Controlled-source electromagnetic (CSEM) method is an important geophysical tool for sensing and studying subsurface conductivity structures. Advanced forward modeling techniques are crucial for the inversion and imaging of CSEM data. In this letter, we develop an accurate and efficient 3-D forward modeling algorithm for CSEM problems, combining spectral element method (SEM) and octree meshes. The SEM based on high-order basis functions can provide accurate CSEM responses, and the octree meshes enable local refinement, allowing for the discretization of models with fewer elements compared to the structured hexahedral meshes used in conventional SEM, while also providing the capability to handle complex models. Two synthetic examples are presented to verify the accuracy and efficiency of the algorithm. The utility of the algorithm is verified by a realistic model with complex geometry.

In the field of geophysical exploration, the application of deep learning techniques has garnered significant attention. This paper proposes a new deep learning model for three-dimensional magnetotelluric inversion, named 3DInception-U. In this model, we integrate the inception module into the network architecture and combine the concatenation layer with a U-Net structure.This model has two advantages: Firstly, the inception module, along with the deep concatenation layer, enhances the network’s capability for feature extraction and representation; Secondly, the skip connections in the U-Net facilitate information propagation, enabling the design of a network with fewer parameters but better performance. We produced 10,000 3D complex samples for training by Gaussian Random Fields (GRF) and compared 3DInception-U with existing 3D MT inversion models and applied it to real geological interpretation. The results demonstrate that this network architecture achieves good inversion accuracy and robustness.

The transient electromagnetic method (TEM) is a widely used technique for metallic mineral, geothermal, and other natural resource exploration. With the continuous development of exploration technologies, the demand for accurate subsurface models and broader application environments presents significant challenges for the forward modeling of TEM, necessitating higher precision forward modeling strategies and faster computation methods. This paper proposes a subspace iterative solution method based on flexible generalized minimal residual(FGMRES) method, utilizing domain decomposition method for parallel acceleration. Specifically, we optimized the grid for long-period transient electromagnetic response calculations, selecting a set of highly adaptable modeling parameters that reduce grid degrees of freedom without compromising accuracy. Furthermore, we replaced the commonly used second-order schemes with a third-order backward Euler difference scheme and conducted forward modeling tests with different time steps, resulting in a more reasonable time step length that improves computational efficiency. The effectiveness of the algorithm was validated by comparing the layered model with semi-analytical solutions and the three-dimensional model with previous results. The comparison results with other open-source codes and numerical experiments on large-scale models indicate that our method achieves high accuracy and efficiency for both simple and complex models, while requiring relatively less memory.

Controlled-source electromagnetic (CSEM) method is a valuable technique used in geophysical prospecting. However, the efficiency of CSEM forward modeling is significantly limited by the number of frequencies. This article proposes a restarted rational Krylov (RK) subspace algorithm, which has significantly improved the computational efficiency of 3D multi-frequency CSEM forward modeling. Initially, a brief introduction is provided on the finite element forward modeling based on octree meshes, which can effectively and accurately discretize the subsurface and allow us to consider the details and complexity of the geological structures. Subsequently, the principle of using the rational Krylov subspace algorithm to solve the forward equations at multi-frequency is given. Then, based on error derivation, we present the correction formula for the approximate solution and the algorithm framework for the restarted rational Krylov subspace algorithm, which solves the problem that the calculation accuracy of the traditional rational Krylov subspace algorithm depends on the subspace dimension. Ultimately, a layered model is used to determine the optimal dimension of the restarted subspace and validate the accuracy and efficiency of the proposed algorithm. The Nihe iron deposit model is also employed to demonstrate the capability of the proposed algorithm in handling practical and complex models.

