多频电磁法概述 - 2. 理论

原作者：M. Elwaseif

翻译自期刊：Computers & Geosciences

2 理论

The basic principle of the EM method is that a transmitter coil is excited with alternating current at a specific frequency, which generates a changing primary magnetic field that in turn induces alternating electrical eddy currents in the subsurface.

电磁法的基本原理是用特定频率的交流电激励发射线圈，产生一个不断变化的初级磁场，进而在地下感应交变电涡流。

The induced currents produce secondary magnetic fields in the subsurface, which are detected by a receiver coil along with the primary field.

感应电流在地下产生二次磁场，与一次磁场一起被接收线圈探测到。

The out-of-phase component of the ratio of the secondary field created by the eddy currents to the primary field is proportional to the conductivity of the subsurface, whereas the in-phase component of the ratio is proportional to subsurface magnetic susceptibility.

由涡流产生的二次场与一次场之比的反相分量与地下电导率成正比，而同相分量则与地下磁化率成正比。

FEMIC only utilizes the out-of-phase data sets during the inversion process given its high signal-to-noise ratio compared with the in-phase data sets (e.g., Huang and Won, 2000).

相对于同相数据集，非同相数据集具有较高的信噪比，因此在反演过程中，FEMIC只使用了非同相数据集。

 Fig. 1 shows the data acquisition setup and a parameterization of the subsurface model. A description of EM theory is provided in the following sections.

图1显示了数据采集设置和地下模型的参数化。下面几节将介绍电磁理论。

2.1 一维正演问题和控制方程

The equations for the magnetic field generated by an oscillating magnetic dipole above a half space are derived from the quasi-static forms of Ampere's and Faraday's laws of induction.

根据安培定律和法拉第定律的准静态形式，导出了半空间上振荡磁偶极子产生的磁场方程。

For a layered earth model, the magnetic field propagates into the subsurface as described by Faraday's law:

对于层状地球模型，磁场沿法拉第定律向地下传播