各向异性介质GPR非结构化网格有限元正演

摘要

In order to more accuratelyunderstandthe propagation law of GPR(ground penetrating radar)wave in anisotropic medium,the wave equations in monoclinic anisotropic mediumwerededuced based on the Maxwell equation, and the finite element method of unstructured meshes and the central difference method were applied to discretize in space domain and time domain respectively.Then, the GPR finite element numerical simulation algorithm of monoclinic anisotropic medium was builtand programmed,and its feasibility and effectiveness were tested by comparing theresults of simulationand analyticalsolution of homogenous anisotropic model.The finite element method based on unstructured meshes was applied to simulate the circle anisotropic model and homogeneous anisotropic model and compared with calculated results of its isotropic medium model.The results show that the simulated resultsby finite element method based on unstructuredmesheshavelowerfittingerror and higher precision compared with the simulated results by FDTD, the electromagnetic wave propagates outward with elliptical circle and its energy attenuates slower duo to the different velocities of wave in different directions.And curvature,energy and two way travel time of reflected wave change significantly compared with those of isotropic medium due to different wave velocitis in different directions.%为了更准确地认识电磁波在各向异性介质中的传播特征，从麦克斯韦方程组出发，推导电磁场在单斜各向异性介质中的波动方程。采用 Delaunay 非结构化网格有限元法进行空间域离散，采用中心差分公式进行时间域离散，导出单斜各向异性介质中GPR时空域有限元方程。在此基础上，建立各向异性介质GPR非结构化网格有限元正演算法。利用以上算法编制的程序对均匀各向异性介质模型进行正演计算，并与解析解对比，验证该算法的正确性和有效性；对均匀各向异性介质模型和圆形异常体模型进行计算，并与背景介质为各向同性介质的计算结果进行对比。研究结果表明：与FDTD计算结果对比，非结构化网格有限元法的拟合误差更小，精度更高；电磁波传播受介质各向异性的影响，波前面呈椭圆状向外扩散传播，其能量衰减较慢；与各向同性介质中圆形异常体反射波相比，各向异性介质的圆形异常体反射波的曲率、能量和双程走时，受不同方向上电磁波速度影响会发生显著变化。