The Xianshuihe fault zone, situated along the southeastern margin of the Qinghai- Xizang Plateau, serves as a boundary between the Sichuan-Yunnan Block and the Bayankala Block. It is also one of the most active strike-slip fault zones in southwestern China. Earthquakes frequently occur along this fault zone, exhibiting distinct segmented characteristics. The 2022 Luding earthquake, which struck the Moxi segment of the fault, provides new data to support research on its seismic tectonics. This study uses deep-weighted inversion based on the WGM2012 Bouguer gravity anomaly data to determine the three-dimensional distribution of the density structure along the Xianshuihe fault within the study area. The results indicate significant lateral and vertical density anomalies near fault, and the distribution of numerous faults corresponds to transitions in the regional density gradient. The epicentre of the Luding earthquake lies within an abrupt low-density anomaly zone, suggesting that the earthquake may be closely linked to crustal stress variations across at deep density interfaces. The research reveals the deep structural characteristics and segmented activity patterns of the Xianshuihe fault, providing new geophysical evidence for understanding the mechanisms of crustal deformation and the seismogenic environment of regional seismic activity along the northern margin of the Sichuan-Yunnan block.

In the field of geophysical forward modeling, neural operator networks are emerging as an effective tool for solving partial differential equations (PDEs). However, the escalating computational cost required to train increasingly complex network models presents a significant challenge. To address this problem, we use the Extended Fourier DeepONet (EFDO) in this study to systematically investigate the trade-off between efficiency and accuracy in multi-GPU distributed training. We first analyze the limitations of two conventional strategies: the fixed-batch-size approach, which often sacrifices model accuracy to accelerate training, and the floating-batch-size approach, which faces performance bottlenecks related to hardware utilization and communication efficiency while maintaining accuracy. Building on this analysis, we propose and validate a novel strategy for dynamically adjusting batch size and learning rate. Numerical experimental results demonstrate that our method effectively reduces training time while simultaneously maintaining the model’s high accuracy and generalization capability. We present an open-source solution that demonstrates the application of multi-GPU parallelism in machine learning-based magnetotelluric forward modeling. This work provides effective strategies, adaptable to various network frameworks, for balancing computational cost and model performance in the parallel training of large-scale neural operator networks for geophysical simulation problems.

Uncertainty quantification is indispensable for reliable magnetotelluric (MT) data interpretation, given the inherent non-uniqueness of MT inverse problem solutions. However, traditional sampling-based probabilistic schemes often require millions of costly forward predictions, making them computationally prohibitive. To address this, we develop a trans-dimensional Bayesian inversion framework that incorporates a novel forward modelling operator and a reversible-jump Markov chain Monte Carlo algorithm for robust uncertainty quantification. The forward modelling method leverages the extended Fourier DeepONet (EFDO) network. Once trained, the EFDO achieves up to a 300-fold acceleration in forward predictions compared to a conventional finite volume-based solver. Furthermore, we utilize an adaptive Delaunay model parametrization during the sampling process to allow for efficient model space exploration. We demonstrate the efficacy of the proposed approach through numerical experiments and application to the COPROD2 MT field data set. Overall, this work advances Bayesian MT inversion by enabling rapid, high-dimensional inference of subsurface electrical resistivity structures, thereby facilitating reliable geological interpretation.

As a crucial branch of geophysical electromagnetic methods, the transient electromagnetic method (TEM) is widely employed in mineral resource exploration. Most mineral targets exhibit significant induced polarization (IP) effects. Forward modeling demonstrates that IP effects cause rapid attenuation of mid-to-late TEM signals and may even induce sign reversal. Consequently, data inversion and interpretation that disregard IP effects not only struggle to fit observed data adequately but also risk yielding erroneous conclusions. Building upon 3D TEM forward modeling that incorporating IP effects, this study develops a corresponding 3D inversion scheme. Given that IP properties are described by multiple interdependent parameters whose simultaneous inversion would incur prohibitive computational costs, we consider a simplified scenario: fixing IP parameters and inverting solely for electrical conductivity. Although idealized, this approach remains valuable for geological settings with minor IP parameter variations and serves as a foundation for future multi-parameter IP inversion. The finite-volume method in the time domain is adopted for 3D forward modeling, with IP effects characterized by the Debye model. For inversion, a Gauss-Newton optimization framework is implemented, integrating implicit sensitivity matrix calculation with conjugate gradient solving of the normal equations to reduce computational time and memory consumption. The efficacy of the proposed 3D inversion algorithm is validated through multiple synthetic models. We compare IP-incorporated versus IP-ignored TEM inversions to underscore the necessity of modeling IP effects, investigate the impact of heterogeneous IP parameter distributions, and present inversion results for a funnel-shaped conductive model of practical geological significance.

