| 克立格估计的分析解释与协方差函数的代数确定 |
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| 引用本文： | 边少锋 Menz.J.克立格估计的分析解释与协方差函数的代数确定[J].地球科学,2000,25(2):195-200. |
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| 作者姓名： | 边少锋 Menz.J |
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| 作者单位： | 1.中国科学院测量与地球物理研究所 武汉430077 |
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| 基金项目： | 德国DFG项目“地质统计学模型下的矿山综合评价”，中国科学院测量与地球物理研究所访问学者基金 |
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| 摘 要： | 首先引入利用旋转面作为基函数的函数逼近概念, 在此基础上经过复杂的矩阵推导证明泛克立格法可表示为传统的带权最小二乘多项式拟合与以旋转面作为基函数的函数逼近, 并在一定条件下(随机场高度连续无块金效应) 论证了协方差(即旋转面) 的参数可通过数学分析的方法确定, 给出了以高斯函数为例确定协方差函数的两个准则.
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| 关 键 词： | 克立格估计 协方差函数 地质统计学 |
| 文章编号： | 1000-2383(2000)02-0195-06 |
| 收稿时间： | 1999-01-30 |
ANALYTICAL INTERPRETATION TO KRIGING ESTIMATION AND ALGEBRAIC DETERMINATION OF COVARIANCE FUNCTION'S PARAMETER |
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| Bian Shaofeng,Joachim Menz.ANALYTICAL INTERPRETATION TO KRIGING ESTIMATION AND ALGEBRAIC DETERMINATION OF COVARIANCE FUNCTION'S PARAMETER[J].Earth Science-Journal of China University of Geosciences,2000,25(2):195-200. |
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| Authors: | Bian Shaofeng Joachim Menz |
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| Institution: | Bian Shaofeng 1 Joachim Menz 2 |
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| Abstract: | The analytical interpretation to Kriging estimation and the algebraic determination of a covariance function's parameter are presented. This paper first introduces the concept of function approximation using a rotating surface as a basic function. Then it is demonstrated that the universal Kriging may be expressed as the traditional weighted least square fitting and as the function approximation with a rotating surface as a basic function. It is also demonstrated that the parameter of a covariance function (i.e. a rotating surface) can be determined by the mathematical analysis on a certain condition (i.e. a highly continuous lump gold_free effect in a random field). Finally, this paper presents two principles for the determination of a covariance function's parameter with the Gaussian function as an example: one is formulated through analysis of the linear combinations of the shifted Gaussian functions, and the other is derived from the equivalence between B_splines and Gaussian functions. |
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| Keywords: | Kriging estimation covariance function geo_statistics |
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