基于克里金和三角剖分联合的数据网格化方法研究  

Data Meshing Method Research Based on Kriging and Delaunay Triangulation

作　　者：彭伟 岳云宝 徐文刚 武斌 杨富强 王茂琦 Peng Wei;Yue Yunbao;Xu Wengang;Wu Bin;Yang Fuqiang;Wang Maoqi(Sichuan Geological Survey and Research Institute,Geophysics Exploration Brigade of Sichuan Bureau of Exploration and Development of Geology and Minerals Resources,Chengdu Sichuan 610072,China;Geological and Mineral Exploration and Development Bureau of Guangxi Zhuang Autonomous Region,Geophysical Survey Institute of Guangxi Zhuang Autonomous Region,Liuzhou Guangxi 545005,China)

机构地区：[1]四川省地质调查研究院四川省地质矿产勘查开发局物探队,四川成都610072 [2]广西壮族自治区地质矿产勘查开发局广西壮族自治区地球物理勘察院,广西柳州545005

出　　处：《工程地球物理学报》2023年第1期99-104,共6页Chinese Journal of Engineering Geophysics

基　　金：四川省地质调查研究院财政支持科研项目(编号:51000023Y000008290166);广西壮族自治区地质矿产勘查开发局科研项目(编号:桂地矿综研[2021]38号);四川省地矿局物探队科研项目(编号:科研申报[2021]025)。

摘　　要：在物化探数据网格化插值计算中,常采用克里金法和三角剖分法。克里金法通过区域限制范围内进行无偏和方差最优估计区域化空间变量取值,可对无数据边界区域进行插值,但异常有位移和弱化现象;三角剖分法利用最小内角最大准则进行Delaunay三角剖分,形成三角形不规则网络TIN(Triangulated Irregular Network),并通过线性插值的方式进行数据网格化,由于保留了原始数据,异常位置准确且无位移,但对于无数据的边界区域无法插值。本文融合克里金法和三角剖分法的优点,采用克里金法进行无偏最优插值,利用Delaunay三角剖分形成三角不规则网络,通过对三角不规则网络等值线追踪绘制等值线。最后利用一组极化率数据进行了对比验证,该方法绘制的等值线图,四周空白区域得到了插值填充,5个原始极值点得到了完整保留。结论表明,该方法既能对无数据区域进行插值,又能保证极值点大小不弱化、位置不偏移,是提高物化探成果精度的有效手段。Kriging method and triangulation method are often used in grid interpolation calculation of geophysical and geochemical data,which can interpolate the blank area without data by unbiased and variance optimal estimation of the regionalized spatial variable value within the region limit,but the anomaly involves displacement and weakening occurences.Using Kriging method for unbiased linear interpolation and regular rectangular network contour tracking,discarding the original data and ineffective use of the original discrete points for contour tracking may lead to the loss of geophysical and geochemical extreme points,weaken and shift the extreme values.Moreover,the use of regular rectangular network contour tracking has low search efficiency,but because Kriging method can interpolate any position,it can fill the data blank area.Triangulation method uses the minimum internal angle maximum criterion to conduct Delaunay triangulation to form triangulated irregular network(TIN)and the data is gridded by linear interpolation.This paper integrates the advantages of Kriging method and triangulation method when tracking contour lines of triangular irregular network,using Kriging method for unbiased optimal interpolation and Delaunay triangulation to form triangular irregular network.Because of the retained original data,the accurate abnormal position and no displacement allowed,the blank area without data cannot be interpolated.Then triangulation method is used for three-point linear interpolation and irregular triangulation contour tracking to make full use of the original discrete points,retain the original data,and conduct three-point linear interpolation within the triangle,resulting in a faster operation.Finally,a set of polarizability data is used for comparison and verification.The contour map drawn by this method has been interpolated in the surrounding blank area,and the five original extreme points have been completely retained.The conclusion indicates that this method can not only interpolate the area without dat

关 键 词：克里金法 三角剖分法 网格化 DELAUNAY TIN 

分 类 号：P624[天文地球—地质矿产勘探]