基于磁偶极子的磁场梯度张量局部缩并及试验验证

基于磁偶极子的磁场梯度张量缩并理论虽然可较好地描述磁源,不受测量系统的朝向的影响,但在实际的磁场梯度张量测量中通常仅可测得部分磁场梯度参数,没有获得磁场梯度张量中的所有张量分量,如何有效利用这些部分磁场梯度参量,已成为目前磁场梯度张量缩并理论及在磁场定位的应用中亟需解决的问题。基于磁偶极子理论提出磁场梯度张量局部缩并的方法,给出磁场梯度张量的局部模量的概念,分析了磁场梯度张量的局部模量及相关参数的三维空间分布规律,结果表明:局部模量CXY及kXY值随着g先增大后减小,在g=39°时取最大值,在g=90°时取最小值;局部模量C_Z及k_Z值随着g先减小后增大,在g=63°时取最小值,在g=0°时取最大值。提出磁场梯度张量局部模量中重要参数的近似计算公式,并通过试验进行验证。试验结果表明,试验值与理论计算值基本一致,可为磁场梯度张量局部缩并理论的应用提供依据和参考。

Theoretical study and experimental verification of magnetic gradient tensor partial contraction using magnetic dipole

The magnetic gradient tensor contraction theory can effectively describe a magnetic source without being influenced by the orientation of magnetic measuring instrument. However, in the actual measurement of magnetic field gradient tensor, only a part of gradient parameters can usually be obtained due to some hardly inevitable factors. To effectively use these parameters, a magnetic gradient tensor partial contraction method is put forward based on magnetic dipole theory, and the conception of magnetic gradient tensor's partial modulus is given. The three-dimensional distribution of magnetic gradient tensor's partial modulus and related parameters is analyzed, and the theoretical formulae of the related parameters are derived. The verification experiments show that the partial modulusCXY and the parameterkXY increases withɡ ranged from 0° to 39°, and decreases withɡ ranged from 39° to 90°. TheCXY andkXY are maximum whenɡ is 39°, and are minimum whenɡ is 90°. The partial modulusCZ and parameterkZ decreases withɡ ranged from 0° to 63°, and increases withɡ ranged from 63° to 90°. TheCZ andkZ are maximum whenɡ is 0°, and are minimum whenɡ is 63°. These experimental values are in accordance with the theoretically calculated values, showing that the proposed method can provide reference for the application of the magnetic gradient tensor contraction theory.