A comprehensive deep learning approach was introduced, encompassing data denoising, inversion imaging and uncertainty analysis. For denoising transient electromagnetic (TEM) data, we utilized a Bidirectional Long Short-Term Memory (BiLSTM) network. In the data inversion process, a combination of convolutional neural network (CNN) and BiLSTM structures was employed, and their outputs were consolidated using a multi-head attention mechanism. To ensure robust performance under challenging noise conditions, we implemented a specialized multi-channel noise training protocol during model optimization. The framework incorporates Monte Carlo (MC) dropout techniques to systematically evaluate prediction reliability throughout the inversion pipeline. This approach has not only been validated on test datasets but has also been successfully applied to the field dataset collected at the Narenbaolige Coalfield in Inner Mongolia, China. The deep learning inversion results obtained from both raw and denoised data exhibit reduced vertical continuity and increased roughness characteristics. In contrast, the Occam's inversion method with smoothness constraints yields results demonstrating superior lateral continuity and vertical smoothness. It is noteworthy that both inversion approaches show consistent interpretations regarding the scale of basalt formations and their contact interfaces with underlying sedimentary layers. Further uncertainty analysis reveals relatively higher uncertainty characteristics in the transition zones between basalt and sedimentary layers, as well as in deeper formations. The elevated uncertainty at interface regions may be attributed to model resolution limitations and inversion ill-posedness issues, whereas the higher uncertainty in deeper formations is more likely caused by the volumetric effects of electromagnetic field detection and the influence of observational data noise.

Water resources underpin human society and economic growth, yet freshwater is unevenly distributed, leaving arid regions severely water-stressed. The Beishan mining district in Inner Mongolia exemplifies this challenge: despite abundant minerals, it lacks surface water and depends almost entirely on groundwater. To improve exploration in such complex settings, we propose a Bayesian joint inversion that leverages the complementary sensitivities of Surface Nuclear Magnetic Resonance (SNMR) and Transient Electromagnetic (TEM) data within a probabilistic framework. Using a transdimensional Markov Chain Monte Carlo (MCMC) algorithm, the method adaptively balances data weighting and model complexity. Tests on synthetic and field datasets show that combining SNMR’s direct sensitivity to water content with TEM’s high-resolution resistivity imaging enhances aquifer detection across depths and enables quantitative uncertainty assessment. Applied in Beishan, the approach delineates promising aquifers, with results confirmed by drilling, offering a robust basis for groundwater exploration and sustainable management in arid regions.

The calculations of magnetotelluric (MT) responses play a fundamental role in the inversion and resolution analysis of MT problems. Conventional numerical methods for forward modeling involve solving a large system of linear equations. Although these methods provide accurate and stable solutions, they are computationally expensive as the model size increases. In this study, we develop an efficient forward-modeling network using an extended modeling in complex continuous media. By efficiently learning the mapping of differential operators from the conductivity models to the MT responses, the EFDO framework can effectively approximate the MT forward operator. Once trained, it can instantaneously predict the MT responses for complex continuous resistivity models under identical model discretization conditions. We first compare the accuracy of the EFDO with a conventional finite volume (FV)-based forward-modeling solver and the existing deep-learning (DL)-based modeling schemes. Numerical experiments demonstrate that the MT responses predicted by the EFDO exhibit high conformity with the solutions computed by the FV method. Compared with other DL-based solvers, such as the extended Fourier neural operator and the UNet-Fourier neural operator, EFDO indicates superior prediction accuracy while significantly reducing training resource requirements. In addition, EFDO exhibits excellent generalization, maintaining outstanding prediction performance for the untrained frequencies of the same class samples. The EFDO can predict the MT re- sponses at approximately 200 times the speed of the FV solver. The huge improvement in computational speed makes the EFDO a feasible solver for high-dimensional MT stochastic inversions, which require many forward evaluations.

