The unmanned aerial vehicle (UAV)-based ground-penetrating radar (GPR) migration imaging encounters substantial challenges in practical applications due to various noise interferences. This study presents a GPU-accelerated imaging algorithm that integrates reverse time migration and total variation denoising (RTM-TVD) to enhance the image quality of UAV-based GPR migration profiles. By employing two acceleration strategies, this algorithm achieves a tenfold increase in speed compared to the traditional RTM method. Additionally, a quantitative evaluation is conducted to assess the effects of terrain roughness, flight altitude (FA), and noise levels (NLs) on imaging quality. This evaluation utilizes two key metrics: image entropy and the structural similarity index (SSIM). Our findings reveal that the relationship between terrain roughness and NLs with entropy values follows a positive linear trend, whereas a negative linear trend is observed in SSIM values. The advantages of the RTM-TVD approach are validated through field GPR data collected from the Lemon Creek Glacier in the U.S.

Current forward modeling approach for three-dimensional (3-D) controlled-source electromagnetic (CSEM) problems in anisotropic media exhibit limited capability in addressing large-scale models. Given that, we have developed an innovative 3-D forward modeling algorithm for anisotropic CSEM problems by using Fourier finite element method (FFEM). Starting from the Maxwell’s equations, the 3-D governing equations of the secondary vector and scalar potentials based on the Coulomb gauge are derived. That secondary field approach can not only effectively eliminate source singularities, but also maintain flexibility for various source configurations. Then, a horizontal two-dimensional (2-D) Fourier transform is employed to convert the 3-D governing equations from the spatial domain into a system of one-dimensional (1-D) ordinary differential equations in the space-wavenumber domain. The resulting equations are discretized and solved via the 1-D finite element method (FEM). Additionally, a contraction operator is applied to iteratively correct the total electric field. By leveraging the computational efficiency of Fourier transform and the stability of iterative techniques, the proposed approach achieves enhanced computational efficiency without compromising numerical accuracy. The validity, performance and convergence of the proposed approach was verified by using 1-D isotropic canonical off-shore hydrocarbon model and 3-D anisotropic prism model. Compared with the open source package PETGEM based on the high-order edge finite element method, the proposed approach using FFEM exhibits obvious efficiency advantages for 1-D isotropic canonical off-shore hydrocarbon model. Finally, two sophisticated geological models were employed to validate the robustness of FFEM in handling complex subsurface conditions, and the influence of frequency on electromagnetic field distribution was also investigated.

Traditional magnetotelluric (MT) denoising methods often encounter limitations in various scenarios. However, with its robust adaptability and high precision, deep learning has exhibited outstanding denoising performance when applied to MT exploration time series data. Recent researches have mainly focused on developing advanced single deep learning models to enhance MT denoising effectiveness. This paper introduces a lightweight ensemble learning approach for MT denoising, aiming to enhance denoising performance via a single deep convolutional network. Our ensemble learning strategy uses a sliding window technique to generate overlapping MT time series segments, thereby providing multiple inputs for a specialized noise-fitting network. This variety of inputs enables a comprehensive understanding of MT data, thereby increasing the probability of identifying complex noise patterns. Then, the outputs from these inputs are integrated using a method that combines shifting averages and adaptive thresholding to obtain more accurate fitted noise contours. Furthermore, we apply a three-layer Density-Based Spatial Clustering of Applications with Noise (DBSCAN) methodology to identify the real noise contours among the fitted noise contours, and then to get the residual signal by subtracting those real noise contours. Subsequently, the residual signal is further processed by the pre-trained denoising network to eliminate noise artifacts. The efficacy of our approach is validated through experiments conducted with both synthetic and field data, demonstrating substantial improvements in denoising, particularly within mid and low frequency ranges. Several interrelated parameters exhibit notable improvements, including apparent resistivity and phase curves, time-frequency domain curves, and so on.

Three-dimensional forward modeling algorithms of conductivity anisotropy with respect to the magnetotelluric method have been widely developed. However, numerical modeling considering the magnetic susceptibility anisotropy is less studied, and the magnetic susceptibility of the underground medium cannot be ignored in some areas of magnetite-rich rocks. In this study, the nodal finite element method and the unstructured tetrahedral grid were utilized to discretize the A-ϕ system for a model with both conductivity and magnetic susceptibility anisotropies, which was solved using the biconjugate gradient stabilized method. By comparing the numerical results with the analytical solutions of two-layered models and a previous vector finite element solution of a single-block model, the accuracy of the implemented algorithm was verified. Then, the influence of magnetic susceptibility anisotropy on magnetotelluric responses was analyzed based on different block models as well as on a quasi-two-dimensional model producing out-of-quadrant phases. Different types of MT data were considered to conduct these analyses, including the apparent resistivity, impedance phase, phase tensor, and tipper. Our findings point to the same conclusion that the effect of magnetic susceptibility anisotropy cannot be ignored in magnetite-rich areas.

