| 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 |
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| 引用本文： | 冯德山, 杨良勇, 王珣. 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[J]. 地球物理学报, 2016, 59(12): 4733-4746, doi: 10.6038/cjg20161232 |
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| 作者姓名： | 冯德山 杨良勇 王珣 |
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| 作者单位： | 1. 中南大学地球科学与信息物理学院, 长沙 410083; 2. 中国科学院地质与地球物理研究所, 北京 100029; 3. 有色金属成矿预测教育部重点实验室, 长沙 410083 |
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| 基金项目： | 国家自然科学基金资助项目（41574116），中南大学创新驱动项目（2015CX008），教育部新世纪优秀人才支持计划（NCET-12-0551），中南大学教师研究基金（2014JSJJ001），中南大学升华育英人才计划，湖湘青年创新创业平台培养对象项目共同资助. |
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| 摘 要： | 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.
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| 关 键 词： | 探地雷达 不分裂卷积完全匹配层 单轴各向异性完全匹配层 倏逝波 时域有限差分法 |
| 收稿时间： | 2015-11-15 |
| 修稿时间： | 2016-09-12 |
The unsplit convolutional perfectly matched layer absorption performance analysis of evanescent wave in GPR FDTD forward modeling |
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| FENG De-Shan, YANG Liang-Yong, WANG Xun. The unsplit convolutional perfectly matched layer absorption performance analysis of evanescent wave in GPR FDTD forward modeling[J]. Chinese Journal of Geophysics (in Chinese), 2016, 59(12): 4733-4746, doi: 10.6038/cjg20161232 |
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| Authors: | FENG De-Shan YANG Liang-Yong WANG Xun |
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| Affiliation: | 1. School of Geosciences and Info-Physics, Central South University, Changsha 410083, China; 2. Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China; 3. Key Laboratory of Metallogenic Prediction of Nonferrous Metals, Ministry of Education, Changsha 410083, China |
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| Abstract: | 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. |
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| Keywords: | Ground Penetrating Radar Convolutional perfectly matched layer Uniaxial perfectly matched layer Evanescent wave Finite difference time domain method |
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