Application of Helbig integrals to magnetic gradient tensor multi-target detection

Abstract

We extended the magnetic gradient tensor Helbig integrals (MGTHI) from classical Helbig integrals (HI), which can be perfectly adapted to the grid measurement of planar-cross magnetic gradient tensor system. With different sizes of windows, we can estimate the MGTHI by using the two-dimensional trapezoidal rule algorithm and calculate the total magnetization direction of grids, where the node with the smallest change in the magnetization direction is target horizontal position. In the targets recognition area determined by the invariant improved tilt angles, the source depth and dipole moment magnitude can be calculated with magnetic vector and tensor field data directly above the source. In experiments, the horizontal position deviation of multiple small magnets in the survey area of 2.1 m × 2.1 m and 1.2 m × 1.2 m is less than 0.08 m, and the buried depth deviation is less than 0.15 m, the positioning accuracy is improved by more than 5 times from the classical HI method.