克里金（kriging）插值方法在煤层分布检测中的应用研究
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摘要
本文是在山西省自然科学基金项目《多源信息融合技术在煤矿水害预测中的研究》资助下完成的,目的是对煤层分布检测方法进行应用研究。
煤矿工程人员要对合理开采煤层做出决策,必须对煤层的分布有一个直观的了解,这就需要知道煤层的分布状态。对地下煤层了解的唯一途径是进行钻探检测,但进行钻探检测要花费很大的代价,所以不可能大规模的钻探。如何根据有限的钻孔检测资料来得到煤层的分布模型,本论文提出了克里金插值方法来解决钻孔数据严重不足的问题。
在论文中,根据空间插值方法的基本原理,对主要的空间插值方法进行了比较,分析了各种方法的适用条件、算法和优缺点。在煤层分布检测中,克里金插值方法不仅考虑了观测点和被估计点的相对位置而且还考虑了各观测点之间的相对位置关系,并且,克里金建模具有无偏、最优的性质,点稀少时插值效果比其他方法好,能给出待估点属性值数学期望最好的近似。文中在确定插值邻域的基础上,利用克里金插值方法的多种模型对研究区散乱数据点的变异函数进行拟合。为了确定哪个插值模型更适合研究区域的三维建模,对多个插值效果图进行了比较,得出普通克里金插值方法的球状模型是最佳的插值模型。主要内容有:
(1)介绍了常用空间插值方法的原理、研究现状、应用领域。分析对比每种方法的优缺点,明确了在煤层分布模型检测方面,克里金插值方法的插值效果较好。
(2)根据空间信息统计学的基本原理,详细说明了变异函数的理论模型和实验模型,改进了变异函数参数的确定方法。
(3)详尽阐述了克里金插值方法的基本原理,分析比较了各种克里金插值方法的优缺点及其应用条件。提出了在研究区域内采用普通克里金插值方法进行数据插值。
(4)对原始采样数据进行了处理,根据改进后的参数确定方法计算出实验变异函数的参数,绘出了实验变异函数分布图,并用理论模型中的三种模型对实验变异模型进行了拟合,并对拟合的结果进行了检验,指出球状模型的效果最好。
(5)采用普通克里金插值方法进行插值,根据输出结果,用Matlab软件对研究区域的煤层进行了三维模拟。
(6)对建立的煤层模型进行分析应用,指出这种方法还可以应用到更多的领域。
This article is sponsored by natural science fund project of Shanxi province, which is "Research of Multi-sources Information Fusion Technique In Water Invasion Prediction of Coal Seam". The aim is to carry on applied research to distributed detection method of coal seam.
The project personnel of coal mine want to make decision to reasonable coal mining, they must have an intuitive understanding to coal seam's distribution, and need to know distributed situation of coal seam. The only way is to drill hole, but it is very expensive, therefore it is impossible to drill large-scale holes. According to the limited drill holes, how to obtain the coal seam's distribution model, this paper proposed kriging interpolation method to solve the problem which is lack of the drill holes data.
In this article, according to the basic principle of spatial interpolation, several important spatial interpolation methods are compared with each other. Their application addition, algorithm, merits and shortcomings are analyzed. During distributed detection of coal seam, kriging not only considers the relative position of the observation points to the estimated points, but also the relative position of the observation points with each other, and kriging has property of unbias and minimum variance. Compared with other methods, the result of kriging interpolation is better especially in few observation points and its result is the best approximation of mathematical expectation. In this article, we determine interpolation neighborhood, fit variogram function of scattered data using many kinds of models of kriging interpolation in research area. In order to determine that which interpolation model is more suitable to three dimensional modeling in research area, several interpolation effect charts are compared, the result is that spherical model of ordinary kriging interpolation method is the best interpolation model. The main research works are as follows:
1, Introduced the basic principle, the research present situation, the application domain of common spatial interpolation. Compared merits with shortcomings of each interpolation method. Pointed out the interpolation effect of kriging interpolation method is better in distributed detection of coal seam.
