基于磁偶极子的频率域电磁系统几何误差分析

Geometric Error Analysis of Frequency-Domain Magnetic Dipole-Dipole System

基于磁偶极子模型的频率域电磁法仪器在进行大地探测的过程中,由于收发线圈的安装误差、晃动以及材料的几何形变等因素影响,收发线圈的位置及姿态角发生变化,从而产生几何误差,而几何误差的定量分析对频率域电磁法仪器在制作、野外实验操作以及校正方面均具有很强的指导意义。本文根据误差来源的不同,将几何误差分为一次场误差和二次场误差两类;通过引入一次场张量矩阵和二次场张量矩阵,基于均匀大地模型正演得到9种线圈架构接收线圈接收到的一次场及二次场,并以微分的方式定量地分析了9种线圈架构收发线圈位置及姿态角变化引起几何误差的变化特征。对9种线圈架构的几何误差分析可知:在几何形变引入的一次场误差中,仅有PERyz、PERzy线圈架构不包含位置变化的一次项误差,仅有VCA、VCP及HCP线圈架构不包含姿态角变化的一次项误差;在几何形变引入的二次场误差中,PERzx、PERxz线圈架构最大,而VCA、VCP及HCP线圈架构受高度及收发距变化的影响很大,需要实时测量并进行校正,VCP线圈架构受收发距变化以及姿态角变化的影响最小。

During the underground exploratio with frequency domain electromagnetic instruments based on magnetic dipole model,systematic errors are caused by the position and attitude changes of transmitting and receiving coils due to installation errors,the sway of instruments,as well as the geometric distortion of materials and other factors.The quantitative analysis of geometric errors for frequency-domain electromagnetic instruments has a great guiding significance in instrumentproduction,field operation and system correction.According to the sources of the errors,the geometric errors were divided into two categories,one is the primary field error,the other is the secondary field error.By introducing the tensor matrixes of the primary field and the secondary field,we forwarded the primary field and the secondary fields from nine configurations based on homogeneous earth model,and quantitatively analyzed the features and changes of the geometric errors of the nine configurations in a differential way.Numerical results show that,in the primary field errors introduced by the geometric distortion,only PERyz and PERzycoil configurations do not contain linear term of the position change;only VCA,VCP and HCP configurations do not contain linear term of attitude change.In the secondary field errors introduced by the geometric distortion,PERzx and PERxz coil configurations have the maximum relative error;VCA,VCP and HCP coil configurations are greatly influenced by the change of height and coil separation,which needs real-time measurement for correction;and the VCP coil configuration is least influenced by the change of coil separation and attitude.