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Acta Armamentarii ›› 2022, Vol. 43 ›› Issue (12): 3122-3131.doi: 10.12382/bgxb.2021.0704

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Second-Order Magnetic Gradient Tensor Contraction Method Using Magnetic Dipole

JIANG Shenghua   

  1. (College of Engineering and Technology, Southwest University, Chongqing 400715, China)
  • Online:2022-05-19

Abstract: Regarding the immature theory of the second-order magnetic field gradient tensor in magnetic localization, the second-order magnetic gradient tensor contraction method based on magnetic dipole is proposed. The full and partial modulus calculation formulas of the second-order magnetic gradient tensor are proposed. The three-dimensional distribution laws of the full modulus, partial modulus and related parameters of the second-order magnetic gradient tensor are analyzed. The approximate calculation formulas of parameters kH,kHxy and kHz are also given. The first-order magnetic gradient tensor, second-order magnetic gradient tensor, and their modulus are compared. The results show that when  is ranged from 0° to 90°, the full modulus CH and the parameter kH decrease with the increase of . The maximums values are obtained when  is 0°, and the minimum values obtained when  is 90°. When  is ranged from 0° to 90°, the partial modulus CHxy and parameter kHxy first increase and then decrease with the increase of . The maximum values are obtained at =35°, and the minimum vaalues obtained at  = 90°. The partial modulus CHz and the parameter kHz first decrease and then increase as  increases. The maximum values are obtained at = 0°, and the minimum values obtained at =71°. The fitted values of kH,kHxy and kHz are highly consistent with those obtained from theoretical inversion. When the distance is small, the second-order magnetic gradient tensor and modulus are more sensitive. When the distance is large, the first-order magnetic gradient tensor and modulus are more sensitive. In practical applications, magnetic localization can be used with the combination of first-order and second-order magnetic gradient tensor and full modulus.

Key words: magneticdipole, second-ordermagneticgradienttensor, contraction, fullmodulus, partialmodulus

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