The use of the shaft-rate electromagnetic fields generated by moving ships for detection and sensing purposes has several advantages, including effective target recognition and excellent concealment. It offers a solution to the challenges faced in detecting underwater targets. In this study, we propose a method to identify and analyze the shaft-rate electromagnetic field signals using an improved deep learning algorithm and a spectral-direction analysis technique. Initially, we apply variational mode decomposition (VMD) to identify the multifrequency characteristics of both synthesized and real extremely low-frequency (ELF) electromagnetic signals, creating a reliable sample library for deep learning. Next, we develop an improved deep learning model that combines the residual network (ResNet) with the aforementioned sample library to accurately detect the weak narrowband electromagnetic field signals hidden within the noise. Additionally, we use the spectral-direction analysis method to estimate the direction of the ship’s movement. Finally, we validate our proposed method through a synthetic model and a field experiment. The results demonstrate the effectiveness of our approach in identifying the shaft-rate electromagnetic field signals and accurately estimating the direction of moving ships. The developed method shows the potential for accurate sensing and localization of moving ships.

Magnetotelluric (MT) has significant value in earthquake prediction, space weather monitoring, mineral resources exploration, and deep Earth structure detection. However, due to the complexity of the environment, MT data collected often are of low data quality due to noise pollution. The noisy data seriously affect the accuracy of the detection of underground structures. Therefore, we propose a magnetotelluric noise suppression method based on a coordinate attention-temporal convolutional network (CA-TCN). First, the CA-TCN is trained with a large dataset of artificially created data to learn the nonlinear mapping relationship between the noisy data and noise contours. Then, the CA-TCN model achieves the mapping transformation from noisy data to noise contours in the MT data. Finally, we subtract the noise contours obtained from the CA-TCN mapping model from the original noisy data to achieve signal-to-noise separation and reconstruct high-quality data. In simulated experiments, the similarity between denoised data and known high-quality data from Qinghai reaches 98%. The results demonstrate that the proposed method exhibits significant advantages compared to convolutional neural network (CNN) methods and so on. These findings validate the feasibility of the proposed approach. We applied the proposed method to the real measured data collected from the LuZong mining area, resulting in smoother and more continuous apparent resistivity curves. This indicates that noise in the MT data has been effectively removed, leading to a significant improvement in the quality of the MT data.

The conventional magnetotelluric inversion method is subject to the influence of the initial model, which leads to an unstable inversion process and a tendency to get trapped at local optimal solutions. In contrast, deep learning technology relies on its powerful non-linear fitting capability and can construct complex non-linear mappings directly from observation data (input) to model (output). In recent years, it has received extensive attention from researchers. Due to the difficulties in creating a sufficiently large dataset and performing extensive neural network training, most current magnetotelluric inversion methods for geophysical exploration remain limited to one-dimensional (1D) or two-dimensional (2D) scenarios. To the best of our knowledge, for deep learning-based three-dimensional (3D) magnetotelluric inversion, currently there is no reported work in the literature. In this work, we propose a 3D magnetotelluric inversion method based on deep learning technology. By designing a neural network architecture for 3D structures (MT3D-Net), we achieve an end-to-end mapping from the network input to output. To alleviate the excessive dependence of the network on the training set, we introduce a joint weighted loss function based on data-driven and physics-driven method, allowing the network to follow the physical constraints of magnetotelluric data during the training process and thus more reasonably guide the update of network parameters. Numerical experiments show that this method combines the advantages of traditional and data-driven inversions, significantly improving the stability and accuracy of magnetotelluric inversion. The proposed method has been successfully applied to synthetic models and measured field data, and has good application prospects.

In this article, we propose a structural constraint method to improve the resolution of 3-D frequency-domain controlled-source electromagnetic (CSEM) data imaging. The subsurface interfaces can be obtained from high-resolution seismic imaging data or reliable geological information. First, we assume that electrical parameters within a given formation are classified, meaning that they exhibit variation around their average value. Then, the structural constraint can be guided by the resistivity averages and ranges obtained from petrophysical measurements. In this way, we can achieve categorical inversion results in known regions or even capture structures that are insensitive to data, thereby enhancing the reliability of the interpretation of CSEM data. In addition, we utilize octree-based nonconforming hexahedral meshes to construct the structurally constrained model to simulate undulating terrain and complex underground interfaces more effectively. We adopt the NLCG algorithm for the inversion of CSEM data. Finally, we test the effectiveness of the proposed structural constraint method using synthetic and field datasets. The inversion results show that our method can constrain the known strata in shallower parts well and significantly improve the resolution of the deeper regions.