2, According to the basic principle of spatial information statistics, introduce the theoretical model and the experimental model of variogram in detail, improve seeking method of parameter of variogram.
3, Elaborate the basic principle of kriging interpolation, contrast the merits and shortcomings, the application condition of each kriging interpolation method, point out that we should use ordinary interpolation method to carry on data interpolation in research area.
4, Process the original sampling data, and compute the parameters of the experimental variogram function according to improved seeking method of parameter. Draw the experimental semivariogram, fit the experimental semivariogram function with three models of the theoretical model, test the fitting result, point that the spherical model is better.
5, Use ordinary kriging interpolation method to carry on data interpolation. According to the output result, simulate the coal seam with Matlab.
6, Carry on the analysis application to the establishment model of coal seam, point out that this method may also apply more domains.
煤矿工程人员要对合理开采煤层做出决策,必须对煤层的分布有一个直观的了解,这就需要知道煤层的分布状态。对地下煤层了解的唯一途径是进行钻探检测,但进行钻探检测要花费很大的代价,所以不可能大规模的钻探。如何根据有限的钻孔检测资料来得到煤层的分布模型,本论文提出了克里金插值方法来解决钻孔数据严重不足的问题。
在论文中,根据空间插值方法的基本原理,对主要的空间插值方法进行了比较,分析了各种方法的适用条件、算法和优缺点。在煤层分布检测中,克里金插值方法不仅考虑了观测点和被估计点的相对位置而且还考虑了各观测点之间的相对位置关系,并且,克里金建模具有无偏、最优的性质,点稀少时插值效果比其他方法好,能给出待估点属性值数学期望最好的近似。文中在确定插值邻域的基础上,利用克里金插值方法的多种模型对研究区散乱数据点的变异函数进行拟合。为了确定哪个插值模型更适合研究区域的三维建模,对多个插值效果图进行了比较,得出普通克里金插值方法的球状模型是最佳的插值模型。主要内容有:
(1)介绍了常用空间插值方法的原理、研究现状、应用领域。分析对比每种方法的优缺点,明确了在煤层分布模型检测方面,克里金插值方法的插值效果较好。
(2)根据空间信息统计学的基本原理,详细说明了变异函数的理论模型和实验模型,改进了变异函数参数的确定方法。
(3)详尽阐述了克里金插值方法的基本原理,分析比较了各种克里金插值方法的优缺点及其应用条件。提出了在研究区域内采用普通克里金插值方法进行数据插值。
(4)对原始采样数据进行了处理,根据改进后的参数确定方法计算出实验变异函数的参数,绘出了实验变异函数分布图,并用理论模型中的三种模型对实验变异模型进行了拟合,并对拟合的结果进行了检验,指出球状模型的效果最好。
(5)采用普通克里金插值方法进行插值,根据输出结果,用Matlab软件对研究区域的煤层进行了三维模拟。
(6)对建立的煤层模型进行分析应用,指出这种方法还可以应用到更多的领域。
This article is sponsored by natural science fund project of Shanxi province, which is "Research of Multi-sources Information Fusion Technique In Water Invasion Prediction of Coal Seam". The aim is to carry on applied research to distributed detection method of coal seam.
The project personnel of coal mine want to make decision to reasonable coal mining, they must have an intuitive understanding to coal seam's distribution, and need to know distributed situation of coal seam. The only way is to drill hole, but it is very expensive, therefore it is impossible to drill large-scale holes. According to the limited drill holes, how to obtain the coal seam's distribution model, this paper proposed kriging interpolation method to solve the problem which is lack of the drill holes data.
In this article, according to the basic principle of spatial interpolation, several important spatial interpolation methods are compared with each other. Their application addition, algorithm, merits and shortcomings are analyzed. During distributed detection of coal seam, kriging not only considers the relative position of the observation points to the estimated points, but also the relative position of the observation points with each other, and kriging has property of unbias and minimum variance. Compared with other methods, the result of kriging interpolation is better especially in few observation points and its result is the best approximation of mathematical expectation. In this article, we determine interpolation neighborhood, fit variogram function of scattered data using many kinds of models of kriging interpolation in research area. In order to determine that which interpolation model is more suitable to three dimensional modeling in research area, several interpolation effect charts are compared, the result is that spherical model of ordinary kriging interpolation method is the best interpolation model. The main research works are as follows:
1, Introduced the basic principle, the research present situation, the application domain of common spatial interpolation. Compared merits with shortcomings of each interpolation method. Pointed out the interpolation effect of kriging interpolation method is better in distributed detection of coal seam.
