Preferred Configuration and Detection Limits Estimation of Magnetic Gradient Tensor System

The magnetic gradient tensor system (MGTS) based on the fluxgate sensors array replaces partial differentials with the sensors reading difference to approximate the magnetic field gradient, but it introduces structural errors at the mean time. A good structure design with reasonable parameters can reduce structural errors and expand the theoretical detection range of the MGTS. From the analysis of the complete 18-uniaxial MGTS, five simplified structures of the MGTS were summarized, which include the plane cross, equilateral triangle, square, right-angle tetrahedron, and regular tetrahedron. The differential magnetic gradient tensor measurement matrixes of different structures were also provided, where we found the plane-cross structure produces the smallest structural error. Moreover, the theoretical detection limits expression of the MGTS to the magnetic dipole was derived. The detection limit boundary of the MGTS is related to the sensor’s accuracy, the array baseline distance, and the magnetization direction and magnetic moment magnitude of the source. In actual heading-line surveys, the magnetic moments of four typical small magnets were successfully estimated by the magnetic dipole positioning method, and the theoretical detection limits of the built plane-cross MGTS aiming at the four magnets were estimated. The results show that the estimation accuracy of the theoretical detection limits of MGTs is ±0.5 m.