Magnetic localization, owing to its immunity to line-of-sight occlusion and non-contact nature, is considered a promising technology for medical applications. While it is intuitive that localization performance degrades as the target moves farther from the sensor array, uncertainty analysis has long been overlooked, which is essential for quantifying localization quality. In this work, we present a pose estimation and uncertainty analysis framework on SE(3) for magnetic source localization using sensor arrays, which enables concise formulation of the problem and quantitative assessment of the results. The volume of the uncertainty ellipsoid is used to characterize localization confidence, while the surface shape in Cartesian space is used for visualization. This also provides insight into the effective workspace of the magnetic localization system prior to deployment. Guided by this analysis, we designed a movable magnetic sensor array to expand the limited sensing volume and mitigate localization uncertainty, thereby enhancing overall localization performance. Simulations and pose tracking experiments validate the effectiveness of this framework. By dynamically moving the sensor array to minimize the volume of the uncertainty ellipsoid, localization errors are reduced compared with static and projection-based strategies by 67.04%, 16.51% in position and 43.87%, 20.73% in orientation, respectively. Furthermore, phantom experiments on distal locking screw alignment and magnetic capsule endoscope tracking demonstrate the system's capability in improving localization accuracy (reducing alignment errors by 71.88%) and expanding the effective workspace by several folds.

At present, the three-dimensional (3D) magnetotelluric (MT) unstructured finite element modelling approaches often adopt the block-wise uniform conductivity parameterization method, in which the Earth conductivity model is discretized into plenty of tetrahedrons with uniform conductivity. However, that block-wise uniform parameterization method is not only difficult to accurately simulate actual continuous subsurface conductivity distribution, but also would substantially increase the unknowns in the subsequent inversion, which largely aggravates the non-uniqueness of inversion. In this study, we propose a three-dimensional unstructured finite element modeling strategy of magnetotelluric problems allowing for continuous variation of conductivity in each tetrahedron. First, the curl-curl governing differential equation of electrical field for the 3D MT problems and the corresponding integral weak form are derived successively. Next, the open-source tetrahedral mesh generator Tetgen is utilized to discretize the computational domain, both the conductivity and the electric field within each tetrahedral element are approximated by using linear interpolation with node and edge vector basis functions, respectively. Then, the closed-form expression of the resulting elemental integral is derived and the Newman type boundary condition is loaded. The resulting system of linear equations is solved by using the direct LU decomposition method. Further, to enhance the accuracy of the solution, a goal-oriented adaptive technology based on the continuity of the normal component of the current density is adopted. Finally, the correctness of the proposed algorithm is verified by using a layered model with continuous conductivity distribution and a 3D topographic model. While the necessity of considering the continuous variation of conductivity in blocks is proved by using two 3D continuum models. The results show that the proposed algorithm can obviously improve the accuracy of the responses at the sites above the region with continuous conductivity distribution and will greatly reduce the unknowns of the subsequent inversion, compared with the traditional algorithm with block-wise uniform parameterization.

Galvanic distortion resulting from near-surface heterogeneity has long been considered a major impediment to the accurate interpretation of magnetotelluric data. As this galvanic distortion effect is approximated by a real tensor, it can be solved numerically in the three-dimensional magnetotelluric inversion. To achieve this goal in a practical way, we have implemented the inverse solution of both the galvanic distortion and resistivity parameters in the widely used software package ModEM. To address the gradient domination problem of the distortion parameter over resistivity, a scaling scheme is proposed to balance their separate roles in the total gradient. Two synthetic datasets of the Block2-3D and the Oblique Conductor models provided in ModEM package were distorted and then used to validate the new implementation. Synthetic inversions demonstrate that the artifacts introduced by fitting the galvanic distortion effect can be removed and the regional structure is better resolved. A field data inversion test was conducted on the magnetotelluric data from the Red River Fault zone and its adjacent areas on the southern margin of the Tibetan Plateau. Using the distortion-free phase tensor, we show that the new inversion significantly removes the galvanic distortion artifacts from the shallower structure. It obtained a slightly different crustal structure and a clearer delineation of the upper mantle structure compared to the previous study.

Anomaly detection for log sequences is a necessary task for system intelligent operation and fault diagnosis. In a log sequence, adjacent logs have the property of local correlation, while long-distance logs have remote dependencies. It is helpful to fully mine these information during modeling for improving the performance of anomaly detection. Meanwhile, there are some redundant information or noise in the log sequence, which has no contribution to the detection, and may even bring negative impact. The existing methods for log sequence anomaly detection do not take the above problems into account when constructing models. In this paper, we propose LSADNET, an unsupervised log sequence anomaly detection network based on local information extraction and globally sparse Transformer model. LSADNET applies multi-layer convolution to capture the local correlation between adjacent logs, and utilizes Transformer to learn the global dependency among long-distance logs. Meanwhile, we propose a globally sparse Transformer model to improve the self-attention mechanism, which can help to retain important information adaptively and eliminate the irrelevant information in the log sequence. In addition, according to the co-occurrence mode of log templates, we put forward the calculation formula of log template transfer value, and apply it to log vectorization. Through sufficient experiments on two public datasets, it is confirmed that LSADNET has better performance than the state-of-art methods.