The unstructured grids are widely used in the processing and interpretation of geophysical data with terrain due to their excellent ability to simulate shape. Among them, the efficiency of the curved hexahedral grid in its gravity forward modeling based on the isoparametric finite-element method is poor due to the complex transformations involving numerous morphological nodes, which limits its application to large-scale data. For this reason, combining with the deep learning technology, the letter proposes a fast forward method of 3D gravity data for the curved hexahedral grid based on the back-propagation (BP) neural network. In the training phase, the method learns the complex mapping of curved hexahedral elements to their gravity sensitivities through the neural network, thereby achieving fast forward modeling during the prediction phase. Numerical examples show that the new method has good simulation accuracy and generalization ability. Under the premise that the training phase can be completed upfront with its cost excluded, its forward efficiency is tens of times higher than that of the isoparametric finite-element method. The successful application of the new method in the actual terrain model of Mount Taishan area in China further proves its practicality.

Traditional 3D magnetic inversion methods often rely on global fine meshes when pursuing high precision imaging, leading to inefficient allocation of computational resources, with particularly significant waste in non target areas. To overcome this bottleneck, this paper proposes a novel adaptive octree-based 3D magnetic inversion method with an intelligent anomaly focusing mechanism, achieving an organic unity of high precision and efficiency through multi stage intelligent control. The proposed method first rapidly completes the initial inversion on a coarse mesh to obtain the overall outline of the subsurface structure. Subsequently, the fuzzy c-means (FCM) clustering algorithm is introduced to automatically identify target regions with significant magnetic anomalies from the coarse solution. Based on this, a multi stage octree mesh is constructed within the identified regions to achieve refined discretization of complex geological boundaries. The refined model then serves as a new starting point for high precision inversion. This "coarse inversion, intelligent identification, local refinement, precision inversion" workflow can be iteratively executed on demand to dynamically allocate computational resources. To address the influence of varying mesh scales, a volume-related depth weighting function is adopted, and smooth-focusing regularization is introduced to ensure inversion stability while enhancing the model’s resolution capability. Modeling experiments validate the advantages of our method in terms of both inversion quality and accuracy of the extracted anomaly. We applied this method successfully to magnetic data from a mining area in the Huzhong district of the Heilongjiang province, validating its efficiency and practicality in complex geological settings and demonstrating its broad application prospects in high precision inversion of large scale magnetic data.

Full waveform inversion (FWI) is currently the most accurate technique for obtaining the properties of subsurface media. The absence of low frequencies in the observed data caused cycle-skipping phenomenon and poor initial model which affect the convergence of FWI. We propose a global-feature-fusion and multi-scale network (GM-Net) in a way of supervised learning to compensate for the absent low frequency components in the observed data trace by trace. The difficulty of extrapolating frequency is to achieve smoothness and continuity when changing from high frequency signals to low frequency signals, which is visually shown in the reduction and movement of the sidelobes in high-frequency signals and the overall oscillation of the signals is slowed down. For achieving better extrapolation, the encoder-decoder architecture with multi-scale feature extraction is designed as the backbone of the network. For avoiding the loss of information, we propose to perform 1/2 down-sampling on the original input signal separately based on the odd and even time samples, and then concatenate them along the channel dimension. Since 1-dimensional (1D) seismic data is a type of time-series signal and the wavelengths of low frequencies are long, we pay more attention to the relevance of contextual information. Thus, dilated convolution layers, gridding convolution blocks and non-local attention blocks are used to enlarger the receptive field both in time and channel dimensions to extract and fuse global features. Numerical tests both on synthetic data and different types of field marine data demonstrate the feasibility and generalization of our method.

