Gravity and magnetic anomalies contain abundant geological information. However, redundant information complicates the study of exploration targets. Existing methods primarily rely on exploiting spectral differences between shallow and deep sources to separate anomalies of different depths. Nevertheless, spectral overlap limits these conventional methods to separating anomalies caused by significantly different depth sources. To reduce effects due to spectral overlap, we propose a novel method for potential field separation. This method capitalizes on the sparsity of gravity and magnetic data in both singular spectrum and model spaces and employs a single-layer equivalent source to represent anomalies induced by target sources. The anomalies caused by sources with different depths can be separated. After sparsely approximating single-layer equivalent sources, we obtain the local anomalies caused by sources within the same layer. Synthetic model experiments demonstrate that the proposed method achieves high separation accuracy, particularly with respect to effectively separating anomalies induced by models with small depth differences. In addition, when comparing the noise resistance of low-rank methods with existing potential field separation methods using synthetic data, the results show that low-rank methods can extract effective signals from signals contaminated by sparse noise and periodic noise. We then apply this method to extract local gravity anomalies caused by intrusive rocks in the Nanling region and effectively identify gravity anomalies associated with various intrusive rocks. This method facilitates the separation of gravity and magnetic anomalies originating from sources at both different and similar depths, thereby expanding the applicability of separation techniques and enhancing the resolution of gravity and magnetic detection.

Accurate estimation of the Earth’s interior temperature is essential for solving fundamental scientific and applied geothermal problems. Currently, there is no universal method for determining deep temperature fields; however, such a method may be based on resistivity, a temperature-dependent proxy parameter. We propose an electromagnetic (EM) geothermometer based on the temperature–pressure coupled resistivity model (TPCRM). This geothermometer can accurately determine the relationship between the normalized resistivity, temperature, and pressure in deep formations based on well-logging, gravity, and EM data, thus allowing to visualize the temperature distribution. The TPCRM is utilized to predict the subsurface temperature in the Xiong’an New Area and shows an accuracy of 76.35%–96.58%. Sensitivity analysis of the critical variables of the TPCRM reveals that the TPCRM relatively weakly depends on the number of constraining boreholes and that the optimization of the subdivision spacing of the well-logging data can significantly improve temperature prediction accuracy. In addition, the effect of the spacing of inverted resistivity normalization grid nodes on the temperature prediction accuracy is relatively weak because the TPCRM considers the factor of the overburden pressure. The TPCRM is a promising tool for studying thermal genetic mechanisms, as well as fine evaluation of geothermal resources for their large-scale and efficient development and utilization.

Three-dimensional inversion of magnetic data can obtain the distribution of subsurface magnetic targets. Deep learning is an effective way to achieve 3-D inversion, which trains a neural network to learn the features of magnetic anomaly data and then generates a 3-D model based on these features. Large training samples are required to achieve persuasive results due to the limited observational data and the multisolution nature of the inverse problem. To reduce the nonuniqueness of the inversion, this article proposes a multivariate magnetic data-based deep learning 3-D inversion strategy. With the proposed strategy, more domain knowledge is incorporated into the training data of the neural network to improve the inversion accuracy. The input data of the neural network adopt multivariate observation data, including multiscale data and multitype data such as magnetic three-component data, magnetic gradient tensor data, and so on, and output a 3-D model to realize 3-D to 3-D mapping. Then, the neural network structure uses the 3-D convolution to extract 3-D spatial information. Both tests on simulation and measured data verify that the proposed strategy can effectively improve the accuracy of the 3-D magnetic inversion.

This paper proposes a method of gravity inversion based on an adaptive mesh-free approach by using a modified radial basis function (RBF). We parametrize the density distribution by using a mesh-free approach. Scattered points are introduced in most mesh-free methods to discretize the given equations. The subsurface space is generally discretized into regular grid cells, while mesh-free methods can avoid the expensive mesh generation and manipulation required in traditional approaches. To deal with the problem of unstructured nodal discretization, we use a mesh-free discretization strategy to establish a mapping of subsurface grid cells to a cloud of discrete points. The nodes are adaptively refined during the inversion process to better recover abnormal bodies. In addition, the hybrid basis function and the modified radial basis function are used to improve the accuracy and stability of the solution. We verify the effectiveness of the proposed method by using several synthetic and real tests.

