The subsurface conductivity of geological media is often anisotropic, making three-dimensional (3D) anisotropic inversion of controlled-source electromagnetic (CSEM) essential for resolving complex geologic settings. However, compared to isotropic inversion, anisotropic inversion involves a substantially greater number of model parameters, increasing the severity of the non-uniqueness problem and enhancing interpretation complexity for large-scale field data. To address these challenges, we present an innovative anisotropic inversion approach that incorporates a Gramian-based constraint, which promotes similarity between horizontal and vertical conductivity models without relying on a prior information. We formulate the inverse problem within a Gauss-Newton framework and employ the finite element method on unstructured grids, leveraging parallel direct solvers for computational efficiency. Synthetic tests on complex anisotropic land and marine CSEM models show that the Gramian-constrained inversion significantly suppresses spurious anomalies and improves reliability compared to conventional anisotropic inversion. Application to field CSEM data from the Huaniushan Pb-Zn mining area in Gansu Province, China, demonstrates high consistency with real geology and drilling results. These findings highlight the proposed approach as a computationally efficient, robust, with direct relevance to hydrocarbon, mineral, and geothermal exploration.

The capturing subsurface structure through geophysical measurements can gain a more comprehensive understanding of groundwater distribution. While geophysical electromagnetic methods yield subsurface resistivity data, converting this into hydrological information is not straightforward. Well-logging offers insights into rock strata vertically but lacks spatial detail on large-scale lithological variations. Consequently, merging geophysical and well-logging data for extensive hydrogeological modeling has emerged as a crucial research area. In this study, we introduce convolutional neural networks and bi-directional long short-term memory (CNNs-BiLSTM) network to process massive towed transient electromagnetic (tTEM) datasets. Our network incorporates the depth-of-investigation (DOI) and smooth constraints for effective tTEM data inversion. We further validate the network’s effectiveness and generalization capacity using synthetic models and real tTEM data from Switzerland’s Aare Valley region. Furthermore, by combining the limited well-logging data, we establish a spatial clay content distribution model using an optimal inversion interpolation method. Leveraging this lithology model, we employ the groundwater modeling system (GMS) platform to determine regional groundwater levels. Our numerical simulation aligns closely with results obtained via the top of the saturated zone (TSZ) method and exhibits strong agreement with observed water table data, affirming the reliability of our comprehensive hydrogeological model. Our proposed method and workflow present an innovative approach to effective hydrological modeling utilizing large-scale geophysical electromagnetic data.

The resistivity distribution obtained from traditional inversion methods for magnetotelluric (MT) data often lacks clarity, making it difficult to delineate boundaries between host media and anomalous targets. To address this, we developed a novel 3-D MT inversion approach based on the multinary transformation of model parameters. This method transforms the model resistivity distribution into a desired step-function-like form, enabling explicit identification of interfaces between geological units. The sharpness of the recovered resistivity model is controlled by the standard deviation of the multinary transformation’s error function, and an adaptive technique is introduced to adjust this parameter during the inversion process to account for deviations between true and discrete values in the multinary space. The inversion problem is solved using a data-space Gauss-Newton approach, which enhances memory efficiency and convergence speed. Additionally, unstructured tetrahedral meshes are utilized to accurately model rugged topography and complex geoelectric structures. Synthetic model studies demonstrate the superiority of the adaptive multinary inversion over conventional maximum smoothness inversion and fixed standard deviation multinary inversion. Finally, the method is applied to image subsurface resistivity in the northwest Geysers geothermal field in California, USA, showcasing its effectiveness.

The magnetotelluric (MT) signals are susceptible to anthropogenic noise and the existing denoising methods have significant shortcomings in low-frequency situations. To address the problem, we propose an innovative denoising approach. It is different from the existing methods that attempt to achieve signal-noise separation through one step. The denoising process is divided into two steps in the proposed approach. The effective low-frequency dominant component and high-frequency component are sequentially extracted through deep learning and dictionary learning. We propose a new deep learning network named DnCNN-GRU which combines the powerful feature extraction capability of Denoising Convolutional Neural Network (DnCNN) and the strong temporal sequence processing ability of Gated Recurrent Unit (GRU), enabling accurate extraction of the low-frequency MT signal. Furthermore, we integrate this network with the K-Singular Value Decomposition (KSVD) dictionary learning to achieve accurately extraction of effective high-frequency components. Tests of synthetic data indicate that our method is the best compared to a series of state-of-the-art (SOTA) algorithms. It is the only method that can completely remove various types and scales of cultural noises while brilliantly preserves both the low and high-frequency signals. In addition, our method is validated on apparent resistivity and phase data and is significantly superior to the commonly used Robust estimation method. These results demonstrate that our method can solve the problem mentioned above and can be a substitute for Robust estimation or remote reference processing.

