Three-dimensional inversion of magnetic data can obtain the distribution of subsurface magnetic targets. Deep learning is an effective way to achieve 3-D inversion, which trains a neural network to learn the features of magnetic anomaly data and then generates a 3-D model based on these features. Large training samples are required to achieve persuasive results due to the limited observational data and the multisolution nature of the inverse problem. To reduce the nonuniqueness of the inversion, this article proposes a multivariate magnetic data-based deep learning 3-D inversion strategy. With the proposed strategy, more domain knowledge is incorporated into the training data of the neural network to improve the inversion accuracy. The input data of the neural network adopt multivariate observation data, including multiscale data and multitype data such as magnetic three-component data, magnetic gradient tensor data, and so on, and output a 3-D model to realize 3-D to 3-D mapping. Then, the neural network structure uses the 3-D convolution to extract 3-D spatial information. Both tests on simulation and measured data verify that the proposed strategy can effectively improve the accuracy of the 3-D magnetic inversion.

Ground Penetrating Radar (GPR), with its high resolution and real-time monitoring capabilities, is widely used in fields such as underground structure detection, archaeological excavation, environmental monitoring, and engineering surveying. However, the complexity of the subsurface, such as geological heterogeneity and inhomogeneity, can cause signal attenuation or incomplete reflection. Additionally, external factors like electromagnetic interference, temperature fluctuations, or other noise can result in data loss or anomalies. To address these challenges, this paper proposes a deep learning-based interpolation method for GPR data. Convolutional Neural Networks (CNNs) are used to learn signal patterns from large datasets, enabling the model to predict missing data and restore the integrity and continuity of the GPR data. Deep learning models also capture complex nonlinear features in GPR data, identifying underlying patterns and correlations. In noisy or high-reflection environments, these methods offer more precise interpolation, significantly improving data quality. Experiments on both synthetic and real-world data show that the deep learning method effectively recovers GPR data features, enhances data continuity and integrity, and reduces interpolation errors. The method exhibits strong adaptability and high-precision performance, making it effective in complex underground structures and varying environments. Whether with synthetic or real-world data, deep learning provides a reliable solution for GPR data processing.

Ground Penetrating Radar (GPR) inversion typically relies on iterative methods, which often involve high computational complexity and challenges in noise handling. These limitations affect the robustness and generalization of traditional approaches. To address these issues, we propose an innovative inversion method using diffusion models (DGPRI-Net) tailored for GPR. Diffusion models inherently capture signal characteristics through progressive noise addition and subtraction, reducing noise impact and enhancing robustness. This approach effectively overcomes the noise management weaknesses of conventional methods. In the reverse generation process, we use the UNet++ network architecture, enhanced with Vision Transformer (ViT) structures and a simple parameter-free attention module (SimAM). This combination improves multiscale feature extraction and contextual understanding, increasing robustness and enabling high-precision permittivity models. To further evaluate the robustness of the model, we prepared three dedicated test sets: one with added noise, one without low-frequency signals, and one with 30% of the columns missing. Comparative experiments with synthetic data showed exceptional inversion accuracy, superior noise management, and enhanced robustness and generalization. We also validated performance with metrics such as Structural Similarity Index (SSIM), Peak Signal-to-Noise Ratio (PSNR), and Mean Squared Error (MSE). Applied to measured data, our method continued to yield impressive results, confirming its practical value and effectiveness. This study highlights the potential of diffusion models in advancing GPR inversion applications.

Noise attenuation is crucial in ground-penetrating radar (GPR) data processing. In recent years, deep learning (DL) methods have shown excellent performance in GPR denoising tasks, but they typically focus only on recovering the target signal, which can lead to over-denoising. To enhance the generalizability and the practicality of denoising networks, we propose a strategy to generate random dielectric models from natural image datasets, which can quickly construct model datasets with low redundancy and reasonable distribution. To enhance the fidelity of GPR denoising, we leverage the powerful nonlinear fitting capabilities of convolutional neural networks (CNNs) and introduce a closed-loop denoising network framework for GPR. The framework consists of a denoising sub-network and a noise extraction sub-network, effectively achieving signal-noise separation in noised GPR data. Specifically, the denoising sub-network is used to recover weak reflection signals and initially remove noise, while the noise extraction sub-network is used to restore the true noise, mitigating the problem of over-denoising. A key innovation of our approach is the integration of bandpass filtering, which enhances the robustness of network training and supports effective weak signal recovery. This network framework forms a closed loop through the residual loss between the signal-noise separation results and the noised GPR data, the closed-loop structure is capable of further refining the signal and noise prediction results of the two sub-networks, thereby enhancing the numerical accuracy of the signal-to-noise separation results. Finally, the effectiveness of the GPR closed-loop denoising network is verified from multiple perspectives using both synthetic and field measured data. The results indicate that our proposed method is more competitive in GPR denoising tasks.

Inversion of seismic data, particularly full waveform inversion (FWI), allows for high-resolution subsurface velocity estimation. However, the inversion of subsurface velocities using only seismic data typically involves severe non-uniqueness. Electromagnetic exploration, due to its broad detection range and low cost, can effectively complement seismic exploration. Although electromagnetic data give a lower resolution resistivity information, they are sensitive to subsurface anomalies. Hence, the joint inversion of electromagnetic and seismic data effectively integrates the complementary information in both data sets to reduce the inversion non-uniqueness to improve accuracy and reliability of the inversion results. Nevertheless, current joint inversion techniques are confronted with issues such as the complexity of objective function design, challenges in achieving convergence, and insufficient coupling between seismic and electromagnetic data. To address these challenges, we propose a Seismic-Electromagnetic joint Inversion Network (SEMI Net) based on joint learning. Our approach leverages the powerful nonlinear fitting capabilities of neural networks for efficient multi-objective optimization. Moreover, we establish coupling between seismic and electromagnetic data across multiple sampling scales. Harnessing the frequency band complementarity of seismic and electromagnetic data, i.e. the low-frequency of the electromagnetic data and the mid-to-high frequency of the seismic data, we obtain high-resolution resistivity and velocity models by SEMI Net. Results on synthetic data and the Overthrust model demonstrate the effectiveness of our approach.

Due to the influence of both the observation environment and the instruments themselves, Ground Penetrating Radar (GPR) data are often contaminated by random noise, which degrades data quality. Salt-and-pepper noise is a common type of such noise. Adaptive median filtering is an effective technique for removing this noise. However, it has the drawback of replacing original values that are not affected by noise with the median, which can lead to a degradation in image quality. In this paper, we propose an improved adaptive median filtering method. First, we assess whether the original value is contaminated by salt-and-pepper noise. If the value is affected, filtering is applied. The window size is adaptively increased, and the window is subdivided into smaller sections. Multiple median calculations are then performed on the segmented windows to ensure the validity of the median. When the noise density is high, the median of the non-noise points within the largest window is selected as the output, thereby minimizing the negative impact of noise on the median calculation. Both synthetic and real-world data validations demonstrate that the improved method significantly outperforms traditional adaptive median filtering, conventional median filtering, and other filtering methods, particularly in high-noise scenarios, thus confirming the superiority of the proposed algorithm.