Audio magnetotelluric (AMT) is commonly used in mineral resource exploration. However, the weak energy of AMT signals makes them susceptible to being overwhelmed by noise, leading to erroneous geophysical interpretations. In recent years, deep learning has been applied to AMT denoising and has shown better denoising performance compared to traditional methods. However, current deep learning denoising methods overlook the characteristics of AMT signals, resulting in reduced denoising accuracy. To enhance the denoising performance of deep learning by better matching the features of AMT signals, we propose a CBAM-based (Convolutional Block Attention Module) method for AMT denoising. This method focuses on the features of AMT signals and improves the process from three aspects: (1) In the establishment of the sample set, we adopt a multi-component form based on the correlation of noise to enable the neural network to explore the potential connections among the components of AMT during the training process, thus constructing a stronger network mapping relationship. (2) In the construction of the neural network, we have introduced the CBAM structure into the residual blocks of the ResNet to enhance the network’s feature learning capability by focusing on the characteristics of noise. (3) In the design of the denoising procedure, we adopt a process of identification before denoising to protect the noise-free data segments from being compromised during the denoising process. Finally, through synthetic, field data experiments, and comparative tests, we demonstrate that our proposed method achieves higher denoising accuracy than some traditional methods and conventional deep learning methods.

Geomagnetic data are widely used in earthquake prediction, mantle conductivity imaging, and other fields. However, the problem of geomagnetic data being contaminated by cultural noise is becoming increasingly serious. Existing denoising methods have shortcomings such as insufficient flexibility and the need for manual intervention. To this end, we modify the U-net and propose a new intelligent geomagnetic signal denoising method based on the network. The novel network not only combines the advantages of denoising convolutional neural network (DnCNN) and U-net, but also utilizes the shortcut connections to prevent network degradation. We obtain a high-precision denoising model through elaborate training sets. The processing results of synthetic data show that the improved U-Net can remove various types of noise in one step, such as impulse noise, square wave noise, and Gaussian noise. The signal-to-noise ratio (SNR) of the denoised signal increases by an average of more than 20 dB, and the average normalized-cross correlation (NCC) between the denoised signal and the high-quality signal reaches 0.9998. Compared with Wavelet threshold denoising, DnCNN, and U-Net, the improved U-Net has obvious advantages. We apply the method to real geomagnetic data collected in Guangxi, Yunnan, Gansu, and Tibet, China. The results demonstrate that the proposed method can significantly improve the tippers, coherencies, and induction arrows. Compared with traditional methods, our method eliminates subjective bias, improves the adaptability to different types of noise, and is conducive to improving the resolution and reliability of geomagnetic depth sounding.

This study developed an efficient 3-D inversion algorithm for controlled-source electromagnetic method (CSEM). The spectral element method based on high-order Gauss-Lobatto-Legendre (GLL) basis functions with infinite element boundary conditions is used to quickly solve forward problems and adjoint forward problems for inversion, which can significantly reduce the computational cost while guarantee the accuracy. Due to the use of forward modeling with the high-order basis functions, we can give priority to the demand of inversion when designing the grid, and then choose the appropriate order for forward modeling based on the size of the grid, which can make the grid more scientific both for forward and inversion. The L-BFGS optimization algorithm without explicit computation and storage of Hessen matrix is used to solve the objective function minimization problem. Furthermore, a new preconditioner is introduced to update the initial approximate Hessian matrix in L-BFGS, which improves the convergence of the algorithm. To further improve the efficiency of the algorithm, we implemented parallelization based on Message Passing Interface (MPI). The synthetic examples show the efficiency of our algorithm compared with the conventional inversion method, and the field example demonstrated the adaptability and utility of the algorithm.

