摘要
近源时间域电磁场具有信号强、探测深度大、精度高等优点,但传统勘探电磁场理论中偶极子近似在近源会引起较大误差,导致这一优势的发挥受到了制约.开展直接时间域电磁场解析式研究,是解决这一问题的途径之一.本文提出在点电荷微元假设下,引入时域格林函数,求取瞬变电磁场时间域解析解.采用积分运算法,把电磁场阻尼波动方程的求解问题转化为求其格林函数积分形式解的问题;建立辅助路径解决奇点问题,利用复分析中的约当引理、留数定理和广义函数等理论和方法,推导计算出时间域格林函数的时空四重广义积分.得到达朗贝尔方程的直接时域格林函数精确解析式,与传统方法"比拟"出的公式具有相同的形式,验证了本文推导的时域格林函数解析公式的正确性;推导出扩散方程的直接时间域解析解.通过与时变点电荷源时间域的电磁响应近似表达式进行对比,得出本文所推导的公式计算精度较高的结论;建立了全空间回线源瞬变电磁场问题的直接时间域求解公式.为解决全场区瞬变电磁场精细探测直接时域解析问题提供了基础理论.
Time-domain near-source electromagnetic method has the merit of strong signal,deep detecting depth and high accuracy. However,the method meet problem,because dipole approximation in the near-source will cause greater error based on traditional electromagnetic theory.Studying direct time domain electromagnetic field analytical formula derivation is one way of solving the problem.Based on point charge hypothesis,TEM field analytical solution has been derived by introducing time-domain Green function in this paper.Integral formula has been used to transform electromagnetic field damping wave equation into Green function integral form.Auxiliary path has been constructed for solving singularity problem.4-tuple generalized integral formula of time-domain electromagnetic field response has been arrived by using Jordan′s lemma,the residue theorem and generalized function method.Direct-time-domain exact solution of D′Alembert equations firstly has been derived,whose form is agree with the traditioanl＂matching＂result,which show that the method of time-domain electromagnetic field based on Green function is right.Then,the direct-time-domain formula of diffusion function also has been given.After the copmaresion the numerical result between point charge Green function exact sulotion and approximate solution,it can be concluded that the derivation formula in this paper has higher precision.Furtherly,the full-space TEM direct-time-domain solution due to loop-source has been derived using integral method.The achievement lay a theoretical fundation for solving the problem of TEM All-Zone detection with directy time domain analytical solution.
出处
《地球物理学报》
SCIE
EI
CAS
CSCD
北大核心
2014年第2期671-678,共8页
Chinese Journal of Geophysics
基金
国家973重点基础研究发展计划(2012CB416605)
国家自然科学基金(41174090)
国家重大科研装备研制项目(ZDYZ2012-1-05-04)资助
关键词
瞬变电磁场
点电荷
时域格林函数
达朗贝尔方程
扩散方程
Transient electromagnetic field
Point charge
Time-domain Green functions
D′Alembert equation
Diffusion equation