2, According to the basic principle of spatial information statistics, introduce the theoretical model and the experimental model of variogram in detail, improve seeking method of parameter of variogram.
3, Elaborate the basic principle of kriging interpolation, contrast the merits and shortcomings, the application condition of each kriging interpolation method, point out that we should use ordinary interpolation method to carry on data interpolation in research area.
4, Process the original sampling data, and compute the parameters of the experimental variogram function according to improved seeking method of parameter. Draw the experimental semivariogram, fit the experimental semivariogram function with three models of the theoretical model, test the fitting result, point that the spherical model is better.
5, Use ordinary kriging interpolation method to carry on data interpolation. According to the output result, simulate the coal seam with Matlab.
6, Carry on the analysis application to the establishment model of coal seam, point out that this method may also apply more domains.
引文
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[3]吴健生,王仰麟,曾新平等.三维可视化环境下矿体空间数据插值[J].北京大学学报(自然科学版),2004(4):635-641.
[4]吴信才.地理信息系统[M].电子工业出版社,2002.172-173.
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[7]张蕾,陈晓宏.珠江三角洲网河区水位空间插值的kriging方法.中山大学学报(自然科学版).2004,43(5):112-114.
[8]尚庆生,郭建文,等.基于Kriging插值的钻孔地温数据体视化[J].遥感技术与应用,2006,8(4):302-305.
[9]颜辉武,祝国瑞等.基于kriging水文地质层的三维建模与体视化.武汉大学学报(信息科学版).2004,29(7):611-614.
[10]刘承香,阮双琛,伍小芹.基于Kriging插值的数字地图生成算法研究[J].深圳大学学报理工版,2004,21(4):295-299.
[11]曾瑜.基于空间插值模型的绿洲地下水时空变化研究_以奇台绿洲为例.[硕士学位论文].新疆:新疆大学,2004
[12]刑延涛,李利军.三维地质体重构中空间数据插值方法的研究.计算机与数字工程,2006,34(12):45-47.
[13]颜慧敏.空间插值技术的开发与实现.[硕士学位论文].成都:西南石油学院.2005
[14]汤国安,刘学军,闾国年.数字高程模型及地学分析的原理与方法[M].北京:科学出版社,2005.
[15]秦涛.Geostatistics Analyst中空间内插方法的介绍.化工矿产地质,2005,27(4):235-240
[16]王靖波,潘懋,张绪定.基于Kriging方法的空间散乱点插值[J].计算机辅助设计与图形学学报.1999,11(6):525-529.
[17]靳国栋,刘衍聪,牛文杰.距离加权反比插值法和克里金插值法的比较[J].长春工业大 学学报,2003,24(3):53-57.
[18]肖朝明.渗流水位空间变异性的分形估值方法.[学位论文].北京:北京林业大学,2004
[19]包世泰,廖衍旋等.基于kriging的地形高程插值.地理与地理信息科学.2005,23(3):28-31
[20]王家华,高海余,周叶.克里金地质绘图技术—计算机的模型和算法[M].北京:石油工业出版社.1999:150-154.
[21]田景文.地下油藏的仿真与预测.[学位论文].哈尔滨:哈尔滨工程大学.2001
[22]苏金明,王永利.MATLAB7.0实用指南[M].电子工业出版社,2004.10
[23]庞博,王振清.基于Matlab的数据处理与三维模拟[J].微计算机信息,2004,20(1):112-113.
[24]李延平.基于VB和MATLAB的三维数据可视化[J].微计算机应用,2002,23(6):378-380.
