基于复频移完全匹配层的辛龙格库塔算法探地雷达正演  

Complex Frequency Shifted Perfectly Matched Layer for Symplectic Partitioned Runge-Kutta Method forward Modeling of Ground Penetrating Radar

作　　者：冯德山[1,2] 谭阳 杨军 张陆军 袁忠明 柳杰 王珣 FENG De-shan;TAN Yang;YANG Jun;ZHANG Lu-jun;YUAN Zhong-ming;LIU Jie;WANG Xun(School of Geosciences and Info-Physics, Central South University, Changsha 410083, China;Key Laboratory of Non-ferrous Resources and Geological Detection, Ministry of Hunan Province, Changsha 410083, China;Guangzhou Municipal Engineering Design & Research Institute Co., Ltd., Guangzhou 510060, China)

机构地区：[1]中南大学地球科学与信息物理学院,长沙410083 [2]有色资源与地质灾害探查湖南省重点实验室,长沙410083 [3]广州市市政工程设计研究总院有限公司,广州510060

出　　处：《科学技术与工程》2022年第9期3473-3484,共12页Science Technology and Engineering

基　　金：国家自然科学基金(41774132,42074161)。

摘　　要：为了消除探地雷达(ground penetrating radar,GPR)正演模拟的截断边界处的非物理反射,需要对模拟区域边界进行特殊处理。目前应用效果较好的边界处理方法为加载完全匹配层吸收边界条件。而复频移完全匹配层(complex frequency shift perfectly matched layer,CFS-PML)可以加强对低频区凋落波、倏失波的吸收效果,还可以压制信号的虚假反射,被引入到GPR正演边界条件处理中。将CFS-PML应用于辛龙格库塔求解二维GPR波动方程的数值模拟中,利用辛算法可以实现对时间坐标和空间坐标的保辛计算,从而实现GPR高精度正演模拟。首先,以横磁(transverse magnetic,TM)波为例,推导了基于CFS-PML的辛龙格库塔GPR波动方程求解公式。其次,利用狭长模型开展了CFS-PML吸收边界条件中的关键参数的选取试验,通过对比反射误差的大小确定了最优参数。此外,通过CFS-PML吸收边界条件与透射边界条件的对比实验,说明大角度掠射下CFS-PML边界条件较透射边界具有更好的吸收效果。最后,为了进一步验证该算法的效果,应用加载CFS-PML边界的辛龙格库塔算法对一个具有起伏地形的地电模型进行了正演。通过剖面法和宽角法得到的正演剖面图,证明该算法具有较好的GPR正演精度。To eliminate the non-physical reflection at the truncated boundary of GPR forward modeling,it is necessary to deal with the simulated region boundary.At present,the well applied method is to load the perfectly matched layer,and the complex frequency shift perfectly matched layer(CFS-PML),which can enhance the absorption effect of litter wave and prosperous lost wave in low frequency region and suppress the false reflection of signals,is widely used in GPR forward modeling.CFS-PML was applied to the numerical simulation of solving the two-dimensional GPR wave equation with the symplectic partitioned Runge-Kutta(SPRK)algorithm,of which the symplectic algorithm could be utilized to realize the symplectic calculation of the time and space coordinates,so as to accomplish the high-precision forward modeling of GPR.Firstly,taking the transverse magnetic(TM)wave as an example,the SPRK of GPR wave equation solution formula was deduced based on CFS-PML.Then,a narrow and long model was utilized to conduct the experiment of the key parameters'selections of CFS-PML absorbing boundary condition,and the optimal parameters were determined by comparing the reflection error.Moreover,the comparison between CFS-PML and transmission boundary showed that the absorption effect of CFS-PML boundary condition at large angle grazing was better than that of transmission boundary.Finally,to further verify the effectiveness of our proposed algorithm,the SPRK program loaded with the CFS-PML boundary condition was conducted on a geoelectric model with undulating topography.Then the forward GPR cross-sectional view,which is attained by using both cross-sectional method and wide-angle method,proved that the algorithm can fit the uneven underground interface well.

关 键 词：探地雷达 辛龙格库塔 复频移完全匹配层 透射边界条件 

分 类 号：P631[天文地球—地质矿产勘探]