地理学报 ›› 1987, Vol. 42 ›› Issue (4): 366-375.doi: 10.11821/xb198704009

• 论文 • 上一篇    下一篇

“Krige”空间内插技术在地理学中的应用

王广德, 过常龄   

  1. 中国科学院国家计委地理研究所
  • 出版日期:1987-10-15 发布日期:1987-10-15

APPLICATION OF THE KRIGING TECHNIQUE IN GEOGRAPHY

Wang Guangte, Guo Changling   

  1. Institute of Geography, Chinese Academy of Sciencese and State Planning Commission of the People’s Republic ofChina
  • Online:1987-10-15 Published:1987-10-15

摘要: 称为“Krige”技术的内插稀疏观测资料的随机方法是Matheron(1970年)提出的,D.R.Krige首先将这一方法应用于找矿上,因而命名于“Krige”技术。本文首先定义和说明了空间协方差曲线,基于无偏估计和最优原理导出了“Krige”内插权重系数的代数方程组,最后给出实例说明该方法如何应用到地理学和水文学中。

关键词: 空间内插, 协方差曲线, 权重系数, 拉格朗日乘子, 随机因素, 地带规律性, 无偏估计

Abstract: A stochastic approach to interpolating sparse observation records in geography referred to as the "Kriging technique" has been developed by Matheron (1970) but was named after D. R. Krige, who first applied some of the concepts underlying this technique to assessing the gold contents of the South Africa mines.A fundamental concept of the kriging theory, i.e, the variogram, is analyzed in the light of the deterministic development and is given a welldefined physical meaning. By minimizing the sum of square deviation between the estimating and measuring values with the constraint of unbiased estimation the "Kriging" system equations could be derived. In principle, the kriging technique should provide more reliable estimates, since the theoretical variogram incorporates a larger amount of information than that related to the available recordls.The primary advantage of the kriging technique is the ability to provide an interpolation value of unmeasured points using available information. The kriging technique could be applied in geography, especially in surface hydrology, groundwater, soil moisture, the regional planning and network design.

Key words: Spatial interpolation, Semivariogram curve, Weight coefficients, Lag-rangian multiplier, Stochastic factors, Zonality, Unbias estimator