Performance Analysis of Non-uniform Sparse Segmentation Integral Method Based on Gauss Integral in EM Forward of Electrical Antenna Under Stratified Ocean

Zongyang Shi,Lichao Ma,Yiyu Zhao,Xiaodong Qu

doi:10.11648/j.sd.20210902.16

Abstract

In order to solve the problem that it is difficult to take into account the computational efficiency and accuracy of electromagnetic field froward modeling of electrical antenna under the stratified ocean, evaluate the performance of two non-uniform sparse segmentation integral calculation methods based on Gauss integrals and improve the efficiency and accuracy of data interpretation in engineering applications, firstly two non-uniform sparse segmentation calculation methods based on Gauss integral nodes (Gauss-Legendre integral nodes and Gauss-Chebyshev integral nodes) are introduced. Then, two fast numerical integration methods corresponding of the time and frequency domain of the electrical antenna electromagnetic field under stratified ocean is established. Finally, by comparing and analyzing the results of the traditional uniform dense segmentation numerical integral calculation from the two aspects of computational accuracy and efficiency, the results show that two non-uniform sparse segmentation integral methods can improve the computational efficiency under the condition that the calculation accuracy is comparable, and the non-uniform sparse integral calculation method based on the Gauss-Chebyshev integral nodes is more significant than the calculation efficiency performance of the method based on the Gauss-Legendre integral node. At the same time, the general parameter setting of the non-uniform sparse segmentation integral method is given in this paper.

Highlights

以海洋可控源电磁方法(Marine Controlled Source Electromagnetic Method, MCSEM)为例,其通常采用几百米长的水平电性天线在海水中(距海底几十米的位置)辐射峰值电流几百安培至千安培、基频在 n ×10−1 Hz至 n ×10 Hz范围内的矩形波电流,通过布置在海底或者拖曳在距天线固定偏移距的电场或磁场传感器观测电场/磁场响应信号[1,2],然后通过采用相应数据处理手段对电磁信号进行处理,运用层状海洋模型正反演算法获得对实测电磁信号的定量反演解释,从而得到海洋中目标电阻率信息,图1 给出了海洋可控源电磁方法示意图,图中示意的传感器阵列位于海底沿电性天线轴向布置,实际应用中传感器根据需要可以布置于海水中或海水表面。
By comparing and analyzing the results of the traditional uniform dense segmentation numerical integral calculation from the two aspects of computational accuracy and efficiency, the results show that two non-uniform sparse segmentation integral methods can improve the computational efficiency under the condition that the calculation accuracy is comparable, and the non-uniform sparse integral calculation method based on the Gauss-Chebyshev integral nodes is more significant than the calculation efficiency performance of the method based on the Gauss-Legendre integral node
对比两种非均匀稀疏分割计算方法与均匀精细分割计算方法的总耗时,结果表明:(1).非均匀稀疏分割计算方法对于频域仿真计算能够获得极大的性能提升,性能提升近15倍;(2).对于时域仿真计算,基于高斯-勒让德积分的非均匀稀疏分割计算方法带来的性能提升有效,而基于高斯-切比雪夫积分的非均匀稀疏分割方法能带来约10倍以上的性能提升。

Summary

Introduction

以海洋可控源电磁方法(Marine Controlled Source Electromagnetic Method, MCSEM)为例,其通常采用几百米长的水平电性天线在海水中(距海底几十米的位置)辐射峰值电流几百安培至千安培、基频在 n ×10−1 Hz至 n ×10 Hz范围内的矩形波电流,通过布置在海底或者拖曳在距天线固定偏移距的电场或磁场传感器观测电场/磁场响应信号[1,2],然后通过采用相应数据处理手段对电磁信号进行处理,运用层状海洋模型正反演算法获得对实测电磁信号的定量反演解释,从而得到海洋中目标电阻率信息,图1 给出了海洋可控源电磁方法示意图,图中示意的传感器阵列位于海底沿电性天线轴向布置,实际应用中传感器根据需要可以布置于海水中或海水表面。. 限值,且在无穷远处,矢量位为零,即 Α(r → ∞) → 0 ; b) 各层分解面上,电场和磁场的切向分量连续。根据边界条件约束,电场 E 、磁场 H 与矢量为 A 和标量位U 之间的关系,采用分离变量法可得到各层中矢量位各分量的解。空气中电场各分量频域计算式为: 其中, φ 为观测点与电偶极源位置连线在XOY平面投影与 x 轴的夹角, sinφ = y , cosφ = x , Idl 表示电偶极源

Results

Conclusion