Three-dimensional frequency-domain controlled-source electromagnetic (CSEM) inversion is an essential technology for subsurface conductivity imaging. In this letter, we develop an efficient 3D inversion scheme for multi-frequency CSEM (MFCSEM) data measured on a topographic earth. Firstly, the model is discretized using the unstructured mesh, which has the ability to simulate the undulating topography. Then, we divide the frequency range into two independent frequency intervals and use the rational Krylov (RK) subspace algorithm with the OpenMP/MPI hybrid parallelization scheme to accelerate the calculations of MFCSEM forward and adjoint forward. Finally, the nonlinear conjugate gradient (NLCG) method is utilized to solve this optimization problem. We invert a synthetic data set to verify the computational performance, and the results show that our algorithm is efficient and can obtain reliable inversion results. Furthermore, it also indicates that ignoring the effect of topography can cause severe distortion to the inversion results.

Controlled-source electromagnetic (CSEM) surveying is a critical tool for sensing and locating underground anomalies and structures. In this letter, based on uniaxial perfectly matched layer (UPML) and rational Krylov (RK) method, we propose a fast algorithm for 3-D Multifrequency CSEM modeling. We use the frequency-independent UPML to truncate the boundaries and adopt an RK method to rapidly solve the 3-D multifrequency CSEM problems. The accuracy and efficiency of our algorithm are verified by two examples, i.e., a two-layer model and a 3-D model. Numerical experiments indicate that our algorithm is computationally efficient, obtaining nearly 20-fold speedup on a laptop compared with the conventional 3-D CSEM using finite element method (3DCSEM) modeling.

As magnetotelluric (MT) is an important method for exploring the geoelectrical structure of the underground, it has motivated in-depth research and application by many geophysicists. Nevertheless, due to the influence of the environment, the collected data are interfered with strong humanistic noise, which might result in a loss of their authenticity. To solve the above problems, many time-frequency domain methods have emerged. Based on the advantages of singular value decomposition (SVD) denoising, we propose a method of magnetotelluric noisy data processing based on multiresolution singular value decomposition (MSVD) and improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), which overcomes the lack of flexibility in the construction of the matrix in SVD data processing. First, we introduce a new signal processing method by generalizing SVD to MSVD to obtain more accurate signal characteristics. Due to the difficulty of matrix selection, we suggest the singular value contribution rate as the standard to determine the suitable Hankel matrix and use MSVD to perform effective decomposition. Second, we propose the ICEEMDAN algorithm for removing impulse noise, which efficiently processes each modal component through adaptively decomposition of different thresholds. Experiments on synthetic and realistic data demonstrate that our proposed method can separate the large-scale contours of the magnetotelluric noisy data and improve the time-domain waveform quality of low-frequency signal. The apparent resistivity-phase curves, coherence and SNR are all obviously promoted.

Controlled-source electromagnetic (CSEM) method is crucial for detecting and locating underground anomalies and structures. However, it is challenging to interpret the field data with multi-frequency via 3D CSEM inversion. To fully excavate and utilize the valuable information of CSEM data at different frequencies, we propose an efficient algorithm for 3D multi-frequency CSEM (MFCSEM) inversion based on rational Krylov (RK) subspace. Within the framework of our algorithm, we first use the three-term Lanczos recursion to construct the RK basis matrix quickly; thus, the fast MFCSEM forward modeling can be realized via the RK approximation. Subsequently, we present a novel cyclic projection and correction (CPC) algorithm to solve the MFCSEM adjoint forward problems. Finally, the nonlinear conjugate gradient (NLCG) method is adopted to seek a solution to this nonlinear inverse problem. We demonstrate the excellent performance of our algorithm by synthetic and field data sets. The inversion results show that our algorithm is computationally efficient, resulting in considerable speedup compared with the conventional method. Our algorithm provides a new idea that would significantly improve the efficiency of MFCSEM inversion.

