中文摘要：

频率领域电磁的方法广泛地已经为 tomographic 成像或电磁的好记载被使用了。然而，与开的洞记载不同，在很好记载的生产存在的金属 casing 在电磁波上有强壮的防护效果，因此把一些困难带到频率领域的申请在很好记载的生产的电磁的方法。根据到在心轴附近的戒指的域来源几何学的关系，频率领域的一般表达式在向轴的方向的电磁的回答对称的分层的传导性的媒介被推出。低频率的电磁波在 cased 洞里引起的繁殖效果也被分析。沿着在心轴的光线的方向的旋涡水流密度和磁性的流动密度的分发曲线显示在心轴以内的旋涡损失与传播信号频率和心轴传导性成正比。不同 casing 材料的第二等的地回答证明传播频率在渗透金属 casing 的电磁波的能力上有重要效果。传播频率应该是极端低的以便使电磁的信号能容易渗透 casing。为不同 casing 的频率回答的数字结果物理参数证明 casing 厚度在传播频率的选择上有重要影响。传播频率上的 casing 半径的效果能被忽视，这也被发现。

英文摘要：

The frequency domain electromagnetic method has already been widely used for tomographic imaging or electromagnetic well logging. However, different from open hole logging, the metal casing existing in production well logging has a strong shielding effect on the electromagnetic waves, thus bringing some difficulties to the application of the frequency domain electromagnetic method in production well logging. According to the relation of the field source geometry to the ring around the mandrel, the general expressions of frequency domain electromagnetic responses in axially symmetrical layered conductive medium are deduced. The propagation effects caused by the low-frequency electromagnetic waves in cased hole are also analyzed. The distribution curves of eddy current density and magnetic flux density along the radial direction in the mandrel indicate that the eddy loss within the mandrel is proportional to the transmission signal frequency and the mandrel conductivity. The secondary field responses of different casing materials show that the transmission frequency has an important effect on the ability of electromagnetic waves penetrating the metal casing. The transmission frequency should be ultra-low in order to enable the electromagnetic signal to penetrate the casing easily. The numerical results of frequency responses for different casing physical parameters show that the casing thickness has a significant impact on the choice of the transmission frequency. It is also found that the effect of the casing radius on the transmission frequency can be neglected.