The presence of remanent magnetization introduces uncertainties in the processing and interpretation of magnetic data. In the literature, a variety of methods have been proposed to extract the intensity and direction of remanent magnetization. However, the existing methods still have some limitations, such as biases in results due to the use of inaccurate prior information and the complex computational process of extracting remanent magnetization information, especially from superimposed anomalies by multiple field sources. In this study, we develop an effective method to extract the intensity and direction of the remanent magnetization based on deep learning. We first use an improved U-Net as the backbone network to obtain the feature of spatial location and remanent magnetization parameters of anomalies and fuse the extracted multiscale feature information. At the same time, residual connections are added between the convolution layers to alleviate the loss of information and reduce gradient disappearance. The network, through continuous training, can directly learn the nonlinear mapping relationship between anomalies and the remanent magnetization intensity and direction, without the need for a prior information and complex calculations. Subsequently, we test the proposed method on synthetic examples and field data example in Yeshan region. All the outcomes demonstrate the capability in accurately extracting intensity and direction of remanent magnetization.

The estimation of the derivatives is an important part of potential field data processing and interpretation. In literature, a lot of methods have been presented to estimate the derivatives accurately and stably. However, existing methods still have some limitations. For example, the derivative estimation of high-noise data is unstable, and the determination of some parameters is difficult. To solve the problems of the classical methods mentioned above, a stable method for estimating the derivatives of potential field data based on deep learning is proposed. The proposed method constructs the network based on U-Net and builds a nonlinear mapping relationship between the noisy data and the derivatives of potential field data. After training with the designed datasets, the proposed network achieved the ability to eliminate the influence of noise and intelligently estimate the derivatives of potential field data. The proposed method is tested on synthetic data and real data in the Goiás Alkaline Province, Brazil, taking estimating the vertical derivatives of gravity anomaly as examples. The results indicate that the proposed method generates stable and accurate derivatives with the noisy data.

Clustering constraint can effectively establish the relationship between petrophysical information and inversion results, thus playing an important role in lithology identification. In practical application, the number of cluster centers should be predetermined based on available rock physical data of the study area, which is often difficult. To solve this problem, this letter innovatively introduces a method for intelligently obtaining the number of cluster centers. The presented method is based on the Dense-Net architecture, which strengthens feature propagation using dense connectivity to achieve the reuse of input data. Also, Bayesian optimization is adopted for unsupervised iteration to determine the suitable combination of hyperparameters. With the abovementioned operations, the loss curve converges effectively and efficiently. The trained network is validated on theoretical cases that do not exist in the training set. The obtained result is very close to the true value. Finally, the gravity field data from the San Nicolas deposit are adopted for real data test. The results are basically consistent with the geological conditions of the study area, proving the practicability of the presented method.

The structural constraint is widely used to establish joint inversion of multiple geophysical data. To implement the above method, weighting parameters for different items (such as data misfit term, regularization term, and structural coupling term) should be pre-set, and global structural consistency assumption should also be made. However, these prerequisites are not easy to set very reasonable. To address the above issues, this article presents a novel deep learning (DL) network method based on a multitask learning strategy to realize joint inversion of gravity and magnetic data. Due to the automatic processing of the DL technique, this method does not consider the weighting parameters. The issue of global structural consistency assumption is addressed using a multitask learning strategy. The proposed network with a multitask learning strategy consists of five tasks. In the overall network, two tasks are used for the independent inversion, one task constructed by a gated network extracts the structural similarity information from the shared information of the independent inversion networks and generates the structural similarity model, and two tasks use the structural similarity information to constrain the independent inversion to achieve the accurate joint inversion. A synthetic example and an application of the real data from the Galinge iron-ore deposit in Qinghai Province demonstrate the effectiveness of the proposed method.

Delineation of the basement relief structure is of great significance for oil and gas exploration in sedimentary basins. In literature, a number of methods have been presented to depict the basement relief with gravity anomaly. However, existing methods still have some limitations, such as local morphological distortion caused by improper use of known depth points, and imprecise solutions yield from inaccurate determination of the underground density contrasts. To address the above two issues, this study proposes an improved high-precision method to characterize the basement relief. For the proposed method, a new prior depth soft constraint, which is based on a cosine attenuation function, is introduced to utilize the known depth at a few points more rationally. Moreover, a physical property constraint, which is based on the least square theory, is employed to constrain the fitting between the recovered gravity anomaly and the observations better. The effectiveness of the proposed method is tested and validated on synthetic data with noise and real data in Sydney, Australia.

With the gradual deepening of mineral exploration, the detection of concealed minerals in the coverage area has become a notable research subject. However, how to strip the geophysical effects due to the shallow coverage layer effectively plays a major role in the success or failure of the application of various geophysical methods. To solve this problem for the application of gravity method, this letter presents a novel scheme for stripping the gravity effects due to the shallow coverage layer. The proposed scheme introduces geological information of the coverage layer to reduce the uncertainty of the separation, and automatically selects the frequency bands to decrease the subjectivity. The effectiveness of the proposed scheme is evaluated by both synthetic and real data. The obtained results demonstrate that the proposed scheme yields better results compared with the conventional preferential filtering method.

