三维Kriging方法中的变异函数套合

姚凌青; 潘懋; 成秋明; 常德峰

三维Kriging方法中的变异函数套合

姚凌青¹,
潘懋²,
成秋明^{1, 3},
常德峰⁴

1.
中国地质大学地质过程与矿产资源国家重点实验室, 湖北武汉 430074
2.
北京大学造山带与地壳演化教育部重点实验室, 北京 100871
3.
加拿大约克大学地球空间科学与工程系, 加拿大多伦多 M3J1P3
4.
山东水利职业学院建筑工程系, 山东日照 276826

基金项目:

国家自然科学基金项目 40638041

国家自然科学基金项目 40502029

教育部创新团队基金 IRT0755

详细信息

中图分类号: P628
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- 被引次数: 0
出版历程
- 收稿日期: 2008-11-14
- 刊出日期: 2009-03-25

Nested Overlap of Variograms in 3D Kriging

1.
State Key Laboratory of Geological Processes and Mineral Resources, China University of Geosciences, Wuhan 430074, China
2.
Key Laboratory of Orogenic Belts and Crustal Evolution, Ministry of Education, Peking University, Beijing 100871, China
3.
Department of Earth and Space Science and Engineering, York University, Toronto M3J1P3, Canada
4.
Department of Architectural Engineering, Shandong Water Polytechnic, Rizhao 276826, China

摘要

摘要:
三维属性建模是利用有限的采样数据, 通过插值或模拟的方法来重构地学属性在三维空间中的分布.将Kriging方法推广到三维空间, 从而演化为三维Kriging方法, 可以为三维属性建模提供可靠的手段.而三维Kriging方法面临的一大难题就是各向异性变异函数的套合.提出了一种简单通用的三维空间变异函数的套合方法.该方法以空间坐标基的变换为基础, 在套合时充分考虑轴向上变异差异的影响, 并由此提出各向异性变化率的概念; 论证了套合方法的可行性, 并通过地下水水质三维属性建模的实例对该方法进行了有效的验证.
- 三维Kriging /
- 变异函数 /
- 结构分析
Abstract:
3D property modeling is hot nowadays in geoscientific researches, the essence of which is mapping geological properties in 3D space from limited samples by interpolation or simulation methods.By extending Kriging to 3D space which evolves to the so-called 3D Kriging, a reliable method can be provided for 3D property modeling.However, one of the most difficult problems in 3D Kriging is the nested overlap of anisotropic variograms.In this paper, a simple but universal method is proposed for the nested overlap.Based on the transformation of coordinate basis, this new method takes into full consideration the difference of variation on each axis direction and puts forward the concept of anisotropy ratio.The feasibility of the new method is demonstrated and testified by a case study about 3D property modeling of groundwater quality.
- 3D Kriging /
- variogram /
- structural analysis

HTML全文

图 1 地下水水质三维属性模型

a.三维显示图; b.栅栏图; c.地下50 m水平切片; d.地下100 m水平切片; e.地下150 m水平切片

Fig. 1. 3D property model of underground water quality

下载: 全尺寸图片幻灯片

表 1 地下水水质分级

Table 1. of underground water quality

参考文献(11)

Dai, B. B., Wang, L. G., Jia, M. T., et al., 2007. Application of 3D digital modeling in a coppermine. Geology andP rospecting, 43 (3): 97-101 (in Chinese with Englisha bstract).
Gallichand, J., Buckland, G. D., Marcotte, D., et al., 1992. Spatial interpolation of soil salinity and sodicity for a saline soil in southern Alberta. Can. J. Soil Res. , 72 (4): 503-516. doi: 10.4141/cjss92-042
Mallet, J. L., 2002. Geomodeling. Oxford Press, Oxford, 1-600.
Pan, G. C., Moss, K., Heiner, T., et al., 1992. A Fortran program for three-dimensional Cokriging with case demonstration. Comput. Geosci. , 18 (5): 557-578. doi: 10.1016/0098-3004(92)90094-8
Triantafilis, J., Odeh, I. O. A., McBratney, A. B., 2001. Five geostatistical models to predict soil salinity from electromagnetic induction data across irrigated cotton. Soil Sci. Soc. Am. J. , 65: 869-878. doi: 10.2136/sssaj2001.653869x
Wang, R. D., Hu, G. D., 1988. Linear geostatistics. Geological Publishing House, Beijing, 1-260 (in Chinese).
Yao, L. Q., Pan, M., Cheng, Q. M., 2008a. 3D property modeling of void ratio by Cokriging. Journal of China University of Geosciences, 19 (4): 410-415. doi: 10.1016/S1002-0705(08)60074-6
Yao, L. Q., Pan, M., Qu, H. G., et al., 2008b. Research on application of Kriging in construction of three-dimensional property model about water content. Applicatio Research of Computers, 25 (8): 2554-2556 (in Chines with English abstract).
戴碧波, 王李管, 贾明涛, 等, 2007. 三维数字建模技术在某铜矿山中的应用. 地质与勘探, 43 (3): 97-101. https://www.cnki.com.cn/Article/CJFDTOTAL-DZKT200703019.htm
王仁铎, 胡光道, 1988. 线性地质统计学. 北京: 地质出版社, 1-260.
姚凌青, 潘懋, 屈红刚, 等, 2008b. Kriging算法在含水量三维属性模型构建中的应用研究. 计算机应用研究, 25 (8): 2554-2556. https://www.cnki.com.cn/Article/CJFDTOTAL-JSYJ200808091.htm