For water dynamics investigation in unsaturated (vadose) zones, ground penetrating radar is a popular hydro-geophysical method because it is non-invasive for soil, has high resolution and the results have a direct link with water content. Soil water content and soil hydraulic properties are two key factors for describing the water dynamics in vadose zones. There has been tremendous progress in soil water content and soil hydraulic properties estimation with ground penetrating radar. The purpose of this paper is to provide an overview of the application of ground penetrating radar for soil water dynamics studies. This paper first summarizes various methods for the determination of soil water content. including traditional methods in the surveys of surface ground penetrating radar, borehole ground penetrating radar, and off-ground ground penetrating radar, as well as relatively new methods, such as full waveform inversion, the average envelope amplitude method, and the frequency shift method. This paper further provides a review for estimating soil hydraulic properties with GPR according to the types of ground penetrating radar data. We hope that this review can provide a reference for the application of ground penetrating radar in soil water dynamics studies in the future.

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.

Since polymetallic ores show higher anomalies in gravity exploration methods, we usually obtain the position and range of ore bodies by density inversion of gravity data. The three-dimensional (3D) gravity focusing density inversion is a common interpretation method in mineral exploration, which can directly and quantitatively obtain the density distribution of subsurface targets. However, in actual cases, it is computation inefficient. We proposed the preconditioned Jacobian-free Newton-Krylov (JFNK) method to accomplish the focusing inversion. The JFNK method is an efficient algorithm in solving large sparse systems of nonlinear equations, and we further accelerate the inversion process by the preconditioned technique. In the actual area, the gravity anomalies are distributed on the naturally undulating surface. Nowadays, the gravity inversion under undulating terrain was mainly achieved by discretizing the ground into unstructured meshes, but it is complicated and time-consuming. To improve the practicality, we presented an equivalent-dimensional method that incorporates unstructured meshes with structured meshes in gravity inversion, and the horizontal size is determined by the gradient of observed gravity and terrain data. The small size meshes are adopted at the position where the terrain or gravity gradient is large. We used synthetic data with undulating-terrain to test our new method. The results indicated that the recovered model obtained by this method was similar to the inversion method of unstructured meshes, and the new method computes faster. We also applied the method to field data in Huayangchuan, Shaanxi Province. The survey area has complicated terrain conditions and contains multiple polymetallic ores. Based on the high-density characteristics of polymetallic ore bodies in the area, we calculate the field data into 3D density models of the subsurface by the preconditioned JFNK method and infer six polymetallic ores.

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.