The observed potential field data are usually corrupted by noises from different sources, and these contained noises pose great adverse impacts on further data processing. In the literature, many noise reduction methods have been introduced to solve this problem, most of which are based on the idea of high-pass filter. However, there are some limitations for most of these conventional methods, such as the elimination of some effective high-frequency components caused by the shallower small-scale sources, resulting in reduced denoising precision, and the difficulties in determining the filter parameters manually. Faced with these problems, a new method based on RevU-Net architecture is first proposed to handle the above issues. The method expands the feature information through the upsampling layer at the expansion path and uses the skip-connection technology to fuse multiscale features. Also, the network updates itself toward the purpose of multiscale signal capture and separation, which provides an intelligent approach and enable it to distinguish the small-scale components and noise without human intervention. The proposed method is tested on several synthetic examples. The results illustrate that this method yields satisfactory results while preserving the features of the shallower small-scale sources without the any manually setting parameters. So, it overcomes the limitations of the conventional methods stated above.

The strip-shaped interferences in aeromagnetic data pose great adverse effects on data interpretation. In literature, a number of methods have been proposed to deal with this problem. However, existing methods still have some limitations. Inspired by the ability of deep learning techniques to extract features from data, this study presents a novel convolutional neural network (CNN)-based method to eliminate the strip-shaped interferences in aeromagnetic data. The proposed method uses the U-Net structure to establish the whole network. The use of up–down sampling and skip connection enables the network to extract multiscale strip-shaped interferences with complex distribution and morphological characteristics. The basic theoretical formulas of the network and its architecture are presented, along with the construction method of the training dataset. Afterward, the presented method is tested on several synthetic examples and real aeromagnetic data collected in Jining, Inner Mongolia, and is compared with the conventional directional cosine filter to display its advantage in accuracy. The results demonstrate that the presented method can eliminate the strip-shaped interferences in aeromagnetic data effectively while preserving the features due to the real geological sources without any subjective parameters.

The data-driven inversion methods based on deep learning for gravity and magnetic data have been well studied in existing literatures due to their advantages such as less constrains requirements and extremely high efficiency compared with various conventional model-driven inversion methods. However, some issues should be further addressed when these methods be applied to the joint inversion, such as how to determine the structural similarity of the divided cells and low depth resolution of the inversion results. To solve the above problems, this paper proposes an optimized deep learning network for the joint inversion of gravity and magnetic data. We designed a network with combined modules, which can extract features of structural similarity and the mapping relationship between raw potential field data and physical parameters at multiple scales. Based on this function, the network improves the accuracy of the joint inversion results by adopting different inversion strategies (independent or joint) in different areas. In addition, the proposed method uses 3D convolution operator to screen and reconstruct the physical parameters, with which the depth resolution of the results can be improved. Numerical examples using synthetic and real data of a metallic deposit area in Northwest China illustrate the effectiveness and advantage of the proposed method.

The joint inversion methods of gravity and magnetic data have been presented in numerous literatures and implemented in many real applications. However, almost all of these existing methods still face the problem of low computational efficiency, although some targeted improvements have been put forwarded. To further address this issue, this study proposes an efficient algorithm for the joint inversion of gravity and magnetic data. The new algorithm is developed from the idea of structural coupling by using the cross-gradient function and employs a sequential strategy. A new formula for efficient minimization of the structural similarity term is derived innovatively, in which the minimization of the structural coupling term is obtained by a technical combination of an alternating strategy and the randomized singular value decomposition (RSVD) algorithm. Using the proposed new formula, the dimension of the original inverse problem can be reduced greatly. Furthermore, the RSVD algorithm is utilized to perform the independent inversion and determine an optimal regularization parameter. Several comparative tests on a synthetic example show that the proposed efficient method poses great advantage in efficiency compared with the conventional sequential cross-gradient joint inversion (CSCGJI) method. The proposed algorithm is also successfully applied to the real data from a metallic deposit area in Xinjiang province, China.

The 3-D marine gravity field plays an important role in many practical applications, such as matching navigation, object monitoring, and resource exploitation. However, the accuracy of the gravity field generated by most existing methods is relatively low. To solve this problem, this study innovatively puts forward a new method for establishing a high-accuracy 3-D marine gravity field by using a joint inversion algorithm. The presented method incorporates gravity fields observed at different altitudes, especially those observed near the seafloor, because they contain more prominent short-wavelength signals of the sources. The final joint inversion formulas are developed from the standard form of independent inversion of single gravity datasets, so it is conducive to include different weighting matrices. To achieve the efficiency of the presented method, the nonlinear objective function is minimized iteratively using a fast randomized singular value decomposition (RSVD) technique. The employing of RSVD also facilitates the determination of an optimal regularization parameter based on the generalized cross-validation criterion. The presented method is tested on both synthetic gravity fields simulated by a theoretical density model and real gravity fields collected in the South China Sea. Numerical results demonstrate that the presented method can provide more accurate 3-D gravity fields than the commonly used iterative downward continuation method in the wavenumber domain (DCW) and the conventional equivalent source (CES) method.