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.

The inversion of audio magnetotelluric (AMT) data is affected by uncertainties stemming from various factors, including noise, initial model assumptions, and regularization parameters. Among the plethora of optimization algorithms available, Bayesian-based global search algorithms enable the determination of meaningful posterior probability distributions for inverted models, offering essential metrics for evaluating the reliability of inversion results. Nevertheless, conventional Bayesian inversion methods are impeded by intricate and time-consuming forward modeling processes. To mitigate this challenge, we propose an innovative one-dimensional AMT deep learning inversion technique based on a residual mixture density network (Res-MDN). We incorporate a new residual structure into the mixture density network(MDN), enabling it to output posterior probability distributions, thereby addressing the vanishing gradient problem and enhancing the reliability of the inversion process. In addition, to improve generalization, a comprehensive set of sample data was generated for network training, allowing it to accommodate a wider spectrum of geological conditions and data variations. Extensive testing using synthetic data was conducted to validate the efficiency, noise resistance, and generalization ability of the newly developed Res-MDN-based one-dimensional AMT inversion technique. The method’s effectiveness was further corroborated by its successful application to field data collected in the Da Qaidam region of Qinghai Province, China. Notably, during these experiments, the posterior probability distributions predicted by the trained Res-MDN were crucial in evaluating the uncertainty associated with the derived resistivity models.

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.

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.

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.