The magnetotelluric (MT) inversion technology is crucial for quantitatively interpreting deep mineral resources, especially when combined with rock physics information, enhancing accuracy in assessing underground structural parameters and spatial distribution. However, the traditional fuzzy c-means (FCMs) clustering-constrained inversion method requires prior rock physics information for each geological unit, limiting their application scope. We propose a guided FCMs (GFCMs) clustering-constrained inversion method based on adaptive virtual rock physics information, referred to as XG-FCM-constrained MT inversion. This method breaks free from the constraints of traditional methods by not relying on prior rock physics information. In terms of extracting virtual rock physics information, we employ a local density clustering algorithm to dynamically extract resistivity model information from MT inversion iterations, automatically determining the number of clusters and cluster centers. Regarding the inversion strategy, we construct an integrated objective function that combines data fitting, smoothing constraint, and GFCM constraint, implementing a two-stage iterative solution strategy of “smoothing first, clustering second.” Model testing demonstrates that compared to traditional smoothing-constrained MT inversion, the XG-FCM-constrained method achieves a significant improvement in the resolution of resistivity model reconstruction, clearly delineating the boundaries of underground anomalies. Even in situations where rock physics information is insufficient or absent, this method can effectively reconstruct high-quality underground resistivity models, reducing the dependence on complete prior information. The application of actual field data further highlights the advantages of the XG-FCM-constrained MT inversion method, providing robust support for accurately delineating geological unit boundaries and precisely identifying potential ore deposit target areas.

Addressing the significant impact of undulating terrain on 3D Direct Current inversion, the unreliability of traditional linearized polarizability inversion for highly polarizable anomalies, and the non-uniqueness of separate resistivity and Time-Domain Induced Polarization inversion, this paper conducts a joint inversion study of 3D Direct Current resistivity and Time-Domain Induced Polarization with structural constraints in undulating topography. A regularly arranged deformed hexahedron mesh simulates undulating surface terrain, transformed into regular hexahedron elements for 3D undulating terrain DC resistivity modeling. Based on the exact inversion of polarization calculated from the inversion results of apparent resistivity and equivalent apparent resistivity data, a joint inversion of resistivity and polarization constrained by cross-gradient is implemented. Synthetic data examples show that the application of arbitrary hexahedron elements significantly reduces the influence of terrain on inversion, and the implementation of joint inversion markedly improves the recovery of high-polarization anomalies while enhancing both the model resolution and the inversion accuracy. The proposed algorithm is applied to the joint inversion of resistivity and polarizability in the lead-zinc mining area of Xiagalaiaoyi River in Huzhong area, the Great Khingan Mountains, northwestern Heilongjiang Province, achieving good results.

Three-dimensional gravity inversion is an effective method for extracting underground density distribution from gravity data. However, traditional deterministic gravity inversion methods suffer from problems such as skin effect, low computational accuracy, and poor efficiency. Therefore, we propose a three-dimensional gravity data focusing inversion algorithm based on the supervised descent method. Supervised descent method (SDM) is a non-linear optimization method based on the combination of machine learning and gradient descent method. In the offline phase, we construct a training set based on a priori information and iteratively learn a set of average descent directions between the initial model and the training model. In the online phase, we introduce a focused regularization into the prediction objective function. This addition aims to obtain a sharp boundary density model that conforms to the physical distribution. Additionally, we incorporate property boundary constraints in both the offline and online phases to control the upper and lower bounds of the density values to ensure consistency with reality. Model tests show that the proposed method can effectively overcome skin effect, improve the resolution of gravity inversion. Moreover, the construction of the training set of the proposed method is less affected by prior information, and it has strong generalization ability. Furthermore, the method does not require solving large-scale linear equations, accelerating the inversion computation speed and having strong noise resistance. Field examples demonstrate that this method has good potential for improving the accuracy and efficiency of actual gravity data inversion.

Gravity and magnetic inversion are important methods for comprehensive quantitative interpretation of data obtained in, e.g., mineral, oil and gas, and geothermal exploration. At present, the 3-D joint inversion technology of gravity and magnetic data is facing challenges from large-scale data exploration applications. In this letter, a new algorithm for 3-D joint inversion of gravity and magnetic data with high accuracy and low computational cost is presented. We use the geometric trellis method to perform fast forward calculations and then introduce the sparse constraint and adaptive sensitivity matrix into the model constraint terms. The inexact structural resemblance method is then used to add the cross-gradient constraint penalty term to the objective function. Finally, an algorithm (DS-TGN) combining data-space (DS) and truncated Gauss–Newton (TGN) methods is used to solve the joint inversion objective function. Numerical experiments with synthetic data show that the proposed algorithm can significantly reduce the computational cost and obtain high accuracy density and magnetization models with structural resemblance and sharp boundaries. We also apply the DS-TGN algorithm to data obtained in the area of Greater Khingan in northwestern Heilongjiang, China. The underground density and magnetization distribution results provide a high-resolution geological model for the detection of skarn-type deposits.

