频散介质探地雷达正演与高速公路实测资料解释

赵 超^{1, 2}， 冯德山¹，柳建新¹，谢 源¹，钟文胜³，杨炳坤¹

(1. 中南大学 地球科学与信息物理学院，长沙 410083；
2. 华东有色地质勘查局，南京 210007；
3. 广东省有色金属地质勘查局 地质工程中心，广州 510080)

摘 要：基于Maxwell方程组，得到满足Debye关系的频散介质探地雷达有限元波动方程，推导有限单元法的离散格式，并编制正演模拟MATLAB程序。选取一典型地电模型，分别对考虑频散与不考虑频散，频散介质中同一模型不同频率天线的雷达探测结果进行分析。结果表明：雷达波在频散介质中传播时，具有波形严重畸变、能量迅速衰减的特性，如果不考虑介质对波吸收衰减的探地雷达正演，其结果与实测的雷达波形存在较大的偏差。并把该结论应用到广东省某高速公路的圆管涵实际资料解释中，有效地解答了实测资料解释中遇到的问题，并对GPR工程实测过程中天线频率的选取提出了有益建议。

关键词：探地雷达；频散介质；有限单元法；正演；高速公路；圆管涵

GPR forward simulation in dispersive medium and interpretation of actual measurement data on highway

ZHAO Chao^{1, 2}, FENG De-shan¹, LIU Jian-xin¹, XIE Yuan¹, ZHONG Wen-sheng³, YANG Bing-kun¹

(1. School of Geosciences and Info-Physics, Central South University, Changsha 410083, China;
2. East China Mineral Exploration and Development Bureau, Nanjing 210007, China;
3. Center of Geological and Engineering, Geology Bureau for Nonferrous Metals of Guangdong Province,
Guangzhou 510080, China)

Abstract:Based on the Maxwell equations, we obtained the GPR wave equation satisfying the Debye relationship in dispersive media, deduced the finite element discretization format of this equation, and made a GPR forward simulation program by MATLAB. Choosing a typical geoelectric model, we analyzed the dispersive media GPR results in different frequencies while we considered dispersion and no dispersion, separately. The results show that the characteristics and rules of GPR waveform wave propagation process often produce distortion and attenuation in dispersive medium, and there is a discrepancy between the GPR forward modeling results without considering the attenuation of the medium and the measured radar waveform. We applied these conclusions to interpret the actual data of pipe culvert in a highway of Guangdong Province, China, which explained the measured data effectively, and made a good suggestion to select the antenna frequency in GPR measurement process.

Key words:ground penetrating radar; dispersive medium; finite element method; forward simulation; highway; circular culvert