探地雷达FDTD数值模拟中不分裂卷积完全匹配层对倏逝波的吸收效果研究

介绍了CPML边界条件的原理,推导了CPML的GPR正演FDTD差分公式,对比分析了Berenger PML、UPML、CPML三种PML对倏逝波的吸收性能.开展了PML边界中关键参数κ和α的选取实验,确定了参数的取值范围与选取原则.然后,以二维TM波为例,研究了倏逝波产生的机理,分析了决定逝波性吸收性能的影响因素.均匀介质的波场快照、检测点的反射误差及全局反射误差对比,说明了3种边界条件对传输波都具有较好的吸收能力,而对低频倏逝波的吸收表现迥异,其中CPML因为引入了参数α,对倏逝波的吸收效果最佳,但离散化造成的全域误差也最大.最后,应用加载UPML和CPML边界条件的FDTD程序,开展了GPR二维剖面法、宽角法矩状地电模型及三维复杂模型的正演,展示了倏逝波反射对雷达正演剖面及波场快照的影响.进一步对比了UPML与CPML对倏逝波的吸收表现优劣,结果显示,CPML可有效减少边界反射误差,并能取得满意的精度,综合考虑对倏逝波的吸收、全域误差、编程难易程度等因素,在GPR正演中推荐使用CPML.

The unsplit convolutional perfectly matched layer absorption performance analysis of evanescent wave in GPR FDTD forward modeling

This article introduces the principle of CPML boundary conditions, and deduces its FDTD formula for GPR forward modeling, and then compares and analyzes the absorption properties of evanescent wave in Berenger PML, UPML, CPML. The numerical experiment of key parameters κ and α in PML were performed so as to determine its range and selection principles. Then, using the two-dimensional TM wave as an example, we studied the mechanism of evanescent wave generation and the influence factors of absorption properties. Wavefield snapshot of uniform medium, reflection error at detection point and global reflection error comparison shows that the three kinds of PML have fabulous absorption capacity to travelling-wave, but quite different to evanescent wave, especially in the low-frequency. Because the parameter α was introduced, the absorption of evanescent wave in CPML is exceptionally excellent; however, the global error is the largest caused by discretization. Finally, we used the FDTD program with UPML and CPML boundary conditions to carry out 2D GPR forward modeling using profile method and wide-angle method on rectangular geoelectric model and 3D uniform medium model. From the experiment, we observed that there is a huge influence of evanescent wave on both the radar forward modeling profile and wavefield snapshot. Furthermore, taking the absorption performance of evanescent wave by UPML and CPML into consideration, we can determine that CPML can effectively reduce the reflection error in truncation boundary, and obtain a satisfying accuracy. Considering the absorption performance of evanescent wave, the global error, programming difficulty and other factors, in the GPR forward modeling, we highly recommend the use of CPML boundary condition in GPR studies.