Magnetotelluric (MT) is an important geophysical exploration method that uses natural sources to study the electrical structure of the earth. This method is advantageous owing to its low cost, large exploration depth range, and high resolution for low-resistivity bodies. However, traditional MT modelling approaches can only invert the resistivity parameters of geological bodies, while natural geological bodies also exhibit the induced polarization (IP) effect. Applying the IP effect of geological bodies could be effective for exploring mineral resources, such as polymetallic ores, oil (gas) fields, and coal fields. To incorporate the IP information into MT inversion, we proposed a multi-parameter MT joint inversion algorithm that considers the IP effect. We used the Cole-Cole model to integrate four IP parameters into the forward algorithm: the zero-frequency resistivity ρ0, chargeability η, frequency exponentc, and time constantt. The influence of each IP parameter on the forward response was analyzed by forward simulations, and we concluded that the parameters ρ0andη should be considered in the inversion. A cross-gradient function was introduced into the objective function of the Occam inversion method to constrain the structural consistency of ρ0and η. Model testing and practical application results illustrated that the algorithm can not only obtain the subsurface resistivity structure that can be achieved by the traditional MT method but also reveal the distribution of the chargeability parameter. The additional information obtained using this algorithm is conducive to interpreting specific geological structures that cannot be distinguished by the traditional MT method.

The joint inversion of structural constraints is a new and rapidly developing detection technology in comprehensive geophysical interpretation. In this article, a new structural constraint 2-D multiphysical parameter joint inversion algorithm for magnetotelluric (MT), gravity, and magnetic data is developed. The structural constraint term is a combination of cosine dot-gradient (CDG) and joint total variation (JTV) constraints, which not only has characteristics of traditional dot product and cross-gradient structure constraints but also avoids the uncertainty of dot product constraints predicting the gradient direction of the model parameters, overcomes the need for high-order differential approximation of the cross-gradient constraint, ignores the influence of the gradient amplitude of different model parameters on the weight of the structural constraint of different regions, and enhances the reconstruction accuracy of the underground discontinuous interface. To more easily combine multiple optimization algorithms to improve the resolution and computational efficiency of joint inversion, an adaptive inexact structural resemblance (IESR) algorithm is developed to minimize numerical solutions to the objective function. Experimental results have demonstrated that the CDG constraint has a wider use range than the traditional structural constraint, the addition of the JTV constraint can recover the underground discontinuous interface, and an inversion result of higher resolution can be obtained using the adaptive IESR algorithm.

Seismic background noise affects the recognition of reflection signals, thereby impeding the subsequent seismic data processing, such as seismic imaging and inversion. In addition, seismic background noise has relatively complex properties, such as non-stationarity and spectral aliasing, which can be further hampered with the deterioration of the exploration environment. Deep-learning methods have been successfully applied to effectively attenuate complex seismic noise and have shown significant improvements over conventional denoising methods. However, most denoising networks only utilize single-scale features, resulting in poor performance when confronted with seismic data in a low signal-to-noise ratio. To further enhance the denoising capability, a novel multiscale residual pyramid network (MRP-Net) was proposed to separate the desired signals and complex seismic noise. Compared with single-scale networks, MRP-Net can take advantage of the multiscale features, thereby improving noise attenuation capability. In general, the pyramid-like framework in MRP-Net can extract the potential features at different scales through down-sampling and up-sampling operations, and skip connections were applied to fuse the global-coarse and local-fine features. On this basis, a double-path spatial attention module was designed to enhance the desired features, further improving the processing performance of separating the desired signals from the intense seismic background noise. Comprehensive experiments on synthetic and field seismic data demonstrate that MRP-Net is effective for complex seismic noise attenuation, both for conventional geophone-acquired data and DAS records.