王洪华^1,2,
吕玉增^1,2,,,
王敏玲^1,2,
龚俊波¹,
张智^1,2
1. 桂林理工大学地球科学学院, 广西桂林 541004
2. 广西隐伏金属矿产勘查重点实验室, 广西桂林 541004

基金项目: 国家自然科学基金项目(41604102, 41604039, 41764005, 41674075), 广西自然科学基金项目(2016GXNSFBA380082, 2016GXNSFBA380215, 2016GXNSFGA38004), 广西中青年教师基础能力提升项目(KY2016YB199)联合资助


详细信息

作者简介: 王洪华, 男, 1986年生, 博士, 讲师, 主要从事探地雷达正反演理论及应用研究

通讯作者: 吕玉增, 男, 1978年生, 博士, 副教授, 主要从事电磁勘探理论及应用研究.E-mail:lyz@glut.edu.cn

中图分类号: P631

收稿日期:2018-10-24
修回日期:2019-03-24
上线日期:2019-05-05

A perfectly matched layer for second order electromagnetic wave simulation of GPR by finite element time domain method

WANG HongHua^1,2,
Lü YuZeng^1,2,,,
WANG MinLing^1,2,
GONG JunBo¹,
ZHANG Zhi^1,2
1. College of Earth Sciences, Guilin University of Technology, Guilin Guangxi 541004, China
2. Guangxi Key Laboratory of Hidden Metallic Ore Deposits Exploration, Guilin Guangxi 541004, China


More Information

Corresponding author: Lü YuZeng,E-mail:lyz@glut.edu.cn

MSC: P631

--> Received Date: 24 October 2018
Revised Date: 24 March 2019
Available Online: 05 May 2019


摘要
摘要:完全匹配层（PML）作为一种稳定高效的吸收边界条件，广泛应用于基于一阶电磁波动方程的探地雷达（GPR）数值模拟中.为解决基于二阶电磁波动方程的GPR数值模拟的吸收边界问题，本文借鉴二阶弹性波动方程的PML边界条件构建思想，提出了一种适合二阶电磁波动方程GPR时域有限元模拟的PML边界条件.从二阶电磁波动方程出发，基于复拉伸坐标变换，推导了PML算法的频域表达式；通过合理构造辅助微分方程，得到了PML算法的时域表达式，并以变分形式（弱形式）加载到GPR时域有限元方程中，实现了PML边界条件在二阶电磁波动方程GPR时域有限元模拟中的应用.在此基础上，对比了无边界条件、Sarma边界条件和PML边界条件下均匀模型的波场快照、单道波形、时域反射误差和能量衰减曲线，结果表明：PML边界条件的吸收效果要远优于Sarma边界条件，具有近似零反射系数.一个复杂介质模型的正演模拟验证了PML边界条件在非均匀地电结构中电磁波传播模拟的良好吸收效果.
关键词: 完全匹配层/
二阶电磁波动方程/
探地雷达/
时域有限元

Abstract:The perfect matching layer (PML), as a stable and efficient absorbing boundary condition, is widely used in the Ground Penetrating Radar (GPR) numerical simulation of first-order electromagnetic wave equation. In order to solve the problem of the absorbing boundary in GPR numerical simulation based on second-order electromagnetic wave equation, this paper proposes a PML boundary condition for Finite Element Time Domain (FETD) simulation of GPR based on second order electromagnetic wave equation according to the PML boundary condition construction idea of second-order elastic wave equation. Taking the two-dimensional TM wave equation as an example, the frequency domain formula of PML algorithm is deduced according to the complex coordinate transformation and its time domain equation is obtained by constructing reasonable auxiliary differential equation. And the PML boundary condition is loaded into the FETD equation of GPR in a form of variation principle (weak form), so that the application of PML in the FETD simulation of GPR second-order electromagnetic wave equation is realized. On this basis, comparison of the wave field snapshots, signal waveforms, time reflection errors and energy attenuation curves of the homogenous model with Sarma, PML boundary condition and without this boundary condition demonstrates that the absorption effect of PML is much better than the Sarma boundary condition with a near-zero reflection coefficient. At last, the numerical simulation of a complex model verifies the good absorbing effect of the PML boundary condition on electromagnetic wave propagation in a heterogeneous geo-electric structure.
Key words:Perfectly Matched Layer (PML)/
Second-order electromagnetic wave equation/
Ground Penetrating Radar (GPR)/
Finite Element Time Domain method (FETD)



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