基于非交错网格频域有限差分法的探地雷达最优化正演算法研究  

Research on optimal forward algorithm of ground penetrating radar based on non-staggered grid frequency domain finite difference method

作　　者：张群慧 ZHANG Qunhui(Hunan Vocational College of Science and Technology,Changsha 410004,China)

机构地区：[1]湖南科技职业学院,湖南长沙410004

出　　处：《实验技术与管理》2022年第12期37-44,共8页Experimental Technology and Management

基　　金：湖南省自然科学基金项目资助(2020JJ7041)。

摘　　要：探地雷达正演模拟是探地雷达观测数据反演成像的重要组成部分。相对于发展较为成熟的时间域计算方法,频率域数值模拟算法在GPR正演方面的研究很少,然而考虑到频域算法具备的优势,该文提出了一种合适的频率域GPR正演算法。从提高GPR正演计算的精度和效率出发,基于TE模式下的频率域电磁波动方程,给出了UPML和CFS-PML两种吸收边界条件的基本公式,推导了经典5点差分网格和混合9点差分网格下的频域有限差分离散方程。为了获取最佳的数值模拟效果,设计了几组模型试验,来确定正演算法中的差分网格形式和吸收边界最佳参数,并将选取的最优化方法和参数应用于复杂地形的合成模型算例中,得到了准确高效的正演结果。该文所提出的频率域数值模拟方法不仅为快速、高精度的正演提供了重要理论参考依据,也为高效定量的GPR反演成像提供了重要基础和技术支撑。The ground penetrating radar forward simulation is an important part of the inversion imaging of the ground penetrating radar observation data. Compared with the more mature time-domain calculation methods,there is little research on frequency-domain numerical simulation algorithm in GPR forward modeling. However,considering the advantages of frequency-domain algorithm, this paper presents an appropriate frequency-domain GPR forward algorithm. To improve the accuracy and efficiency of GPR forward calculation, based on the frequency-domain electromagnetic wave equation in the TE mode, this paper gives the basic formulas of two absorption boundary conditions, UPML and CFS-PML, and derives the finite difference dispersion equation in the frequency domain under the classical 5-point difference grid and the hybrid 9-point difference grid. To obtain the best numerical simulation results, several sets of comparison tests are designed in the paper to determine the differential grid form, absorption boundary and the best parameters in the forward algorithm. Then the proposed optimal method and the selected parameters are further applied to the synthetic model containing complex terrain,showing accurate and efficient numerical simulation results. The frequency domain numerical simulation method proposed in this paper not only provides an important theoretical reference for fast and high-precision forward modeling technique, but also provides an important foundation and technical support for efficient and quantitative GPR inversion imaging.

关 键 词：探地雷达 频率域有限差分 正演模拟 

分 类 号：P631[天文地球—地质矿产勘探]