矩形回线激发的电磁场与磁场的对称关系研究

Relationship between electromagnetic field and magnetic field’s symmetric excited by rectangular loop

由垂直磁偶极源激发的电场,对其磁矩按回线面积积分,推导出矩形回线激发的电场表达式;根据法拉第电磁感应定律,利用电场强度阶跃响应求得磁感应强度脉冲响应;根据柱状坐标系中垂直磁偶极源激发的水平磁场只有径向分量的特点,推导出直角坐标系中磁场脉冲响应水平分量的对称关系,应用正、余弦函数的关系,得到磁场脉冲响应x和y分量之间的转换关系。研究结果表明:磁场脉冲响应x分量关于x轴对称,关于y轴负对称;y分量关于y轴对称,关于x轴负对称。这种对称关系和转换关系为简化三维正演赋初始值提供了理论依据,只需计算1/4回线内磁场脉冲响应的1个水平分量即可。

From the electric field excited by vertical magnetic dipole, the total electric field excited by a rectangular loop was deduced using loop area integral for magnetic moment. Based on Faraday law of electromagnetic induction, impulse responses of magnetic induction were deduced from electric field strength step responses. Based on the fact that horizontal component of magnetic field which is emitted by vertical magnetic dipole has radial component only in cylindrical coordinate system, some symmetrical relationships of magnetic induction were concluded. Conversion relationship between component x and component y was obtained from sine and cosine function relation. The results show that component x of magnetic field impulse response is symmetrical to x axis and negative symmetrical to y axis; component y is symmetrical to y axis and negative symmetrical to x axis in Cartesian coordinate system. These symmetrical relationships and conversion relationships provide theoretical basis for simplifying 3D forward＇s initial condition. Computing one of horizontal components of magnetic field impulse responses only in quarter loop region is sufficient.