冯德山^1,2,,
王珣^1,2,,
1. 中南大学地球科学与信息物理学院, 长沙 410083
2. 有色金属成矿预测教育部重点实验室, 长沙 410083

基金项目: 国家自然科学基金项目（41574116，41774132），中南大学创新驱动项目（2015CX008），教育部新世纪优秀人才支持计划（NCET-12-0551），中南大学教师研究基金（2014JSJJ001），中南大学升华育英人才计划，湖南省研究生科研创新项目（CX2017B052）共同资助


详细信息

作者简介: 冯德山, 男, 1978年生, 汉族, 湖南祁阳人, 博士, 教授, 从事地球物理数据处理与正反演研究.E-mail:fengdeshan@126.com

通讯作者: 王珣, 男, 1990年生, 博士研究生, 主要从事电磁法数值模拟研究.E-mail:wangxun0727@csu.edu.cn

中图分类号: P631

收稿日期:2017-08-30
修回日期:2018-03-12
上线日期:2018-11-05

Fast Ground Penetrating Radar double-parameter inversion based on GPU-parallel by time-domain full waveform optimization conjugate gradient method

FENG DeShan^1,2,,
WANG Xun^1,2,,
1. School of Geosciences and Info-Physics, Central South University, Changsha 410083, China
2. Key Laboratory of Metallogenic Prediction of Nonferrous Metals, Ministry of Education, Changsha 410083, China


More Information

Corresponding author: WANG Xun,E-mail:wangxun0727@csu.edu.cn

MSC: P631

--> Received Date: 30 August 2017
Revised Date: 12 March 2018
Available Online: 05 November 2018


摘要
摘要:探地雷达（GPR）时间域全波形反演计算量巨大，内存要求高，在微机上计算难度大.本文中作者基于GPU并行加速的维度提升反演策略，采用优化的共轭梯度法，避免了Hessian矩阵的计算，在普通微机上实现了时间域全波形二维GPR双参数（介电常数和电导率）快速反演.论文首先推导了二维TM波的时域有限差分法（FDTD）的交错网格离散差分格式及波场更新策略.然后，基于Lagrange乘数法，将约束问题转化为无约束最小问题，构建了共轭梯度法反演目标函数，采用Fletcher-Reeves公式与非精确线搜索Wolfe准则，确保了梯度方向修正因子及迭代步长选取的合理性.而GPU并行计算及维度提升反演策略的应用，数倍地提升了反演速度.最后，开展了3个模型的合成数据的反演实验，分别从观测方式、梯度优化及天线频率等方面，分析了这些因素对雷达全波形反演的影响，说明双参数的反演较单一的介电常数反演，能提供更丰富的信息约束，有效提高模型重建的精度.
关键词: 探地雷达/
全波形反演/
共轭梯度法/
维度提升/
GPU并行

Abstract:The time domain full waveform inversion (FWI) of ground penetrating radar (GPR) is difficult to calculate on personal computer due to its calculation and high memory requirements. In this paper, we use the optimized conjugate gradient method based on the GPU parallel acceleration with the dimensionality lifting scheme, and the calculation of Hessian matrix is avoided, realizing the fast inversion of the two-dimensional GPR double-parameter (dielectric constant and conductivity) in the time domain. Firstly, the staggered grid discrete difference scheme and wave field updating strategy of 2D TM wave finite difference time domain (FDTD) method are derived. Then, based on the Lagrange multiplier method, the constraint problem is transformed into the unconstrained minimum problem, and the conjugate gradient method is used to invert the objective function. The Fletcher-Reeves formula and the inexact line search Wolfe conditions are used to ensure the rationality of the selection of gradient direction correction factor and iteration. The introduction of GPU-based parallel computing and dimension to enhance the inversion strategy can improve the inversion speed several times. Finally, the inversion experiments of synthetic data of three models are carried out. The influence of these factors on the full waveform inversion is analyzed in detail from the aspects of observation mode, gradient optimization and antenna frequency, respectively. The results show that the inversion result of the two parameters can provide richer information constraints to a single dielectric constant inversion and improve the accuracy of model reconstruction, effectively.
Key words:Ground Penetrating Radar/
Full waveform inversion/
Conjugate gradient method/
Dimension promotion/
GPU parallel



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