用于大回线源瞬变电磁场一维正演计算的两种方法对比

Two calculation methods comparison for 1D large loop source transient electromagnetic field forward

本文利用偶极子合成回线方式计算了回线源一维瞬变电磁场.首先推导了水平电偶极子和垂直磁偶极子合成方回线源瞬变电磁场的计算公式,并对部分计算过程做了改进.然后将这两种算法在方回线中心点计算结果分别与面积相同的圆回线中心点解作对比,并分析了积分方式和回线框大小对计算精度的影响,得到下述三点认识:(1)在早期道,偶极子合成回线正演相对误差较大,但随着测量时间道的增加,相对误差减小;(2)对于电偶极子合成方回线的正演,一般采用高斯-勒让德5点求积便可达到最高精度,对于磁偶极子合成方回线正演,一般回线框越大,便需要更精细的积分才能达到最高精度;(3)偶极子合成方回线中心点正演在早期存在较大的误差并非由计算方法导致,而是等效面积相等的方回线和圆回线激发的二次磁场本身存在差异所致.最后利用偶极子合成回线正演方式可以较准确的计算回线框内外任意一点的瞬变电磁场,将为回线源瞬变电磁全区勘探和一维反演提供理论指导.

In this paper,dipoles synthesis loop method is used to calculate TEM field of loop source. Firstly, horizontal electric dipoles and vertical magnetic dipoles source synthesis square loop calculation formulas of TEM field are derived and the parts of the calculation processes areimproved. Then these two kinds of calculation resultsin loop centerare compared with solutions of same area circularcentral loop,and analyzing the integral method and loop size influencing on calculation accuracy,three points have been drawn：（ 1） At the early gates,the relative errorsare bigger,but with the increasing of measurement time gates,relative errorsare decreasing.（ 2） For electric dipoles synthesis square loop forward,by Gauss-Legendre 5 points quadrature achieving the highest accuracy,for the magnetic dipolessynthesis square loop forward,the larger loop,needingthe elaboratorquadrature to achieve the highest accuracy;（ 3） The dipoles synthesis square loop forwardhaving bigger errors at early gates is not caused by calculation methods itself,but area equaledsquareloop and circular loop exist difference of the secondary magnetic field. Finally using dipoles synthesis loop forward can accurately calculate any point inside and outsideof loop which will providetheoretical guidanceon loop source TEM whole region explorationand1 Dinversion.