Magnet position and magnetic moment inversion based on first-order spatial gradient tensor

Abstract Magnetic inversion, as a promising method, is employed to locate underground oil pipelines by identifying anomalies in their magnetic moment, thereby aiding in integrity assessment and facilitating periodic maintenance. Building on this requirement, the study validates a magnet inversion algorithm that diagonalizes the symmetric first-order spatial gradient tensor matrix, thus establishing a new coordinate system. Within this system, the magnet’s three-dimensional directional components and magnetic moment components are decoupled and transformed into Cartesian coordinates, yielding its position and moment. Using an optimal sensor array with a 5/3 side-to-height ratio and 36 points, finite element simulations yielded an average positioning error of 0.00512 m. The average relative errors for the magnetic moment’s orientation and magnitude were 0.69% and 4.29%, respectively. Accuracy improved significantly when the magnetic moment was parallel to the sensor array. This orientation reduced the positioning error to 0.00301 m and the relative errors to just 0.18% for orientation and 2.34% for magnitude. This enhancement occurs because the parallel orientation maximizes the separation of the tensor’s eigenvalues, leading to a more stable and robust inversion. These results highlight the validated algorithm’s effectiveness in reducing inversion uncertainties under multiple observation points.