Conventional Euler deconvolution is widely used for interpreting profile, grid, and ungridded potential field data. The Tensor Euler deconvolution applies additional constraints to the Euler solution using all gravity vectors and the full gravity gradient tensor. These algorithms use a series of different-sized moving windows to yield many solutions that can be employed to estimate the source location from the entire survey area. However, traditional discrimination techniques ignore the interrelation among the Euler solutions, so they cannot be employed to separate adjacent targets. To overcome this difficulty, we introduced multivariate Kernel Density Derivative Estimation (KDDE) as an extension of Kernel Density Estimation, which is a mathematical process to estimate the probability density function of a random variable. The multivariate KDDE was tested on a single cube model, a single cylinder model, and three composite models consisting of two cubes with various separations using gridded data. The probability value calculated by the multivariate KDDE was used to discriminate spurious solutions from the Euler solution dataset and isolate adjacent geological sources. The method was then applied to airborne gravity data from British Columbia, Canada. Then, the results of synthetic models and field data show that the proposed method can successfully locate meaningful geological targets.

In the inverse problem, the traditional way to obtain a stable solution is based on the maximum smoothness criteria. However, this approach cannot generate clearer and more focused images. In this study, we propose an improved inversion method based on the smoothness constraints. In the algorithm, the model weighting functions are updated by adding a model’s total gradient module matrix, which can effectively constrain the boundary of the recovery model in the iterative operation. We invert the 3D magnetization intensity for the three-component magnetic data in the spatial domain by spherical coordinates. The preconditional conjugate gradient algorithm is introduced to improve the efficiency of the solutions. We design two sets of synthetic examples to evaluate the inversion effects, which show that the improved method is more reliable than the smoothness constraint method. The boundary of the magnetic bodies is more precise, and the magnetization ranges are more focused. The method does not rely on the initial model and is suitable for magnetic vector data inversion. We also apply the algorithm to a set of Dabie orogen three-component magnetic data derived from a geomagnetic field model and verify the effectiveness of the inversion method.

For regional or even global geophysical problems, the curvature of the geophysical model cannot be approximated as a plane, and its curvature must be considered. Tesseroids can fit the curvature, but their shapes vary from almost rectangular at the equator to almost triangular at the poles, i.e., degradation phenomena. Unlike other spherical discrete grids (e.g., square, triangular, and rhombic grids) that can fit the curvature, the Discrete Global Grid System (DGGS) grid can not only fit the curvature but also effectively avoid degradation phenomena at the poles. In addition, since it has only edge-adjacent grids, DGGS grids have consistent adjacency and excellent angular resolution. Hence, DGGS grids are the best choice for discretizing the sphere into cells with an approximate shape and continuous scale. Compared with the tesseroid, which has no analytical solution but has a well-defined integral limit, the DGGS cell (prisms obtained from DGGS grids) has neither an analytical solution nor a fixed integral limit. Therefore, based on the isoparametric transformation, the non-regular DGGS cell in the system coordinate system is transformed into the regular hexagonal prism in the local coordinate system, and the DGGS-based forwarding algorithm of the gravitational field is realized in the spherical coordinate system. Different coordinate systems have differences in the integral kernels of gravity fields. In the current literature, the forward modeling research of polyhedrons (the DGGS cell, which is a polyhedral cell) is mostly concentrated in the Cartesian coordinate system. Therefore, the reliability of the DGGS-based forwarding algorithm is verified using the tetrahedron-based forwarding algorithm and the tesseroid-based forwarding algorithm with tiny tesseroids. From the numerical results, it can be concluded that if the distance from observations to sources is too small, the corresponding gravity field forwarding results may also have ambiguous values. Therefore, the minimum distance is not recommended for practical applications.

Physical property inversion techniques are the methods to reveal the internal structures of Earth’s lithosphere. In this study, we introduce an Occam-type inversion algorithm into a spherical coordinate system, and invert the magnetization based on the three-component magnetic anomalies. The synthetic model tests show that the inversion effects of the vertical components are relatively stable, while the anti-noise ability is strong. We apply the algorithm to a set of vertical component anomalies derived from the satellite magnetic field model and obtain Dabie orogen 3D magnetization distribution. Multiple magnetic sources are identified within the orogen and adjacent areas, and the related tectonic evolution processes are analyzed. The significant magnetization characteristics of the orogen can be associated with mantle upwelling caused by the Early Cretaceous lithospheric delamination, along with the partial melting of the mafic–ultramafic lower crust that had not participated in the delamination. The magnetic sources near the Mozitan–Xiaotian fault, and those located in the western Dabie area, are also restricted by Mesozoic and Jurassic–Cretaceous deep melt activities, respectively. The study provides evidence for the suture line position of the plate subduction in the deep lithosphere. Furthermore, the results display certain indications of mineralization activities in the middle–lower Yangtze Valley metallogenic belt.

In large-scale potential field data inversion, constructing the kernel matrix is a time-consuming problem with large memory requirements. Therefore, a spherical planting inversion of Gravity Recovery and Interior Laboratory (GRAIL) data is proposed using the L1-norm in conjunction with tesseroids. Spherical planting inversion, however, is strongly dependent on the correct seeds’ density contrast, location, and number; otherwise, it can cause mutual intrusion of anomalous sources produced by different seeds. Hence, a weighting function was introduced to limit the influence area of the seeds for yielding robust solutions; moreover, it is challenging to set customized parameters for each seed, especially for the large number of seeds used or complex gravity anomalies data. Hence, we employed the “shape-of-anomaly” data-misfit function in conjunction with a new seed weighting function to improve the spherical planting inversion. The proposed seed weighting function is constructed based on the covariance matrix for given gravity data and can avoid manually setting customized parameters for each seed. The results of synthetic tests and field data show that spherical planting inversion requires less computer memory than traditional inversion. Furthermore, the proposed seed weighting function can effectively limit the seed influence area. The result of spherical planting inversion indicates that the crustal thickness of Mare Crisium is about 0 km because the Crisium impact may have removed all crust from parts of the basin.