复频率参数完全匹配层吸收边界在瞬变电磁法正演中的应用

Application of the complex frequency shifted perfectly matched layer absorbing boundary conditions in transient electromagnetic method modeling

本文将复频率参数完全匹配层(Complex Frequency Shifted Perfectly Matched Layer,CFS-PML)吸收边界应用到瞬变电磁法(Transient Electromagnetic,TEM)三维正演中,以替代传统的狄利克雷边界条件,使用时域有限差分法(Finite-difference time-domain,FDTD)进行空间离散和时间步进.本文给出了扩散场在CFS-PML内部的平面波解,分析了常规PML在TEM正演中失效的原因,并给出了CFS-PML在TEM正演中参数设置准则.最后分别使用全空间和半空间模型进行有效性检验.全空间检验结果表明,使用CFS-PML的解在我们正演的所有延迟时间内均与理论解吻合得非常好,而使用狄利克雷边界的解可与理论解偏离一个量级以上.半空间检验结果表明,CFS-PML亦明显优于狄利克雷边界,然而CFS-PML对空气中的场吸收甚微,相对误差依然会随着延迟时间缓慢增加,正演时需要根据误差容忍度设计适当的模型.

Instead of the conventional Dirichlet boundary condition （DBC） ,the complex trequency shifted perfectly matched layer （CFS-PML） absorbing boundary condition was applied in transient electromagnetic （TEM） method modeling. A finite difference time domain （FDTD） method was used for space discretization and time stepping. We obtained the plane wave solutions inside the CFS-PML and pointed out the reason why the regular PML fails for TEM modeling. We also provided a criterion for the selection of the parameters of CFS-PML. These ideas were validated for both the whole space and the half space models. The results of a whole space model using CFS-PML showed excellent consistency with the analytical solutions, while those using DBCdeviated more than one order of magnitude at the latest delay time. The model also showed great superiority of CFS-PML compared to DBC. results of However, a half space the lack of absorbing ability of CFS-PML in the air caused some errors which could increase with time slowly. Proper models should be designed according to the permitted error.