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.

Electrocardiogram (ECG) is the foundation of the analysis of cardiac disease. In the hospital clinical ECG diagnostic scenarios, when doctors analyze ECG signals or when an ECG intelligent diagnostic system is used, there might be strong noises like baseline wander or muscle artifact in the ECG signals due to the unstable state of the subjects, and such interferences are usually difficult to be filtered out by traditional filters, which can lead to serious errors in the subsequent signal analysis. To solve this problem, we propose a novel network which integrates hybrid transformer and multi-receptive feature extraction mechanism into score-based diffusion model. We used score-based diffusion model to reconstruct the clean ECG signals from noisy ones. The experiment was conducted on the QT Database and the MIT-BIH Noise Stress Test Database to verify the feasibility of our method. Baseline methods are used for comparison. The evaluation results show that our method can achieve an outstanding performance on four distance-based evaluation metrics by at least 26% overall improvement in the comparison with the best baseline method. The study demonstrates that the signal denoising and reconstruction method based on the self-designed score-based diffusion model can effectively remove the interferences in the ECG signals, thereby facilitating the subsequent diagnosis in real-world situation. It also has huge potential for establishing the ECG intelligent analysis system.

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.

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.

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.

This paper proposes a new approach for picking raster entities in the intelligent raster editing process of line drawing images. The proposed method is based on the run-graph encoding principle and involves several key steps including: tracing the line in both positive and negative directions, recognizing line junction areas, property consistent tracing, and reconstructing line junction areas. It is shown, both in theory and experiments, that the algorithm provides a robust performance in recognizing the line junction areas and their reconstruction. By this approach, two kinds of basic raster entities could be picked up completely even in noise disrupted line drawing images.