小尺度地磁场勒让德多项式建模方法

The Legendre polynomials modeling method of small-scale geomagnetic fields

根据地面实测地磁场数据,提出一种基于勒让德多项式的对小尺度地磁场的模型建立方法,结合数据预处理、最小二乘拟合方法,采用高阶的模型描述典型小尺度区域的地磁场,绘制出地磁图.通过实验验证,模型拟合实验点的数据与真实数据的磁场总强度平均误差小于30nT,并且反映出小尺度区域中磁场的精细结构,有效地抑制了边界效应,大大提高了地磁场建模能力.另外讨论了勒让德多项式建模方法的优缺点以及使用范围.这为地磁场在空间延拓、探矿、地下结构分析提供了重要的方法和理论基础.

Based on ground-based geomagnetic surveys,we propose a small-scale geomagnetic field modeling method using Legendre polynomials.Combined with the data preprocessing techniques and the least squared estimation,a high-degree model is constructed to describe the small-scale structure of the field and draw the geomagnetic field maps.The results of the experiments show that the average misfit of total field intensity between the predicted model and the real observations is less than 30 nT.At the same time,fine structures of the field can be predicted,and the boundary effect is effectively suppressed,which facilitate improvement of modeling of the geomagnetic field.We also discuss the advantage and shortage of this modeling technique and its application scope.It is of great significance for application of the geomagnetic field to space exploration,minerals prospecting and subsurface structure probing.