| 磁偶极子梯度张量的几何不变量及其应用 |
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| 引用本文： | 尹刚,张英堂,李志宁,张光,范红波.磁偶极子梯度张量的几何不变量及其应用[J].地球物理学报,2016,59(2):749-756. |
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| 作者姓名： | 尹刚 张英堂 李志宁 张光 范红波 |
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| 作者单位： | 军械工程学院七系, 石家庄 050003 |
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| 摘 要： | 磁梯度张量系统姿态的变化将影响梯度场测量和数据解释的精度,使得具有坐标变换不变性特点的张量不变量成为磁梯度张量数据解释的研究热点.本文在对磁偶极子产生的磁梯度张量进行特征值分析的基础上得到了:测量点与磁偶极子位置形成的位置矢量、磁偶极子磁矩矢量与绝对值最小的特征值对应的特征向量垂直;位置矢量和磁矩矢量与最大及最小特征值对应的特征向量共面,且两矢量间的夹角可由磁梯度张量矩阵的特征值表示.最后,将本文所得磁偶极子梯度张量的几何不变量用于磁性目标的跟踪中,取得了较好的实时跟踪效果.
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| 关 键 词： | 磁偶极子 磁梯度张量 几何不变量 特征值 张量不变量 |
| 收稿时间： | 2014-06-16 |
Research on geometric invariant of magnetic gradient tensors for a magnetic dipole source and its application |
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| YIN Gang,ZHANG Ying-Tang,LI Zhing-Ning,ZHANG Guang,FAN Hong-Bo.Research on geometric invariant of magnetic gradient tensors for a magnetic dipole source and its application[J].Chinese Journal of Geophysics,2016,59(2):749-756. |
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| Authors: | YIN Gang ZHANG Ying-Tang LI Zhing-Ning ZHANG Guang FAN Hong-Bo |
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| Institution: | Department 7th, Mechanical Engineering College, Shijiazhuang 050003, China |
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| Abstract: | As attitude change of the magnetic gradient tensor system may affect precision of gradient measurements and data interpretation, the rotational invariants which are invariant under rotation of the reference frame have been extensively studied for magnetic gradient tensor data. Based on the eigenvalue analysis of magnetic gradient tensors produced by the magnetic dipole, some invariant geometrical relationships, which are defined as geometric invariants, are deduced in this paper. Firstly, the eigenvector corresponding to the eigenvalue which has the smallest absolute value is perpendicular to both the dipole moment and source-dipole displacement vector. Secondly, source-dipole displacement, dipole moment and eigenvectors corresponding to the maximal and minimal eigenvalues are coplanar. Thirdly, the angle between dipole moment and source-dipole displacement vector can be calculated by eigenvalues of magnetic gradient tensors. At last, the proposed geometric invariants are used to track a magnetic target, and simulation and experimental results confirm the correctness and practicability of the proposed geometric invariants. |
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| Keywords: | Magnetic dipole Magnetic gradient tensor Geometric invariant Eigenvalue Tensor invariant |
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