首页 | 本学科首页   官方微博 | 高级检索  
     

基于Pade逼近的Cole-Cole频散介质GPR有限元正演
引用本文:王洪华, 王敏玲, 张智, 刘海. 2018. 基于Pade逼近的Cole-Cole频散介质GPR有限元正演. 地球物理学报, 61(10): 4136-4147, doi: 10.6038/cjg2018L0214
作者姓名:王洪华  王敏玲  张智  刘海
作者单位:1. 桂林理工大学地球科学学院, 桂林 541004; 2. 广西隐伏金属矿产勘查重点实验室, 桂林 541004; 3. 广州大学土木工程学院, 广州 510006
基金项目:国家自然科学基金项目(41604102,41604039),广西自然科学基金项目(2016GXNSFBA380082,2016GXNSFBA380215),广西中青年教师基础能力提升项目(KY2016YB199)和广西有色金属隐伏矿床勘查及材料开发协同创新中心创新团队项目(GXYSXTZX2017-Ⅱ-5)联合资助.
摘    要:

针对Cole-Cole频散介质中的复介电常数是jω的分数次幂函数,传统的时域有限元法难以离散及计算时间域分数阶导数,本文采用Pade逼近算法将含有时间分数阶导数的Cole-Cole频散介质电磁波方程推导为一组整数阶辅助微分方程,提出了一种适用于Cole-Cole频散介质的GPR有限元正演模拟算法.在复数伸展坐标系下,通过在频率域Cole-Cole频散介质电磁波方程中引入2个中间变量,并将其变换到时间域,从而以变分形式将PML边界条件加载到Cole-Cole频散介质GPR有限元方程组中,并给出了详细的求解公式.在此基础上,编制了基于Pade逼近的Cole-Cole频散介质GPR有限元正演程序,利用该程序对均匀模型进行计算,并与解析解进行对比,验证了本文构建的GPR有限元正演算法的正确性和有效性.设计了一个复杂Cole-Cole频散介质GPR模型,利用本文构建的GPR有限元正演算法进行模拟并与非频散介质模型的模拟结果进行对比,分析了电磁波在Cole-Cole频散介质中传播衰减增强、子波延伸,分辨率降低等传播规律,有助于实测雷达资料更可靠、更准确的解释.模拟结果表明,基于Pade逼近的GPR有限元正演算法可用于复杂Cole-Cole频散介质结构模拟,且具有较高的计算精度.



关 键 词:探地雷达   Cole-Cole频散介质   时域有限元法   Pade逼近
收稿时间:2017-09-18
修稿时间:2018-04-04

Simulation of GPR in Cole-Cole dispersive media by finite element method based on the Pade approximations
WANG HongHua, WANG MinLing, ZHANG Zhi, LIU Hai. 2018. Simulation of GPR in Cole-Cole dispersive media by finite element method based on the Pade approximations. Chinese Journal of Geophysics (in Chinese), 61(10): 4136-4147, doi: 10.6038/cjg2018L0214
Authors:WANG HongHua  WANG MinLing  ZHANG Zhi  LIU Hai
Affiliation:1. College of Earth Sciences, Guilin University of Technology, Guilin 541004, China; 2. Guangxi Key Laboratory of Hidden Metallic Ore Deposits Exploration, Guilin 541004, China; 3. School of Civil Engineering, Guangzhou University, Guangzhou 510006, China
Abstract:Since the complex permittivity of Cole-Cole dispersive media is a fractional power function of jω, it is difficult to calculate the time domain fractional derivative by using the finite element time domain (FETD) method. In this paper, a set of auxiliary integer order differential equations are derived from the fractional derivative Maxwell equations in the Cole-Cole dispersive media by the Pade approximation algorithm and a FETD algorithm for simulating ground penetrating radar (GPR) in the Cole-Cole dispersive media is proposed. A perfect matched layer (PML) boundary condition in the variational form is applied to the Cole-Cole dispersive media through introducing two intermediate variables to the Maxwell equations in the frequency domain, which is then transformed into the time domain. We firstly validate the proposed FETD algorithm through simulating the GPR waves propagating in a homogeneous dispersive medium and comparing the results with the analytical solution. Then we design a complex subsurface model of the Cole-Cole dispersive media, compare the simulated GPR profile with that from the counterpart model of non-dispersive media. We find that the medium dispersion can cause larger attenuation of GPR waves and elongate the GPR wavelet and degrade the resolution. We conclude that the proposed FETD algorithm can simulate GPR waves in the Cole-Cole dispersive media with a high accuracy and can aid in the reliable interpretation of the field GPR data.
Keywords:Ground Penetrating Radar (GPR)  Cole-Cole dispersive media  Finite element time domain (FETD) method  The Pade approximation
本文献已被 CNKI 等数据库收录!
点击此处可从《地球物理学报》浏览原始摘要信息
点击此处可从《地球物理学报》下载免费的PDF全文
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号