Electrical resistivity tomography (ERT) is a key geophysical technique that provides detailed information on subsurface structures by measuring the distribution of electrical resistivity underground. ERT suffers from limitations in electrode arrangement, interference from environmental and instrument noise, and existing data processing algorithms that fail to adequately consider geological heterogeneity and uncertainty, resulting in insufficient inversion resolution. Traditional ERT methods rely on simplified algorithms and a limited number of observation points, which smooths model details and further reduces resolution. To address the resolution issues in ERT, this article proposes a deep learning inversion method that integrates prior physical information. This method uses low-resolution inversion results as prior knowledge to provide the deep learning algorithm with a constrained initial model, thereby combining the physical basis of traditional methods with the data-driven advantages of deep learning. The method not only retains the strengths of traditional inversion but also enhances the resolution and imaging efficiency of the inversion model using deep learning technology. Synthetic data experiments demonstrate that integrating deep learning significantly improves the model’s ability to detail subsurface structures, especially in the transition zones of shallow structures and the recovery of deep anomalies. Results from measured data indicate that the proposed method not only achieves high-resolution inversion but also maintains good consistency with prior information.

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 letter, 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 nonnoise points in 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.

Magnetic anomaly pole transformation converts magnetic field data into an equivalent response at the true magnetic pole, eliminating shifts and distortions, simplifying the interpretation of subsurface magnetic bodies, and improving data interpretation and inversion accuracy. However, the main challenge in magnetic anomaly pole transformation lies in the nonlinear nature of the signals, making traditional methods difficult to apply. The interaction between the shape, depth, and magnetic inclination of magnetic bodies, especially in high- and low-latitude regions, can distort the transformed signal, leading to unclear causal relationships. To address this, this article proposes a deep learning-based approach that automatically extracts high-dimensional features and establishes nonlinear mappings to enhance the correlation between magnetic anomaly signals and geological structures. Deep learning does not require explicit physical models and, through training with large datasets, demonstrates stronger robustness and accuracy, especially in areas where traditional methods fail. The proposed method is validated using both synthetic and measured data. Synthetic data simulates magnetic bodies of various shapes, depths, and magnetic inclinations, confirming the method’s stability and accuracy in handling complex nonlinear signals. The measured data evaluates its pole transformation advantages in typical ore deposit regions. The results indicate that the deep learning model significantly enhances the accuracy of pole transformation, particularly in areas with complex magnetic anomaly signals, effectively preventing signal distortion and demonstrating exceptional generalization capabilities.

Given the limited number of labeled magnetotelluric (MT) filed data samples, current neural network (NN) inversions for MT are primarily rely on synthetic data, which may not fully capture the complexity of true underground resistivity structures. This letter introduces a novel inversion scheme that combines attention U-Net with transfer learning (AUTL) to bridge this gap. The proposed method improves inversion accuracy by integrating field data into the training process through transfer learning (TL), using 3-D models derived from real field measurements as the target dataset. This enhances the authenticity and reliability of the inversion results. Additionally, the incorporation of attention gates (AGs) significantly improves feature extraction by focusing on relevant features. We validate the effectiveness of the AUTL approach using both synthetic and measured data, demonstrating its superior performance in reconstructing underground resistivity structures with high accuracy and noise resistance. This method offers a promising solution for training inversion networks with limited field MT data and lays the groundwork for expanding datasets with more diverse 3-D models in the future.

Most recently, Zhang et al presented a verifiable data aggregation scheme for smart grids in IEEE Transactions on Dependable and Secure Computing (doi: 10.1109/TDSC.2021.3124546). The authors claim that the privacy of the user's electricity data is preserved, and the control center can check whether the aggregator honestly computes the aggregated ciphertext. However, we indicate that Zhang et al's scheme fails to provide the properties of data privacy and aggregate correctness guarantee. Specifically, by offering concrete attacks, we illustrate that the adversary who has the ability to obtain the decryption key of control center can decrypt any user's ciphertext to get the detailed electricity data, and a misbehaved aggregator will not be detected when it does have some malicious behavior.

The Earth’s interior consists of multiscale structures that range from micrometer-scale mineral assemblages to 1000-km-scale heterogeneities. Mantle plumes are one such mega-scale structure that connects the core–mantle boundary with Earth’s surface. Reconstructing these structures can provide insights into mantle material and energy convection, as well as Earth’s long-term evolution. However, mantle plume has not yet been convincingly reconstructed by electromagnetic (EM) induction; even they have significantly high electrical conductivity compared with the surrounding mantle. Here, we numerically reconstruct mantle plumes by employing a deep Earth EM induction method—geomagnetic depth sounding (GDS). We build the electrical structure of mantle plumes and conduct inversion tests to investigate how different station coverage areas, station spacings, noise levels, and response period ranges influence the construction. The test results indicate that the reconstruction of a broad 10° diameter plume head near the mantle transition zone (MTZ) requires a station coverage area of at least 10$^{\circ }\,\,\times10^{\circ }$and a 2° station spacing; the station spacing can be increased to 5° for a 20$^{\circ }\,\,\times20^{\circ }$coverage area. A continuous two-year record with ~5% noise is sufficient to recover the electrical structure of the plume head. Plumes with different types and roots can be distinguished by images near the MTZ, while reconstruction of the narrow tail in the deep lower mantle seems to be difficult due to the limited resolution of GDS. A mantle plume beneath South China is discovered by GDS from the field geomagnetic data. GDS is expected to be used for reconstructing the mantle plume beneath important locations and contributing to the study of Earth’s dynamics.

As the traditional grid produces a large amount of greenhouse gas and cannot adapt to such new demands as dynamic electricity prices, data analysis, and early warning, smart grid with high efficiency and reliability is increasingly valued. It plays a key role in achieving carbon neutrality. Nonetheless, smart grid requires the collection of real-time power data, and personal privacy may be leaked through the frequent electricity measurement reports. With the requirements of data analysis and prediction while preserving users’ personal privacy, data aggregation schemes have emerged. However, existing schemes cannot resolve all the troubles well. Some schemes do not consider the failures for smart meters, and most of the schemes have expensive computation cost. In view of this, an efficient privacy-preserving data aggregation scheme with fault tolerance in smart grid is put forward in this paper. To be specific, the proposed scheme is lightweight due to the application of the symmetric homomorphic encryption technology and the elliptic curve cryptography. Even if some smart meters are destroyed, the proposed scheme can still successfully obtain aggregated data. Moreover, the proposed data aggregation scheme is proved to be secure, and all security requirements can be satisfied. Performance evaluation illustrates the relatively low computation cost and communication overhead of the proposed scheme compared to other related schemes.