基于磁偶极子的2阶磁场梯度张量缩并方法

针对磁场定位中2阶磁场梯度张量的理论尚不够完善的现状，提出基于磁偶极子的2阶磁 场梯度张量缩并方法。给出2阶磁场梯度张量的全局模量和局部模量计算公式，分析2阶磁场梯度张量的全局模量和局部模量及相关参数的三维空间分布规律，并给出相关参数k_H、k_Hxy和k_Hz的近似计算公式，比较1阶磁场梯度张量和2阶磁场梯度张量及其模量的分布规律及与距离的关系。计算结果表明：全局模量C_H及参数k_H值在0°≤≤90°时，随着增大而减小，在=0°时最大，在=90°时最小；局部模量C_Hxy和参数k_Hxy值在0°≤≤90°时，随先增加、后减少，当=35° 时最大，当=90°时最小；局部模量C_Hz和参数k_Hz随先减少、后增加，当=0°时最大，当=71°时最小；k_H、k_Hxy和k_Hz的拟合值与理论反演值高度吻合；在距离较近时，2阶磁场梯度张量及模量更敏感；在距离较远时，1阶磁场梯度张量及模量更敏感；在实际磁场定位的应用中，可结合1阶和2阶磁场梯度张量及全局模量进行使用。

Second-Order Magnetic Gradient Tensor Contraction Method Using Magnetic Dipole

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 k_H，k_Hxy and k_Hz 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 C_H and the parameter k_H 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 C_Hxy and parameter k_Hxy 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 C_Hz and the parameter k_Hz 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 k_H，k_Hxy and k_Hz 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.