The magnetotelluric (MT) method is highly advantageous in geothermal resource exploration because of its deep probing capability, low cost, and sensitivity to key geothermal system elements, such as heat sources, reservoirs, and caprocks. To address the challenge of balancing the MT inversion resolution and computational efficiency, we develop a Gauss-Newton optimization inversion algorithm based on the solution space dimensionality reduction (SSDR) technique. This algorithm uses SSDR to establish algebraic mapping relationships between the edges of grid cells, effectively reducing the degrees of freedom in the linear equation system required for forward and pseudoforward modeling, thereby saving computational costs. In addition, during the inversion process, a multiple right-hand direct-iterative hybrid solver is used to solve the dimensionally reduced linear equations, further enhancing the computational efficiency of the inversion. We then validate and analyze the accuracy and efficiency of the forward and inversion algorithms using various synthetic models. Finally, we apply this inversion strategy to field MT data from the Dabie Mountain geothermal area in eastern China. On the basis of the inversion results, we then analyze the thermal genesis model of the region, providing technical support for the exploration and development of deep geothermal resources.

Identifying geothermal property characteristics and accurately assessing geothermal resource potential are crucial foundations for achieving precise zoning and large-scale,efficient development and utilization of geothermal energy.Xiong'an New Area,one of the typical low-temperature geothermal systems in the North China plain,is selected as the study area.The study aims to obtain the thermal reservoir properties of the Wumishan Formation,predict the three-dimensional temperature distribution,improve the resource assessment algorithm,and evaluate the geothermal resource potential under heterogeneous conditions for various thermal properties and stratigraphic parameters.The research results indicate that the geothermal resource quantity of the Wumishan Formation above 5 000 m is equivalent to 3.219 5×105 million tons of standard coal.Using the balanced injection and production method,the calculated extractable geothermal fluid resource quantity is 436.64×106 m3 per year,equivalent to 508.217 4 thousand tons of standard coal in extractable heat.The extractable resource quantity and heat calculated by the balanced injection and production method are 48.7 times and 50.3 times greater,respectively,than those calculated using the extraction coefficient method.The geothermal resource per unit area and the geothermal fluid resource per unit area are the largest in the Rongcheng area.The calculated resource indicators under heterogeneous conditions are 2.29 to 2.95 times higher than those under homogeneous conditions.

Summary Bayesian methods provide a valuable framework for rigorously quantifying the model uncertainty arising from the inherent non-uniqueness in the magnetotelluric (MT) inversion. However, widely-used Markov chain Monte Carlo (MCMC) sampling approaches usually require a significant number of model samples for accurate uncertainty estimates, making their applications computationally challenging for 2D or 3D MT problems. In this study, we explore the applicability of the Hamiltonian Monte Carlo (HMC) method for 2D probabilistic MT inversion. The HMC provides a mechanism for efficient exploration in high-dimensional model space by making use of gradient information of the posterior probability distribution, resulting in a substantial reduction in the number of samples needed for reliable uncertainty quantification compared to the conventional MCMC methods. Numerical examples with synthetic data demonstrate that the HMC method achieves rapid convergence to the posterior probability distribution of model parameters with a limited number of model samples, indicating the computational advantages of the HMC in high-dimensional model space. Finally, we applied the developed approach to the COPROD2 field dataset. The statistical models derived from the HMC approach agree well with previous results obtained by 2D deterministic inversions. Most importantly, the probabilistic inversion provides valuable quantitative model uncertainty information associated with the resistivity structures derived from the observed data, which facilitates model interpretation.

We present a multidimensional inversion methodology for loop source time-domain electromagnetic data. The developed algorithm is a robust, efficient, and user-oriented tool for the multidimensional inversion of typical loop source time-domain electromagnetic configurations. A time-domain finite volume (FV) method and a direct solver are utilized for solving the 3-D forward problem, while the iterative Gauss-Newton (GN) optimization method is implemented for the inversion kernel. The code is parallelized for calculating multiple sources simultaneously to accelerate the inversion. Based on different exploration tasks, we present three different inversion experiments on typical field scales for commonly used loop source TEM configurations. These examples verify the effectiveness and benchmark the developed 3-D algorithm. Considering that TEM data are often gathered along profiles, we carried out an analysis using the 3-D inversion algorithm for 2-D data by adjusting the model roughness along the different domain directions, which seem to sufficiently constrain but not over-regularize the model along the strike direction to retrieve the true model structure. Besides using the vertical signal component for large-scale moving and fixed loop configurations, the horizontal components are also included in the 3-D inversion. The inversion algorithm is further verified with dense boat-towed central loop TEM data recorded on a volcanic lake in the Azores, Portugal. The reconstructed model is consistent along the profile line and the main features agree with the 1-D stitched models. Moreover, the 3-D model depicts additional reasonable features not visible in the 1-D models.

