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.

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.

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 the Huangling coal mine. Our approach involved acquiring high signal-to-noise ratio electromagnetic (EM) data near the transmitting line source, using unstructured tetrahedral meshes to simulate complex topography, and employing a quasi-Newton optimization algorithm for detailed 3-D 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.

The conventional magnetotelluric (MT) inversions rely primarily on L2norm to quantify the misfit between the observed data and the predicted ones. However, it often suffers from issues of unreasonable weighting of inversion data, sensitivity to outliers, and poor resolution to weak anomalies. To address these limitations and achieve better data fitting across varying scales, we propose to replace the L2norm with the Wasserstein distance to measure the distributional discrepancy between the predicted and observed data. This method adopts the Wasserstein Generative Adversarial Network (WGAN) framework and utilizes the Kolmogorov-Arnold Network (KAN) as the discriminator to implement the Wasserstein metric. By substituting the neural generator in WGAN with a physics-based forward modeling, we achieve a purely physics-driven iterative process that is similar to the conventional MT inversion workflows to ensure an adequate data fitting. Numerical experiments on synthetic models demonstrate that MTGAN-KAN can better fit data distributions and yield higher-resolution inversion results than the conventional methods. Compared to WGAN that employs a fully connected neural network (FCNN) as the discriminator, the incorporation of KAN can significantly improve the convergence and stability of MTGAN. An inversion test using MT data from Newer Volcanic Province in Australia further highlights the superior characteristics of data fitting and resolution of MTGAN-KAN in the inversion of MT data.

At present, the mainstream technology for leachate detection in landfills is electrical resistivity tomography (ERT), known for its efficiency and nondestructive 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 3-D 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 3-D inversions, we employ an 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 limited-memory quasi-Newtonian (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 and provide more accurate imaging results compared to the conventional methods. In addition, 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.