To improve the signal-to-noise ratio (SNR) of controlled-source electromagnetic (CSEM) data observed in strong interference environments, a new deep learning network is proposed and named gated temporal convolutional network (GTCN) to map noisy sequences to high-quality sequences. This network is an improvement of two state-of-the-art (SOTA) networks specifically designed for time series processing, temporal convolutional network (TCN) and gated recurrent units (GRUs). A carefully crafted sample set is created by utilizing shift-invariant sparse coding (SISC) methods and used to train the newly proposed network and six other SOTA deep learning networks. Experimental results of the synthetic data indicate that the new network not only outperforms SISC in accuracy and efficiency but also is significantly superior to the other six SOTA deep learning methods. The proposed GTCN method can improve the 0 dB noisy signals to 32.6749 dB and improve the average SNR from −5 to 23.5999 dB. The effectiveness and reliability of the proposed method are also verified through measured data from Sichuan and Yunnan, China. The time series processed by the new approach exhibits more pronounced periodic characteristics, resulting in smoother and more continuous apparent resistivity curves. All these experiments demonstrate that the new scheme is an effective method to improve the quality of CSEM data and contribute to the reliability of CSEM exploration.

In this study, we present an efficient and memory saving 3D inversion algorithm for interpreting controlled-source electromagnetic (CSEM) data using the total electric field formulation. To tackle CSEM problems involving complex geometries, we discretize the study domain for both forward and inversion problems using unstructured tetrahedral elements. Our inversion scheme combines the parallelized finite element (FE) method with the Gauss-Newton optimal strategy. Additionally, we transform the conventional model space inversion into data space inversion, significantly reducing the computation time and Random Access Memory (RAM) requirements during the inversion process. To begin, we validate the effectiveness and stability of the developed data space inversion algorithm by utilizing a synthetic land CSEM basin model and a synthetic marine CSEM model with bathymetry. These validation experiments further demonstrate that compared with the conventional model space inversion method, the computational efficiency of the data space inversion scheme is greatly improved and the memory required is significantly reduced. Furthermore, we apply the inversion method to survey CSEM data to demonstrate the practical applicability of the new inversion scheme.

Three-dimensional (3-D) inversion technique has become an important and practical approach for magnetotelluric (MT) data interpretation. In this article, we developed a 3-D parallelized MT inversion scheme using the edge-based finite element method and applied the developed method to the newly collected MT data in the Xinjiang Luntai area. The distorted hexahedral element is adopted to incorporate topography into the forward modeling and inversion for complicated scenarios. We use the Gauss–Newton optimization method to minimize the objective functional for MT inversion. The developed algorithm is parallelized using MPI over frequencies and parallel direct solvers when solving the forward and adjoint problems for each frequency. We compare the performance of the least-square QR (LSQR) factorization and preconditioned conjugate gradient (PCG) solvers for the model update within each Gauss–Newton iteration and found that the LSQR solver is more stable. The developed inversion algorithm is validated using several synthetic models. Finally, we applied the inversion algorithm to the subsurface resistivity imaging in the Luntai area. The recovered geoelectric model from full 3-D inversion fits well with the known geological and geophysical information. The recovered model shows a low resistivity layer which may be caused by the salt strata. Besides, the inversion results reveal the movement tectonic in this survey area within a depth of 9 km.

Presently, the 3-D inversion technique has started playing a more important role in controlled-source electromagnetic (CSEM) data interpretation. With the development of hardware and computation algorithm, 3-D inversion technique has developed rapidly during the past decades. In this article, we present a newly developed 3-D parallelized inversion algorithm in the frequency domain with hexahedral discretization. Within the framework of this approach, we use the finite-element method (FEM) in the forward modeling and Gauss-Newton optimization technique in the inversion. We solve the forward modeling and adjoint problem efficiently with Math Kernel Library (MKL) Pardiso parallel direct solver. Considering the fact that the forward modeling and sensitivity calculation are frequency independent, we further parallelize the algorithm over frequency using Message Passing Interface (MPI) to speed up the modeling and inversion process. The sensitivity matrix is calculated explicitly, which enables us to estimate the optimized regularization parameter easily based on the spectral radius estimation. We proposed a new roughness operator for hexhedral discretization which works well for CSEM inversion problems. We applied the developed algorithm to several realistic CSEM models. The inversion results demonstrate the effectiveness and stability of our inversion scheme.