Accurate estimation of the Earth’s interior temperature is essential for solving fundamental scientific and applied geothermal problems. Currently, there is no universal method for determining deep temperature fields; however, such a method may be based on resistivity, a temperature-dependent proxy parameter. We propose an electromagnetic (EM) geothermometer based on the temperature–pressure coupled resistivity model (TPCRM). This geothermometer can accurately determine the relationship between the normalized resistivity, temperature, and pressure in deep formations based on well-logging, gravity, and EM data, thus allowing to visualize the temperature distribution. The TPCRM is utilized to predict the subsurface temperature in the Xiong’an New Area and shows an accuracy of 76.35%–96.58%. Sensitivity analysis of the critical variables of the TPCRM reveals that the TPCRM relatively weakly depends on the number of constraining boreholes and that the optimization of the subdivision spacing of the well-logging data can significantly improve temperature prediction accuracy. In addition, the effect of the spacing of inverted resistivity normalization grid nodes on the temperature prediction accuracy is relatively weak because the TPCRM considers the factor of the overburden pressure. The TPCRM is a promising tool for studying thermal genetic mechanisms, as well as fine evaluation of geothermal resources for their large-scale and efficient development and utilization.

Objective In geothermal exploration, a clay cap is a typical hydrothermal geothermal system, and its depth and distribution range can provide crucial information for delineating the scope of geothermal resources and determining the location of geothermal drilling. Clay caps are usually composed of a clay layer formed through hydrothermal reactions and are characterized by low resistance. The low-resistivity cap can be effectively imaged using the audio-frequency magnetotelluric method. To obtain uncertainty information about the distribution of clay cap layers and imaging results, this paper employs the 1D trans-dimensional Bayesian inversion method to investigate the detection capabilities of low-resistance cap layers in geothermal areas through audio electromagnetic data. Methods In this paper, a model test is first carried out to establish a geoelectric model of a typical geothermal system.Subsequently, a 1D trans-dimensional Bayesian algorithm is used to invert the synthetic data to obtain the uncertainty information of the subsurface electrical structure and interface position. Then, the method was applied to the processing of measured audio frequency magnetotelluric data in the Yanggao geothermal area of Shanxi Province. Results This method has relatively accurate identification ability for low-resistivity clay caps, and the obtained uncertainty analysis results of the upper and lower interfaces of low-resistivity caps are also relatively reliable according to numerical tests. It was found that this method has a good ability to identify shallow low-resistivity caps and can provide an uncertainty evaluation of the clay cap interface position via field data tests. The 2D inversion results of this survey line verify the reliability of the 1D inversion. Conclusion This method has relatively accurate imaging capabilities and uncertainty analysis capabilities for shallow geothermal clay caprocks and has strong application prospects in geothermal detection.

Central loop transient electromagnetic (TEM) data are often interpreted by conventional 1-D or quasi-2-D inversion techniques. For example, the lateral constrained inversion (LCI) is a powerful technique for quick interpretation of central loop TEM data, and can produce spatially consistent resistivity images for profile data by assuming spatial correlation between adjacent model parameters. Such quasi-2-D techniques are very powerful in cases multidimensional effects are small or negligible. However, the inverse solution of conventional LCI methods strongly depends on subjective interpreter choices such as the model regularization and the imposed lateral constraints. Due to inherent non-linearity and nonuniqueness of the TEM inverse problems, this can result in biased model parameters and their estimated model uncertainties. We present a transdimensional Markov chain Monte Carlo method for the quasi-2-D inversion of TEM data using a Bayesian inference framework. We term the approach quasi-2-D, since the model is parametrized in 2-D with unstructured Voronoi cells, whereas the TEM response at each station is predicted using a 1-D forward solution to make the problem computationally affordable. During the inversion, the number of Voronoi cells as well as their positions and resistivities are variable. Accordingly, the level of model complexity is automatically determined by the framework and adapted to the spatial resolution of the data, thus avoiding the need for subjective model regularization or spatial constraints. The approach is validated using synthetic data and compared to 1-D Bayesian and conventional Gauss Newton inversion techniques. The application to dense field data from a floating TEM survey leads to a consistent subsurface image with unbiased uncertainty estimates and a plausible depth of investigation. The quantitative uncertainty information provided by the Bayesian framework is beneficial in identifying resolution.

