基于k均值聚类多道奇异谱分析的探地雷达绕射波分离与成像  

Diffraction wave separation and imaging of ground penetrating radar based on k-means clustering in multiple singular spectrum analysis

作　　者：王敏玲 王浩林 王洪华[1] 周鑫 赵婕 WANG MinLing;WANG HaoLin;WANG HongHua;ZHOU Xin;ZHAO Jie(College of Earth Science,Guilin University of Technology,Guilin 541004,China)

机构地区：[1]桂林理工大学地球科学学院,桂林541004

出　　处：《地球物理学进展》2025年第1期337-348,共12页Progress in Geophysics

基　　金：国家自然科学基金项目(42364010);广西自然科学基金项目(2022GXNSFAA035595)联合资助.

摘　　要：探地雷达(Ground Penetrating Radar,GPR)被应用于城市道路病害检测、考古等浅层精细结构探测时,地下小尺度地质体如空洞、裂缝等通常是最为关注的对象.然而,实测GPR剖面中由地下小尺度地质体产生的双曲线绕射波能量要比地下分层界面产生的线性反射波能量弱,易被能量更强的反射波所混叠或掩盖,严重干扰小尺度地质体的精确识别与解释.为此,本文提出基于k均值聚类算法的多道奇异谱分析方法分离出GPR剖面中的绕射波场,该方法首先对不同频率的GPR数据构造Hankel矩阵并进行奇异值分解,以获得多道奇异谱;然后应用k均值聚类算法对所有道的奇异谱进行聚类分析,根据相似性将奇异谱中的奇异值分为k类,并将表征反射波以及噪声的几类奇异值置零,保留表征绕射波的部分奇异值来重构GPR绕射波场.数值实验表明:基于k均值聚类算法的多道奇异谱分析方法可高效实现反射波与绕射波的分离;与分离前GPR数据的逆时偏移结果相比,分离后的绕射波逆时偏移结果中,小尺度地质体的成像分辨率更高、更易被识别,为小尺度地质体的高精度成像与解译提供了一种可行有效的方法.Ground Penetrating Radar(GPR)is widely used in the fine detection of shallow structures such as urban road disease detection and archaeology,etc.Small-scale underground geological bodies such as cavities and cracks are usually the most concerned detection objects.In general,the energy of hyperbolic diffracted waves generated by small-scale underground geological bodies in the measured GPR profile is weaker than the linear reflected waves generated by the subsurface layered interface,and is easily mixed or masked by the reflected waves with stronger energy,which seriously interferes with the accurate identification and interpretation of small-scale targets.To this end,this paper proposes a multiple singular spectrum analysis method based on k-means clustering algorithm to separate the reflected and diffracted waves in the GPR profile.Then,the k-means clustering algorithm is used to cluster the all singular spectrum,and the singular values in the singular spectrum are divided into k classes according to the similarity,and the several types of singular values representing the reflected wave and the noise are set to zero,and some of the singular values representing the diffracted wave are retained to reconstruct the GPR diffraction wave field.Numerical experiments show that the multiple singular spectrum analysis method based on k-means clustering algorithm can efficiently separate the reflected wave from the diffracted wave.Compared with the reverse time migration of the unseparated GPR data,the imaging resolution of the small-scale geological body is higher and easier to be identified in the separated diffraction wave reverse time migration,which provides a feasible and effective method for the high-precision interpretation of small-scale targets.

关 键 词：探地雷达 绕射波分离 HANKEL矩阵 多道奇异谱分析 K均值聚类 

分 类 号：P631[天文地球—地质矿产勘探]