均匀磁化长方体的磁张量无解析奇点正演方法

Singularity-free forward calculation method of uniformly magnetized cuboid magnetic tensors

长方体的磁张量正演公式存在解析奇点,降低了边界检测的实验效果、三维反演的收敛性。以均匀磁化长方体磁异常无解析奇点正演公式为基础,推导了直立长方体磁张量的无解析奇点正演公式,借助坐标变换方法,构建了倾斜长方体磁张量的无解析奇点正演算法。实验表明,推导的长方体磁张量无解析奇点正演算法是正确的;地磁倾角与磁偏角能够影响磁张量的幅值与分布、磁异常向张量的转换精度,说明化磁极是磁张量高精度处理与解释的必要环节。

In view of the reduced experimental effect of the edge detection and the convergence of 3D inversion due to the existence of analytical singularity in the magnetic tensor forward formulas of a cuboid,the study involves deducing singularity-free forward formulas of an upright cuboid magnetic tensors,constructing forward algorithms of inclined cuboid magnetic tensors without analytic singularities based on the singularity-free forward formula of a uniformly magnetized cuboid magnetic anomaly.The model tests show that the derived singularity-free forward calculation algorithms are correct;the amplitude and distribution of magnetic tensors and the conversion accuracy of magnetic anomaly to tensors are affected by geomagnetic inclination and declination.This study shows the necessity of the reduction to the pole for high-precision processing and interpretation of magnetic tensors.