An alternating joint inversion method for controlled-source electromagnetic (CSEM) and seismic data is developed. The structural constraint is used for correlating and constraining the electromagnetic (EM) resistivity and seismic velocity parameters during the inversion. The structural coupling used is the joint total variation (JTV) constraint, which is incorporated into the objective function of the individual EM or seismic inversion to enforce the structural similarity between the resistivity and velocity. In this paper, the conventional cross-gradient constraint is not preferred as it can only be used for enforcing structural similarity for 2-D or 3-D case since it is always zero for 1-D joint inversion. The JTV constraint can be applied for 1-D joint inversion, as well as for the 2-D/3-D case, which is of a broader interest. The improved Gauss-Newton (GN) is used for minimizing the objective function and for reconstructing the subsurface resistivity and velocity. The alternating joint inversion algorithm is applied for integrating land CSEM data with cross-well seismic data for subsurface reservoir evaluation and water-oil identification. Numerical examples show that the developed joint inversion can improve the inversion results significantly over those from the separate EM or seismic inversion.

The presence of shallow conductive heterogeneities can cause static shift in controlled source audio-frequency magnetotellurics (CSAMT) apparent resistivity sounding curves. This is observed as a shift along the apparent resistivity axis in double logarithmic coordinates. Such effect can cause difficulties in CSAMT data interpretation. In this letter, we established a new method to identify and correct the CSAMT static shift based on the high-resolution Radon transformation. We took advantage of the property that the static shift of apparent resistivity curves behaves as a point in the Radon domain. We presented 3-D synthetic study to demonstrate that the static shift can be effectively removed from the apparent resistivity curve. However, due to the low resolution and precision, the traditional Radon transform can generate “scissor-tail” and then, the static shift may not be completely removed. We proposed to use a new high-resolution Radon transform by improving the regularization matrix using the least squares inversion. Our numerical simulation shows that by using this high-resolution Radon transform, the static shift converges accurately to a point without showing the “scissor-tail.” In the application to field CSAMT data, the high-resolution Radon transform method was able to correct the static shift effectively; thus, it can improve the precision and accuracy in data interpretation.

It is well known that both gravity and magnetolluric (MT) methods can be used for the depth-to-basement estimation due to the density and conductivity contrast between the sedimentary basin and the underlaid basement rocks. In this case, the primary targets for both methods are the interface between the basement and sedimenary rocks as well as the physical properties of the rocks (density and conductivity). The solution of this inverse problem is typically nonunique and unstable, especially for gravity inversion. In order to overcome this difficulty and provide a more robust solution, we have developed a method of joint inversion to recover both the depth to the basement and the physical properties of the sediments and basement using gravity and MT data simultaneously. The joint inversion algorithm is based on the regularized conjugate gradient method. To speed up the inversion, we use an effective forward modeling method based on the surface Cauchy-type integrals for the gravity field and the surface integral equation representations for the MT field, respectively. We demonstrate the effectiveness of the developed method using several realistic model studies.

Determining the sediment-basement interface is the major step in evaluating the mineral resource potential of a region. The magnetotelluric (MT) method can be effectively used for solving this problem because there exists a strong contrast in resistivity between a conductive sedimentary basin and a resistive basement. Conventional inversions of MT data are aimed at determining the volumetric distribution of the conductivity within the inversion domain. The recovered distribution of the subsurface conductivity is typically diffusive, which makes it difficult to select the sediment-basement interface. This letter develops a novel approach to 3-D MT inversion for the depth-to-basement estimate. The key to this approach is selection of the model parameterization, with the depth to basement being the major unknown parameter. In order to estimate the depth to the basement, the inversion algorithm recovers both the thickness and the conductivities of the sedimentary basin. The forward modeling is based on the integral equation approach. The inverse problem is solved using a regularized conjugate gradient method. The Fréchet derivative matrix is calculated based on quasi-Born approximation. The developed method and the algorithm for MT inversion for the depth-to-basement estimate are illustrated on several realistic geoelectrical models.

This letter introduces a new method for the modeling and inversion of magnetic anomalies caused by crystalline basements. The method is based on the 3-D Cauchy-type integral representation of the magnetic field. Traditional methods use volume integrals over the domains occupied by anomalous susceptibility and on the prismatic representation of the volumes with an anomalous susceptibility distribution. Such discretization is computationally expensive, particularly in 3-D cases. The technique of Cauchy-type integrals makes it possible to represent the magnetic field as surface integrals, which is particularly significant in solving problems of the modeling and inversion of magnetic data for the depth to the basement. In this letter, a novel method is proposed, which only requires discretizing the magnetic contrast surface for modeling and inversion. We demonstrate the method using several synthetic models. The results show that the new method is fast and capable of providing high-resolution depth estimation for the sediment-basement interface.