三角网格剖分时域有限元法的探地雷达正演模拟  

GPR numerical simulation of triangulation meshing Time Domain Finite Element Method(FETD)

作　　者：崔凡[1,2] 陈毅 薛晗鹏 张永琦 CUI Fan;CHEN Yi;XUE HanPeng;ZHANG YongQi(School of Geosciences and Surveying Engineering,China University of Mining and Technology(Beijing),Beijing 100083,China;State Key Laboratory of Coal Resources and Safe Mining,China University of Mining and Technology(Beijing),Beijing 100083,China)

机构地区：[1]中国矿业大学(北京),地球科学与测绘工程学院,北京100083 [2]中国矿业大学(北京),煤炭资源与安全开采国家重点实验室,北京100083

出　　处：《地球物理学进展》2022年第2期797-809,共13页Progress in Geophysics

基　　金：国家重点研发研发计划(2019YFC1805504);国家自然科学基金项目:(52074306);国家能源投资集团科技创新项目(GJNY2030XDXM-19-03.2);陕煤化集团重大项目(2018SMHKJ-A-J-03)联合资助.

摘　　要：在探地雷达正演方法中,射线追踪法只能获取了波的运动学特征,时域有限差分法虽然能得到波的动力学特征,但是由于时空离散采用规则的结构化Yee单元,不能模拟复杂地质构造下波的传播规律.为了构建更复杂的地电模型和获取雷达波在不同地下构造中传播的波场特征,本文采用三角网格剖分的时域有限元法对探地雷达做正演模拟.时域有限元法可采用非结构化的拓扑网格对求解区域进行网格划分,选择三角形网格剖分物性区域可进一步解决矩形网格剖分对物性参数分布复杂以及几何特征不规则模型适应性差的问题.时域有限元法的求解首先以电磁波的麦克斯韦方程为基础,根据电磁场的本构关系,导出雷达波的波动方程,将波动方程作为微分控制方程并定义时域电磁场中的边值问题,对求解区域进行三角网格剖分后,采用线性插值基函数,应用Galerkin加权余量法对微分方程求解形成线性矩阵方程组,并在解线性方程组时采用LU分解的双共轭梯度法,加快了收敛速度,减小了迭代次数.在时间差分近似时采用Newmark-β法消除由时间步长过大带来的数值色散,实现无条件稳定.在求解区域边界外加完全匹配层吸收外向传播的电磁波,压制来自截断边界处的反射波.通过对构建的地电模型做正演模拟,其研究结果表明:使用三角网格剖分的时域有限元法进行复杂地质构造下的GPR正演数值模拟,构建的正演模型更加接近实际地质构造,具有更高的模拟精度,能进一步解译雷达数据剖面.In the Ground-Penetrating Radar(GPR)forward modeling method,the ray-tracing method can only obtain the kinematic characteristics of the wave.Although the finite-difference time-domain method can obtain the kinetic characteristics of the wave,it cannot simulate the law of wave propagation under complex geological structures since the regular structured Yee unit is used in the time-space discretization.In order to build a more complex geoelectric model and obtain the wavefield characteristics of radar waves propagating in complicated underground structures,this paper uses the time-domain finite element method of triangular meshing to simulate the ground penetrating radar.The time-domain finite element method can use unstructured topological grids to mesh the solution area.Choosing triangular meshes to divide the physical property area can further solve the problem of rectangular grid division has poor adaptability to models with complex physical parameter distribution and irregular geometric features.The solution of the time-domain finite element method is first based on the Maxwell equation of electromagnetic waves.According to the constitutive relationship of electromagnetic field,the wave equation of radar wave is derived.The wave equation is used as the differential control equation,and the boundary value problem in the time-domain electromagnetic field is defined.After the area is divided into triangular meshes,linear interpolation basis functions are used.The Galerkin weighted residual method is applied to solve the differential equations to form a linear matrix equation set.When solving the linear equation set,the double conjugate gradient method of LU decomposition is used to speed up Convergence speed reduces the number of iterations.In the time difference approximation,the Newmark-βmethod is used to eliminate the numerical dispersion caused by the excessively large time step and achieve unconditional stability.A perfect matching layer is added to the boundary of the solution area to absorb the electromag

关 键 词：探地雷达 时域有限元法 三角形网格 Galerkin加权余量法 NEWMARK-Β法 完全匹配层 

分 类 号：P631[天文地球—地质矿产勘探]