For the mineral exploration in complex terrain areas, the semi-airborne transient electromagnetic (SATEM) technology is one of the most powerful methods due to its high efficiency and low cost. However, since the mainstream SATEM systems only observe the component dBz/dt and the data are usually processed by simple interpretation or one-dimensional (1D) inversion, their resolutions are too low to accurately decipher the fine underground structures. To overcome these problems, we proposed a novel 3D forward and inversion method for the multi-component SATEM system. We applied unstructured tetrahedron grids to finely discretize the model with complex terrain, subsequently we used the vector finite element method to calculate the SATEM responses and sensitivity information, and finally we used the quasi-Newton method to achieve high-resolution underground structures. Numerical experiments showed that the 3D inversion could accurately recover the location and resistivities of the underground anomalous bodies under the complex terrain. Compared to a single component data, the inversion of the multi-component data was more accurate in describing the vertical boundary of the electrical structures, and preferable for high-resolution imaging of underground minerals.

We present an efficient method for uncertainty quantification in 3D magnetotelluric (MT) inversions based on variational inference principles and the variational autoencoder (VAE) framework. In this approach, we replace the VAE’s encoder and decoder respectively with a forward modeling and a 3D optimization module, where the latent variables represent updates in the constrained model space. Utilizing reparameterization, the gradient of objective function can propagate back to the mean and variance of the latent variables, and thus restores the Gaussian distribution of resistivity models. By setting appropriate prior and initial distributions, our method explores the solutions with high log-variance to fit the data. To ensure a stable convergence, we apply a smooth constraint on the log-variance of latent variables and employ a modified adaptive moment estimation (Adam) optimizer. Numerical experiments confirm that our method can accurately estimate both the resistivity model and standard deviation at a time cost only 2-3 times that of conventional inversion, which provides a highly efficient solution for uncertainty analysis. The tests with varying regularization parameters reveal that the standard deviation estimates are sensitive to both the Kullback-Leibler (KL) divergence and log-variance smoothness terms, while the adaptive smoothing strategy can well balance these effects. The application to a dataset from USArray survey in the Northwestern US demonstrates the method can achieve robust inversion and uncertainty quantification.

Localized water-rich areas in aquifers can cause severe accidents during coal mining, including property damage and casualties. Traditional ground-based geophysical methods often struggle in the mountainous terrains where coal mines are typically located. To address this, we applied a high-resolution exploration and interpretation strategy based on advancements in semi-airborne transient electromagnetic (SATEM) technology, integrating drilling and logging to detect water-rich areas in Huangling coal mine. Our approach involved acquiring high signal-to-noise ratio electromagnetic data near the transmitting line source, using unstructured tetrahedral meshes to simulate complex topography, and employing a quasi-Newton optimization algorithm for detailed 3D inversion. Synthetic tests demonstrate the accuracy of this method in resolving underground conductivity structures, even in challenging terrains. Field data inversion showed a good fit with observed data and good agreement with resistivity logging, confirming the reliability of the results. This study not only addresses the critical need for efficient water hazard detection in coal mining but also offers significant potential for mineral exploration, geological surveying, and disaster prevention.

To improve the efficiency of 3D forward modeling in airborne electromagnetic (AEM) methods, we propose a novel high-fidelity surrogate modeling approach based on the Hybrid DeepONet-Fourier Neural Operator (HDF). This method leverages the DeepONet’s Branch-Trunk network to the input data, which is then processed in a higher-dimensional Fourier space for enhanced information extraction and learning. The architecture preserves the deep neural network’s capacity to solve multiple partial differential equations (PDEs) while utilizing Fourier transforms to improve generalization. The training dataset was generated using the Gaussian random field (GRF) method, which efficiently creates smooth, random geometric shapes across various scales, representing complex geological structures. The theoretical experiments demonstrate that the hybrid architecture outperforms conventional DeepONet and FNO models under the same training conditions, it reduces the relative errors by nearly an order of magnitude. When applied to the real geological model of the Byneset region in Norway, the hybrid architecture achieves a prediction accuracy comparable to traditional numerical methods, and outperforms DeepONet and FNO in terms of prediction errors. Additionally, the proposed approach is approximately 1000 times faster than the finite difference methods, making it a highly efficient solver for future data inversions.

Magnetotelluric (MT) and teleseismic tomography are critical techniques in deep Earth exploration for geodynamic studies, internal energy circulation, plate tectonics, volcanic systems and so on. However, due to the uneven data distribution, the inherent non-uniqueness of inversion, and differing sensitivities to subsurface media, the velocity and resistivity structures derived from independent inversions often exhibit substantial discrepancies and contradict conventional geological understanding. To address these issues, we propose a novel three-dimensional (3D) joint inversion method for MT and teleseismic traveltime data, applicable to different types of grid discretization. The method first establishes a parameter mapping for different grid types. Then, a joint inversion framework based on the local Pearson correlation constraints (LPCC) is developed using a virtual grid technique. The inversion alternately updates the resistivity and velocity models by ensuring structural similarity between them. Numerical experiments demonstrate that the proposed method can effectively integrate the advantages of both techniques, enhance resolution and stability. Additionally, the tests on hyperparameter selection provides guidance for optimizing joint inversion parameters. Finally, the developed joint inversion method is applied to MT and teleseismic traveltime data in southeastern Australia and yields a constrained 3D resistivity and velocity model of the region. The results offer significant theoretical and practical insights into the lithospheric structure, the magma transport pathways, and the geodynamic processes in this area.

At present, the mainstream technology for leachate detection in landfills is electrical resistivity tomography (ERT), known for its efficiency and non-destructive nature. However, the conventional ERT data interpretation primarily uses inversion based on structured grids, which cannot accurately simulate the complex and thin impermeable layers of landfills, leading to unreliable results. To address this issue, we propose a novel ERT observation system and a new three-dimensional (3D) inversion technology. In our observation system, all measuring electrodes are placed around the landfill at once, and only a limited number of transmitting sources are needed to sequentially inject current, which effectively reduces the time for data acquisition. For 3D inversions we employ unstructured tetrahedral grid for fine discretization of structures at various scales. The node-based finite-element method is used for high-precision forward and adjoint forward calculations, while the gradient filtering method in combination with L-BFGS algorithm is used to update the inversion model. Numerical experiments indicate that the proposed method can mitigate the influence of thin impermeable landfill layers, provide more accurate imaging results compared to the conventional methods. Additionally, we also test the effects of water-bearing layers, faults, and near-surface interferences on the leakage inversion results. The results show that the proposed method can achieve reliable high-resolution imaging under various conditions, making it an effective technique for landfill leachate detection.