversion of gravity and magnetic data is a commonly used way, which requires dividing the subsurface into closely arranged cells with structured or unstructured grids to solve the physical properties of the discrete subsurface. Unstructured grids can more effectively fit undulating terrain and irregular geological bodies than structured grids. However, the existing cross-gradient joint inversion method with structured grids cannot be used to complete the inversion with unstructured grids. We proved that the second-order Taylor formula is more suitable for calculating the cross-gradients of unstructured grids; therefore, we first proposed and implemented the second-order Taylor formula cross-gradient (2-TCG) method for the cross-gradient joint inversion of gravity and magnetic data with unstructured grids, which can calculate the cross-gradient item more easily than other ways because the first few coefficients of Taylor formula are gradient items. The model tests showed that the 2-TCG joint inversion method can accurately achieve the 3-D joint inversion of gravity and magnetic data with unstructured grids, and this method can better describe the detailed information of irregular geological bodies in complex terrain. To explore the minerals and analyze the metallogenic model in the Huanggang–Ganzhuermiao metallogenic belt of the southern Greater Khingan Range, Inner Mongolia, we measured gravity and magnetic data on a scale of 1:10000. We estimated the mineral distributions with 150–280 m depth by 2-TCG joint inversion. We analyzed the relationship between ore bodies and faults, and we established a mixed metallogenic model of the skarns and hydrothermal veins in the survey area.

The subsurface density and magnetization distribution obtained from joint inversion of gravity and magnetic data could map ore distribution. In order to consider irregular terrain, irregular geological body and remanent magnetization, the gravity and magnetic joint inversion scheme developed here employs tetrahedral unstructured grid. We also employ a volume weighting function in order to improve the convergence of the scheme. Model comparison showed that the developed method with volume weighting function can yield accurate density and magnetization inversion results. The tetrahedral unstructured grid with small volume differences has a higher inversion resolution than that of prismatic structured grid. The method has been applied to gravity and magnetic data from the Huanggangliang-Ganzhuermiao metallogenic belt from mineral exploration. We predicted the favorable area for mineralization in the survey area according to the characteristics of the known deposits, and the favorable mineralization areas are mainly distributed along the faults. Combined with the analysis of deep inversion results, we found that the Baiyinnuoer and Shuangjianzishan mineral deposits have the same metallogenic material source, and the magma migrated upward along the Y-shaped magma channel. Therefore, it was speculated that the difference of these two deposits was caused by the different migration structural environments.

Airborne magnetic and gradient measurements are commonly used geophysical remote sensing tools to obtain the distribution features of ore mineral bodies. It is known that ore mineral bodies generally contain remanent magnetization, and magnetization vector inversion (MVI) can produce the magnetization intensity and direction of the source, which is more suitably used to interpret measured airborne magnetic and gradient data. To accurately reveal the underground magnetization vector distribution, we proposed a high-precision method with double constraints on the data and physical structure, and we used the cross-gradient inversion of airborne magnetic anomalies and the combination matrix of airborne magnetic and gradient (CMG) data to recover the physical parameters of the sources with different depths. We used the combination matrix to produce the different component data constraints and the cross-gradient function to finish the inversion to provide structural constraints. For anomaly sources at similar depths, joint inversion based on the cross-gradient of magnetic gradient data and CMG data is more suitably used. The superiority of the double constraints method is proven by theoretical model tests. We apply the proposed method to interpret airborne magnetic and gradient data in Shandong Province to detect iron mineral resources, and we select the cross-gradient inversion of airborne magnetic anomalies and CMG data depending on the nonlinear features of the power spectrum. The main ore bodies have a northeast distribution with a depth range of 1048–1800 m, successfully giving the distribution range of the high-magnetic bodies; a better mineral potential is in the northern part of the survey area.

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.

Gravity and magnetic measurements are common remote sensing strategies to obtain the property change of observed targets. Nowadays, the characteristic value of the derivatives of gravity and magnetic anomalies is commonly used to detect the source horizontal edge. We found that the horizontal coordinates of the characteristic value of different-order derivatives are not directly corresponding to the edge of the source, which varies with the depth and size of the source. The spatial different-order derivative (SDD) method of gravity and magnetic anomalies was developed, and we proved that the spatial intersection of different-order derivatives is corresponding to the location of the source, and used this feature to obtain horizontal location and depth of the source simultaneously. The model tests proved that the SDD method has high accuracy and strong anti-noisy. According to the corresponding relationship between the potential field data and lithology, we used the SDD method to delineate the potential metalorganic area in the survey region, which provides the basis for subsequent exploration.