Abstract The karst cavern is common undesirable geological body in limestone areas, which can bring great safety hazards to the construction and operation of tunnels, bridges and highways. Transient electromagnetic method (TEM) can effectively detect hidden karst structures based on the difference in electrical property between the karst cavern and the surroundings. Traditionally, 1D inversion is commonly used for the interpretation of TEM data due to its high efficiency. However, this may lead to artifacts due to 2D or 3D effects in practical surveys. In this study, we present a Gaussian-Newton approach to 3D inversion of TEM data for karst cavern detection. The numerical test on synthetic TEM data demonstrates that 3D inversion can effectively delineate the location and geometry of concealed karst cavern compared to the 1D inversion results.

为了解湘东南永兴地区上地壳地质构造特征及圈定潜在的找矿靶区,对郴州永兴地区的5条大地电磁剖面数据进行了分析与处理,并应用非线性共轭梯度法进行二维反演,获得了该地区上地壳电性结构.结果显示该地区电性分布不均匀,横向上出现高低阻相间分布,纵向无明显电性分层特征.结合湘东南区域地质资料,详细分析了研究区电性结构的地质构造含义.研究表明茶郴断裂带为深大断裂带,控制着研究区内的地质构造及成矿流体上涌通道.根据南岭成矿带铅锌金属矿的成矿规律,结合区域电性结构特征,对研究区内两处铅锌矿体成矿机理与电性结构之间的关系进行了分析讨论.研究结果对认识湘东南永兴地区上地壳的结构特征及寻找潜在矿体具有很好的参考.

Owing to its sensitivity to hydrothermal alteration and geothermal fluids, the distribution of subsurface electrical conductivity provides critical information for characterizing geothermal systems. For geothermal exploration, the controlled-source electromagnetic (CSEM) technique provides a crucial tool to image the subsurface resistivity structures, especially in areas with strong cultural noise. Usually, land-based CSEM surveys are carried out with dozens of operating frequencies to enhance spatial resolution. However, the 3D inversion of multifrequency CSEM data using the commonly used direct solver is challenging with limited computational resources. In this study, we implement a practical inversion strategy for interpreting 3D multifrequency CSEM data. By combining a hybrid direct-iterative solver with the inexact Gauss-Newton optimization, 3D inversion of CSEM data involving multiple frequencies can be performed effectively on typical workstations. First, we test the effectiveness of the developed approach using synthetic multifrequency 3D CSEM data generated for a simplified geothermal model. The inversion strategy is then applied to the multifrequency CSEM field data collected for the geothermal exploration at Tianzhen region in Shanxi Province, China. The comparison between the inversion results using the sparse data set (six frequencies) and the dense data set (12 frequencies) highlights the necessity of using data from more frequencies in the inversion to improve the resolution. The resulting 3D resistivity model clearly delineates the clay alteration layers and shallow thermal reservoirs of the potential high-temperature geothermal system within the study area, while its deep heat source is not revealed owing to the limited investigation depth of the survey.

Abstract The presence of subsurface karst caverns could pose significant threat to highway construction safety, and the knowledge about the locations and volumes of the caverns is crucial for evaluating potentially hazardous areas. In this work, we present a transdimensional Bayesian approach for characterizing undercover caverns by inverting direct current resistivity data., This approach provides a robust measure of uncertainty associated with the resulting resistivity model. We evaluate the effectiveness of the algorithm on a synthetic 2D resistivity model. The results demonstrate that quantitative uncertainty information on the derived model parameters is vital for reliable data interpretation and facilitates decision making.

The development of underground artificial cavities plays an important role in the exploitation of urban spatial resources. As the rapidly growing number of underground artificial cavities with different depths and scales increases, the detection and identification of underground artificial cavities has become a key issue in underground engineering studies. Geophysical techniques have been widely used for the construction, management, and maintenance of underground artificial cavities. In this study, we present two identification methods for underground artificial cavities. Apparent resistivity imaging is the most popular technique for quickly identifying underground artificial cavities, using the forward simulation results of a three-dimensional earth model and comparing these with the preset positions of artificial cavities, as demonstrated in the experiment. To further improve the efficiency of underground artificial cavity identification, we developed a fast recognition approach for underground artificial cavities based on the Bayesian convolutional neural network (BCNN). Compared to a traditional convolutional neural network, the performance of the BCNN method was greatly improved in terms of the classification accuracy and efficiency of identifying underground artificial cavities with apparent resistivity image datasets.