The distribution of physical features in the Earth’s interior could be estimated by geophysical inversion from the acquired data at or above the surface. Inverse problems are generally considered as least-squares optimization issues in high-dimensional parameter space. Existing approaches are largely based on linear inversion methods, which are limited by the initial model. Nonlinear inversion methods, despite their significant ability in uncertainty quantification, still remain a formidable computational task. In this letter, a new gravity inversion approach is developed based on convolutional neural networks (CNNs). Although the training stage of this method is time-consuming, the actual prediction can be performed in only seconds. Thus, the high computational time of geophysical inversion can be considerably decreased once an appropriate network is constructed. The tests on synthetic data demonstrate that good results could be attained by applying this method to gravity data inversion compared with the least-squares regularization inversion and fully convolutional networks (FCNs).

Identification of lineament structure plays a vital role in determining the metallogenic area and distribution of the geologic structure. Edge detection methods are mostly used to recognize the lineaments and define the geologic boundaries. Cooperatively using edge detection results of the gravity, magnetic and remote sensing data to recognize lineaments would obtain more geologic information. In this paper, new edge detectors of potential field derivatives are proposed to determine the sources’ boundary, named second tilt derivative, tilt of vertical derivative, and normalized second vertical derivative, respectively. Presented approaches are characterized by producing zero amplitude over sources’ edges and equalizing anomalies from different depths. Compared with original edge detection techniques including other second derivative methods, synthetic examples reveal significant superiorities of suggested approaches in providing more accurate and sharper edges and are especially effective in distinguishing superimposed anomalies. The experiments also demonstrate that the normalization to the edge detectors will make images cleaner and geologic edges more easily captured. Applied to airborne gravimetric and magnetic data in the Pobei area (NW China), the proposed methods display more geologic details and lineaments. Canny, Sobel, and Prewitt operators are applied to extract boundaries of remote sensing image. Lineaments picked by the three different types of data are combined collectively to get a comprehensive lineaments structure interpretation.

An efficient algorithm for the$\mathrm {L}_{ \mathrm {p}}$-norm joint inversion of gravity and magnetic data using the cross-gradient constraint is presented. The presented framework incorporates stabilizers that use$\mathrm {L}_{ \mathrm {p}}$-norms ($0\leq \mathrm {p} \leq 2$) of the model parameters, and/or the gradient of the model parameters. The formulation is developed from standard approaches for independent inversion of single data sets, and, thus, also facilitates the inclusion of necessary model and data weighting matrices, for example, depth weighting and hard constraint matrices. Using the block Toeplitz Toeplitz block structure of the underlying sensitivity matrices for gravity and magnetic models, when data are obtained on a uniform grid, the blocks for each layer of the depth are embedded in block circulant circulant block matrices. Then, all operations with these matrices are implemented efficiently using 2-D fast Fourier transforms, with a significant reduction in storage requirements. The nonlinear global objective function is minimized iteratively by imposing stationarity on the linear equation that results from applying linearization of the objective function about a starting model. To numerically solve the resulting linear system, at each iteration, the conjugate gradient algorithm is used. This is improved for large scale problems by the introduction of an algorithm in which updates for the magnetic and gravity parameter models are alternated at each iteration, further reducing total computational cost and storage requirements. Numerical results using a complicated 3-D synthetic model and real data sets obtained over the Galinge iron-ore deposit in the Qinghai province, north-west (NW) of China, demonstrate the efficiency of the presented algorithm.

Both imaging and inversion of potential fields allow the estimation of the source-property distribution. Here, we compare these methods in order to assess their relative advantages and performances. Specifically, we use an iterative imaging algorithm, which is based on the compact depth from extreme points (CDEXP), and the data-space inverse algorithm. This choice was determined because both the methods use a depth weighting function and a compacting function, i.e., they yield a compact source solution. Inverted and imaged solutions are compared with each other, for two sets of noise-corrupted synthetic data, one relative to a simple prism and the other to two oppositely dipping dikes. In both cases, the two models show a noticeable similarity. However, the execution times are substantially different, with the inversion times being an order of magnitude greater. Finally, we interpret two real gravity data sets by using both the approaches: gravity data sets acquired over 1) the Galinge iron-ore deposit of Northwest China and 2) Jiaodong gold deposit of East China. We found that the source models obtained by imaging and inversion methods are once again similar.