Recently, several techniques using gravitational data such as gravitational field and its gradient tensor have been developed to localize underwater multiple objects. However, performances of these existed techniques largely rely on proper selections of the initial values and, thus, are likely trapped into local minima. To deal with this issue, a global optimization algorithm, named as the state transition algorithm (STA), is investigated to localize multiple objects with both gravitational field and gravitational gradient tensor data sets in this letter. Using a heuristic random search strategy, the proposed algorithm features good global search capability and avoids the dependence of using proper initial values. To assess the performance of the proposed method, different models which contain three and four underwater objects are tested. The experimental results demonstrate that the proposed method is promising with sound stability and strong antinoise ability for dynamic localization problem with multiple objects.

Magnetic object localization techniques have significant applications in automated surveillance and security systems, such as aviation aircrafts or underwater vehicles. In this letter, a practical localization algorithm was presented to determine the center coordinates and magnetic moments of multiple underwater magnetic objects using a combination of the magnetic field vector and its gradient tensor data. It formulates the localization of underwater magnetic objects into a nonlinear problem, which was solved by the Levenberg–Marquardt algorithm. The regularization parameters in the nonlinear problem were adaptively varied in terms of information of the Jacobian matrix. Good initial values of the center coordinates and magnetic moments of this nonlinear problem were automatically determined by a novel and analytical single-object localization algorithm based on magnetic field vector and its gradient tensor. Simulations with two and three underwater objects were adopted to study the feasibility of the magnetic gradiometry technique in multiple underwater objects localization. We have demonstrated that our algorithm can produce reliable results to locate multiple underwater magnetic objects.

We present a novel algorithm to locate multiple underwater objects in real time using gravity field vector and gravity gradient tensor signals. This algorithm formulates the task of localization of multiple underwater objects into a regularized nonlinear problem, which is solved with the standard Levenberg-Marquardt algorithm. The regularization parameters are estimated by cross validation. The initial coordinates and masses of these underwater objects are automatically determined by solving a single-object localization problem. A synthetic navigation model with two underwater objects was adopted to validate the proposed algorithm. The results show that it has good stability and antinoise ability for multiple underwater objects localizations.

Object localization techniques have significant applications in civil fields and safety problems. A novel analytical formula is developed for accurate underwater and aerial object real-time localization by combining gravitational field and horizontal gravitational gradient anomalies. The proposed method enhances the accuracy of object localization and its excess mass estimation; it also effectively avoids the possible numerical instability and the singularity in the previous works. Finally, a synthetic underwater object navigation model was adopted to verify its performance. The results show that our newly developed method is more practical than existing methods.

In this letter, a target tracking approach, which combines short-time Fourier transform (STFT) and linear predictive coding (LPC), is proposed for a Doppler through-wall radar. The LPC is applied to extend the known echo data in each STFT sliding window, thus helping in improving the estimation accuracy of target instantaneous frequency. Compared with the traditional LPC process which determines the prediction data size empirically, the proposed approach takes advantage of the fitting error array as a control parameter to intelligently adjust the data size and reduce the prediction error. Moreover, the proposed approach can also enhance the radar processing efficiency by preventing the unqualified prediction data, which is of great importance for real-time detecting applications. Series of experimental measurements are presented as a preliminary assessment of the proposed approach.

Radar backscattering from human objects is subject to micro-Doppler modulations because of their flexible body articulations and complicated movement patterns, which can help identify the interested targets and provide valuable information about their motion dynamics. In this paper, a novel theoretical method to extract target micro-Doppler trajectories from continuous-wave radar echo is proposed with a united application of a modified high-order ambiguity function and an adaptive denoising technology. Through this method, multiple components corresponding to different target scattering parts and their micro-Doppler trajectories can be accurately extracted and estimated even in a time-varying low signal-to-noise ratio environment. Finally, a series of simulations is conducted to illustrate the validity and performance of the proposed techniques.