多重分形与Kriging插值在地层模型生成中的应用  

Application of multifractal and Kriging interpolation to reconstruction of stratum

作　　者：王长虹[1] 朱合华[2] 

机构地区：[1]上海应用技术学院轨道交通学院,上海200235 [2]同济大学地下建筑与工程系,上海200092

出　　处：《岩土力学》2011年第6期1864-1868,1885,共6页Rock and Soil Mechanics

基　　金：国家科技攻关项目世博专项资助(No.2005BA908B06)

摘　　要：为了建立三维数字地层,采用钻孔信息构建三棱柱,以适合工程地质和岩土工程特点。钻孔数据具有局部的、随机的、异常的特征,另外,钻孔数据具有一定的结构特点。传统的数理统计方法无法很好地解决空间样本点的选取、空间估值和2组以上空间数据的关系等问题,借鉴地质统计学的Kriging方法给出全局区域内一种距离加权插值算法,先根据空间数据得到统计特征,再根据统计特征进行插值,并引入多重分形理论弥补Kriging方法的滑动加权平均缺陷,度量区域化变量的局部奇异性。通过对地层模型插值结果的观察,得出该算法可以获得良好的全局和局部特征插值效果。In order to generate 3-dimensional stratum,a stratum data model of tri-prism based on borehole data is first presented,which is applicable to geological engineering and geotechnical engineering.Due to the local variance and spatial structure among attributes of boreholes,the geological properties at unknown location have to be estimated or interpolated by some special methods.However,classic statistical methods could not resolve such problem which includes selection of sample points,spatial estimation and comparison of bilateral data.A distance-weighted interpolation method for scattered borehole data points is proposed,which exploits the Kriging method in global geostatistics.On the premise that the distributed statistics characters of the spatial borehole data were obtained at first;accorded to the distributed statistics characters,the spatial interpolation was presenting successively.Moreover,Multi Fractal is presented to depict the local singularity which should be ignored by sliding weighted average algorithm of Kriging method.Case study shows that the generation of 3-dimensional stratum by proposed interpolation methods could give a good result in global and local occasions.

关 键 词：钻孔 地层数据模型 空间散乱点插值 KRIGING方法 多重分形 

分 类 号：TB115[理学—数学]