差分磁梯度张量测量极限估计

Estimation method for differential magnetic gradient tensor measurement limits

为了研究磁梯度张量系统(Magnetic Gradient Tensor System,MGTS)的理论探测极限,利用磁偶极子正演公式、张量矩阵特征方程和张量不变量推导了差分磁梯度张量测量范围公式,提出了MGTS理论探测极限估计方法。利用磁梯度张量空间衍生不变关系定位方法估计目标体磁矩,并利用差分计算原理在背景场静态采样中估计MGTS的张量分量测量准确度。利用提出的方法估计现场MGTS的理论探测极限。滑动磁性物体远离MGTS并进行连续采样,记录张量信号实际可观测范围并对估计结果进行验证。结果表明,MGTS的理论探测极限与基线距离d、测量准确度q、目标磁矩强度M、观测点与目标磁矩间夹角θ等有关;d越长,q越高,M越大,MGTS理论可探测距离越远;d越长,观测距离越近,MGTS测量的理论误差越大;探测距离在MGTS平行于磁矩方向时最大,在垂直于磁矩方向时急剧减小。实验表明,平面十字形MGTS针对4个典型磁铁的探测极限估计准确度为±0.4 m。

To study the theoretical detection limit of the magnetic gradient tensor system(MGTS),the differential tensor measurement range formula was derived with the magnetic dipole forward equation,the tensor matrix characteristic equation and the tensor invariant,and the MGTS theoretical detection limit estimation method was proposed. First,the target magnetic moment was estimated with the magnetic gradient tensor derivative invariant relations,and the difference calculation principle was used to estimate the measurement accuracy of the tensor component of the MGTS in the static sampling of the background field;then,the theoretical detection limit of on-site MGTS was estimated with the proposed method;and finally,the magnetic object was slided away from the MGTS and continuous sampling was performed,recording the actual tensor signal observable range,and verifying the estimation result of detection limit.The results show that the theoretical detection limit of MGTS is related to the baseline distance d,the measurement accuracy q,the target magnetic moment intensity M,the angle θ between the target magnetic moment and the observation point,etc.;The longer d,the higher q,and the larger M,the farther detect distance;The longer d and the closer observation,the greater the theoretical differential measurement error;The detection range of MGTS reaches the maximum in the direction parallel to the magnetic moment,but decreases sharply in the direction perpendicular. The experiments show that the estimation accuracy of detection limit of the planar-cross MGTS for four typical magnets is ± 0. 5 m.