Integrated gravity and gravity gradient 3-D inversion can effectively improve the resolution of inversion results. This study aims to find a better way to extract geological information from gravity and gravity gradient data and to obtain the recovered model with a higher resolution. We present three different methods for integrating gravity and gravity gradient data in inversion: directly integrating gravity and gravity gradient data (DIGG), the sequential inversion of gravity and gravity gradient data (SIGG), and integrating gravity and gravity gradient components using a weighting matrix (IGGW). In addition, we propose a new discrete method for smooth inversion. We discretize the stabilizing functional into two parts. One is the square of the 2-norm of the model parameter, and the other one is the square of the Frobenius norm of the gradient of the model parameter. We adopt a conjugate gradient algorithm (CGA) to solve the objective function. We used the DIGG, SIGG, and IGGW inversion methods in a dip-slab model with multiple anomalous bodies. The inversion results show that by integrating gravity and gravity gradient in inversion, more reasonable results are obtained than by inverting a single data type. Among the presented methods, the IGGW method achieved the best performance in using information contained in gravity and gravity gradient data, followed by the SIGG method, and finally, by the DIGG method. We used the methods on actual data from Vinton salt dome, southwestern Louisiana, USA. The obtained results support the abovementioned conclusions.

Geophysical joint inversion is more frequently applied to deep crust probes. For the potential field data, it requires the introduction of large-scale observed data and sensitivity matrices. Massive matrix-vector multiplications occur during iterations, and the obtained data cannot be effectively interpreted by merely using desktop computers. To improve the resolution and the computing ability of inversion, we here propose the parallel joint nonlinear inversion of full tensor gravity gradiometry data. As the inversion is affected by linear searches, it is associated with certain classical computing performance issues. Hence, we addressed the memory and efficiency limitations, which are caused by very large calculation volumes. Also, we performed a quantitative and comprehensive feasibility analysis of parallel computing. Then, we identified the main factor influencing the inversion performance and clarified the correspondence between the cell number and the memory. A parallel inversion solution was proposed via graphics processing unit (GPU) based on the sensitivity matrix compression. The data tests demonstrated that inversion has antinoise property and that it can obtain accurate underground density distributions. Also, the parallel solution was found to be suitable for inverting cells at the million cell scale and greater because of its ability of acceleration and matrix compression. A design pattern was applied for gravity or magnetic anomaly inversion of 100 $\times 100\times20$ cells, and the run time was less than 1 min. Overall, we believe that the proposed solution can help implement massive potential field data inversions and promote the application of the parallel technique in other inversion research.

Airborne gravity gradiometry is an effective tool for its high efficiency and sensitivity to the interesting buried targets, which has been increasingly introduced in mineral and petroleum exploration. When compared to gravimetry, full tensor gradient (FTG) measurements provide higher resolution and signal-to-noise ratio. In this article, we build and test models with different sampling intervals and compare the performances of individual components or their combinations in minimum structure inversion to evaluate the benefits of FTG combinations. As part of a theoretical study, the singular value spectrum (SVS) and depth-resolution plot (DRP) are examined to determine how much information and resolution different datasets provide in the underdetermined inverse problem. The synthetic examples show that integrating more components in inversion improves the resolution of the recovered model, and the inversion result of gravity or individual component cannot accurately restore the distribution of anomalous bodies. With the increasing sampling interval, joint inversion of FTG data still provides enough information corresponding to the source density distribution, and the limit survey interval is tested through models. In addition, we use a real survey over the Vinton dome as a case study and discover that $V_{\mathrm {zz}}$ component fails to reconstruct the caprock model at coarse line spacing, whereas FTG combinations recover the acceptable geometry flawlessly. It also reflects the benefit of FTG combinations for inversion processing, which reduces the interference of measured noise on inversion results and allows for longer sampling intervals during the survey, effectively lowering the cost of an airborne survey and improving exploration efficiency

In practical problems concerned with an exploration of geological mineral resources, to enhance the resolution for its geological interpretation, downward continuation of the gravity anomaly is usually performed, as downward continuation can highlight local and shallow gravitational sources related to the ore body, which plays a very important role in the following processing and interpretation of gravity data. However, downward continuation is an ill-posed issue and has been a research topic for gravity exploration.General classical methods for the downward continuation of gravity anomalies mainly include spatial-domain methods, of which, however, their convolution calculations are complicated; frequency-domain methods, the product calculations by Fourier transform from spatial-domain convolution, according to which not only do downward continuation factors have amplification effects, but also errors from the discretization and truncation of the Fourier transform cause oscillations in results. Improved methods, such as regularization filtering methods and generalized inverse methods, according to which although the stabilities of these downward continuations are improved, their downward continuation depths are not significant (generally no more than 5 times the measured interval); the integral iteration method, according to which stable results can be achieved for noise-free data and the depths of its downward continuation are large, but its number of iteration is giant, resulting in the reducing of computational efficiency and the accumulation of noises; Adams-Bashforth methods and Milne methods established by numerical solutions of the mean-value theorem, according to which they are easy to calculate and with greater depth of downward continuation (more than 15 times the measured interval). However, measured vertical derivatives are needed use to improve their accuracy.As the coverage of measured vertical derivatives is low and their costs are high in real gravity explorations of geological mineral resources, which means it is not always possible to utilize measured vertical derivatives. To widen the real application for downward continuation methods of numerical solutions, instead of the measured vertical derivatives, we use the calculated ones by the ISVD (integrated second vertical derivative) method. At the same time, to improve the accuracy of the result using calculated derivatives, we present two new methods, Adams-Moulton and Milne-Simpson, based on implicit expressions of numerical solutions of the mean-value theorem for gravity anomaly downward continuation. These two methods have mathematical significance for improving the accuracy of numerical solutions. To demonstrate their effectiveness, we compare these four methods for downward continuation in the same degree including an Adams-Bashforth method, a Milne method, an Adams-Moulton method and a Milne-Simpson method by texting on the synthetic and real data of gravity exploration. The results show that the two implicit methods have higher accuracy, which has practical significance for the resolution improvement of gravity anomaly downward continuation in exploration interpretation.