王贺元^1,,
薛国强^2,3,,,
郭华¹,
周楠楠^2,3
1. 辽宁工业大学理学院, 辽宁锦州 121001
2. 中国科学院地质与地球物理研究所, 北京 100029
3. 中国科学院大学, 北京 100049

基金项目: 国家重点研发计划（2017YFC0601204，2016YFC0600101），国家自然科学基金（11572146，41174090，41474095），辽宁省教育厅科研基金（L2013248）和锦州市科技专项基金（13A1D32）资助


详细信息

作者简介: 王贺元, 男, 1963年生, 教授, 主要从事电磁场数值计算.E-mail:wangheyuan6400@sina.com

通讯作者: 薛国强, 男, 1966年生, 研究员, 主要从事电磁探测理论与应用研究.E-mail:ppxueguoqiang@163.com

中图分类号: P631

收稿日期:2016-11-25
修回日期:2017-09-16
上线日期:2018-02-05

Numerical analysis for direct response of the transient electromagnetic field in the time domain in a homogeneous half space

WANG HeYuan^1,,
XUE GuoQiang^2,3,,,
GUO Hua¹,
ZHOU NanNan^2,3
1. College of Sciences, Liaoning University of Technology, Liaoning Jinzhou 121001, China
2. Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China
3. University of Chinese Academy of Sciences, Beijing 100049, China


More Information

Corresponding author: XUE GuoQiang,E-mail:ppxueguoqiang@163.com

MSC: P631

--> Received Date: 25 November 2016
Revised Date: 16 September 2017
Available Online: 05 February 2018


摘要
摘要:近源时域电磁场具有信号强、探测深度大和精度高等优点，但传统瞬变电磁场理论中偶极子近似在近源区会引起较大误差，推导瞬变电磁场直接时域解析式是解决这一问题的关键.本文在点电荷微元假设下通过时域格林函数，采用分离变量等方法推导出了上半空间一次有源波动场和反射波的时域解析式和下半空间二次无源波动场的时域解析式，结合均匀半空间瞬变电磁场的边界条件给出了均匀半空间瞬变电磁场的直接时域解析式，进而利用第一型曲线积分，通过沿回线源叠加推导出圆回线源在瞬变电磁场中的直接时域解析式.然后在半空间表面上，与传统的电偶极源假设下的表达式作了比较.数值结果表明两者在远源区的计算结果相差甚微，而近源区则存在很大误差.本文利用真正点元（点电荷）严密推导给出的均匀半空间表面上瞬变电磁场的直接时域解析式适用于全场区探测，克服了偶极子假设下只适用远场区的不足，为瞬变电磁法的进一步发展和实际勘探提供了新的理论基础.
关键词: 均匀半空间/
瞬变电磁场/
电偶极子假设/
点电荷源

Abstract:The time-domain near-source electromagnetic field has the merits of strong signal, deep detecting depth and high accuracy. However, dipole approximation in the near-source can cause major error in the traditional transient electromagnetic (TEM) theory. To solve this problem, this paper derives the direct expression of the transient electromagnetic field in the time domain. Based on the assumption of a point charge element, we derive time domain analytical formula of an active wave field and reflection waves in the upper half space and the quadratic passive fluctuations field in lower half space by using the variable separation method and time-domain Green function. Combined with boundary conditions of the transient electromagnetic field of a homogeneous half space, a direct time domain analytical formula of the electromagnetic field is given, and using the first kind of curve integral, through along the loop source superposition method we present direct time domain analytical formula of a circular loop source. Then they are compared with the formula of electric dipole approximation on the surface of a uniform half space. The numerical results show that they are approximate in the far-source zone but has a major difference in the near-source zone. In sum, based on the point charge hypothesis and integral method we derive TEM direct-time-domain solution in a rigorous manner, which is applicable for TEM all-zone detection and lays a theoretical basis for further development of the TEM technology.
Key words:Homogeneous half space/
Transient electromagnetic field/
Electric dipole approximation/
Point charge source



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