At present, the three-dimensional (3D) magnetotelluric (MT) unstructured finite element modelling approaches often adopt the block-wise uniform conductivity parameterization method, in which the Earth conductivity model is discretized into plenty of tetrahedrons with uniform conductivity. However, that block-wise uniform parameterization method is not only difficult to accurately simulate actual continuous subsurface conductivity distribution, but also would substantially increase the unknowns in the subsequent inversion, which largely aggravates the non-uniqueness of inversion. In this study, we propose a three-dimensional unstructured finite element modeling strategy of magnetotelluric problems allowing for continuous variation of conductivity in each tetrahedron. First, the curl-curl governing differential equation of electrical field for the 3D MT problems and the corresponding integral weak form are derived successively. Next, the open-source tetrahedral mesh generator Tetgen is utilized to discretize the computational domain, both the conductivity and the electric field within each tetrahedral element are approximated by using linear interpolation with node and edge vector basis functions, respectively. Then, the closed-form expression of the resulting elemental integral is derived and the Newman type boundary condition is loaded. The resulting system of linear equations is solved by using the direct LU decomposition method. Further, to enhance the accuracy of the solution, a goal-oriented adaptive technology based on the continuity of the normal component of the current density is adopted. Finally, the correctness of the proposed algorithm is verified by using a layered model with continuous conductivity distribution and a 3D topographic model. While the necessity of considering the continuous variation of conductivity in blocks is proved by using two 3D continuum models. The results show that the proposed algorithm can obviously improve the accuracy of the responses at the sites above the region with continuous conductivity distribution and will greatly reduce the unknowns of the subsequent inversion, compared with the traditional algorithm with block-wise uniform parameterization.

Galvanic distortion resulting from near-surface heterogeneity has long been considered a major impediment to the accurate interpretation of magnetotelluric data. As this galvanic distortion effect is approximated by a real tensor, it can be solved numerically in the three-dimensional magnetotelluric inversion. To achieve this goal in a practical way, we have implemented the inverse solution of both the galvanic distortion and resistivity parameters in the widely used software package ModEM. To address the gradient domination problem of the distortion parameter over resistivity, a scaling scheme is proposed to balance their separate roles in the total gradient. Two synthetic datasets of the Block2-3D and the Oblique Conductor models provided in ModEM package were distorted and then used to validate the new implementation. Synthetic inversions demonstrate that the artifacts introduced by fitting the galvanic distortion effect can be removed and the regional structure is better resolved. A field data inversion test was conducted on the magnetotelluric data from the Red River Fault zone and its adjacent areas on the southern margin of the Tibetan Plateau. Using the distortion-free phase tensor, we show that the new inversion significantly removes the galvanic distortion artifacts from the shallower structure. It obtained a slightly different crustal structure and a clearer delineation of the upper mantle structure compared to the previous study.

Conventional resistivity inversion methodologies encounter constraints in perpetual monitoring, owing to the necessity for recurrent measurements. In response, this research leverages a 3D finite element method to formulate an approximate geometry imaging of cross-borehole resistivity during forward modelling, circumventing the direct computation of Jacobian matrix equations in the electric field. This study meticulously explores the complex relationship among apparent resistivity (ρa), CO2resistivity (ρCO2), and the volume of the CO2storage area (VCO2). Remarkably, the impact of ρCO2on ρais found to be more pronounced than that ofVCO2, attributed to the repulsion effect emanating from the high-resistance storage area. A robust linear correlation between ρaandVCO2is identified across various multi-horizontal layer models, while the relationship between ρaand ρCO2adheres to a rational function. The intricate correlation between ρaand CO2concentration is dissected, offering a quantitative perspective for inferring the resistivity of the CO2storage area. These findings are further validated through field formation models featuring salt caverns, highlighting the effectiveness of cross-borehole resistivity imaging for CO2storage monitoring. Beyond enhancing our understanding of subsurface geological behaviour, our study underscores the feasibility of utilizing salt caverns for CO2storage, presenting a pioneering approach towards navigating the monitoring of subsurface CO2storage.

As a trenchless detection approach, the transient electromagnetic method (TEM) can effectively detect well-conducted geoelectric structures, such as groundwater structures. The nonlinear TEM inversion process represented by neural network (NN) inversion does not rely on the initial model, which helps it efficiently and accurately obtain geoelectric structures. In this article, a factor analysis (FA)-based deep belief network (DBN) inversion framework built on hybrid memetic pretrained (HMP), HMP-FADBN, is proposed. We construct a DBN with restricted Boltzmann machines (RBMs) and backpropagation NNs (BPNNs) as the base fitting skeleton. FA is used to reduce the dimensionality of the feature space of the DBN. The hybrid memetic (HM) whale optimization algorithm (WOA) pretrains the network parameters and uses the memetic strategy to adjust the coordinated development system of social and individual cognition to enhance the network training effect. Numerical examples show that the prediction accuracy of the proposed HMP-FADBN for TEM geoelectric models is improved from more than 10% to approximately 2%. Moreover, 5%, 10%, and 15% noise tests show that the trained NN has good generalization and denoising abilities, and the prediction accuracy is less than 3% (affected by the maximum noise). Finally, the developed method is successfully applied to a landslide TEM survey, and the predicted quasi-2D geoelectric structure is consistent with the original geological structure.

Neural networks (NNs) are efficient tools for rapidly obtaining geoelectric models to solve magnetotelluric (MT) inversion problems. Training an NN with strong predictive power requires numerous training samples to prevent underfitting. To reduce the computational burden of generating a large number of training samples, this work analyzes the influence of the sample features and distribution on the training effect for an NN and proposes an efficient method of sample generation. This innovative method consists of three steps: 1) geoelectrically simplifying the features; 2) removing unnecessary features on the basis of realistic geological characteristics; and 3) mapping the samples to a higher-dimensional space. Numerical examples based on simple stratified models show that the number of samples can be reduced to below one-millionth of the original number while improving the predictive effect of the NN. The performance and effectiveness for processing more complex structures are verified by the inversion results obtained for a public data set, COPROD2. We conclude that this advanced method can generate high-quality training samples at a greatly reduced computational cost. The analysis of the sample features and distribution not only advances the state of research on the use of machine learning in geophysical inversion but also is a forward-looking study on the mechanisms of underfitting, tracing the source of these phenomena back to the training samples used.