[25]孙家广,杨长贵.计算机图形学[M].北京:清华大学出版社,1995.
[26]郑光辉,黄克龙,等.运用克里金空间插值技术进行土地级别划分[J].南京师大学报(自然科学版).2007,30(1):112-116.
[27]唐咸远.应用MATLAB进行地理三维地貌可视化和地形分析[J].广西工学院学报,2006,17(2):17-19.
[28]颜辉武,祝国瑞.地下水的体视化研究[M].武汉大学出版社,2004.8
[29]孟庆生,樊玉清,孔庆馥.地质模型中离散数据点的等值线绘制方法[J].山东轻工业学院学报,2002,16(2):6-9.
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[34]Dubrule O.Comparing splines and Kriging[J].Computer&Geosciences,1984,10(2):327-328.
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[2]僧德文,李仲学,李春民.空间数据插值算法与矿体形态模拟的研究.矿业研究与开发,2005,25(3):67-69
[3]吴健生,王仰麟,曾新平等.三维可视化环境下矿体空间数据插值[J].北京大学学报(自然科学版),2004(4):635-641.
[4]吴信才.地理信息系统[M].电子工业出版社,2002.172-173.
[5]林振山,袁林旺,吴得安.地学建模[M].气象出版社,2003.
[6]李新,程国栋,卢玲.空间内插方法比较[J].地球科学进展,2000,15(3):260-265.
[7]张蕾,陈晓宏.珠江三角洲网河区水位空间插值的kriging方法.中山大学学报(自然科学版).2004,43(5):112-114.
[8]尚庆生,郭建文,等.基于Kriging插值的钻孔地温数据体视化[J].遥感技术与应用,2006,8(4):302-305.
[9]颜辉武,祝国瑞等.基于kriging水文地质层的三维建模与体视化.武汉大学学报(信息科学版).2004,29(7):611-614.
[10]刘承香,阮双琛,伍小芹.基于Kriging插值的数字地图生成算法研究[J].深圳大学学报理工版,2004,21(4):295-299.
[11]曾瑜.基于空间插值模型的绿洲地下水时空变化研究_以奇台绿洲为例.[硕士学位论文].新疆:新疆大学,2004
[12]刑延涛,李利军.三维地质体重构中空间数据插值方法的研究.计算机与数字工程,2006,34(12):45-47.
[13]颜慧敏.空间插值技术的开发与实现.[硕士学位论文].成都:西南石油学院.2005
[14]汤国安,刘学军,闾国年.数字高程模型及地学分析的原理与方法[M].北京:科学出版社,2005.
[15]秦涛.Geostatistics Analyst中空间内插方法的介绍.化工矿产地质,2005,27(4):235-240
[16]王靖波,潘懋,张绪定.基于Kriging方法的空间散乱点插值[J].计算机辅助设计与图形学学报.1999,11(6):525-529.
[17]靳国栋,刘衍聪,牛文杰.距离加权反比插值法和克里金插值法的比较[J].长春工业大 学学报,2003,24(3):53-57.
[18]肖朝明.渗流水位空间变异性的分形估值方法.[学位论文].北京:北京林业大学,2004
[19]包世泰,廖衍旋等.基于kriging的地形高程插值.地理与地理信息科学.2005,23(3):28-31
[20]王家华,高海余,周叶.克里金地质绘图技术—计算机的模型和算法[M].北京:石油工业出版社.1999:150-154.
[21]田景文.地下油藏的仿真与预测.[学位论文].哈尔滨:哈尔滨工程大学.2001
[22]苏金明,王永利.MATLAB7.0实用指南[M].电子工业出版社,2004.10
[23]庞博,王振清.基于Matlab的数据处理与三维模拟[J].微计算机信息,2004,20(1):112-113.
[24]李延平.基于VB和MATLAB的三维数据可视化[J].微计算机应用,2002,23(6):378-380.
[25]孙家广,杨长贵.计算机图形学[M].北京:清华大学出版社,1995.
[26]郑光辉,黄克龙,等.运用克里金空间插值技术进行土地级别划分[J].南京师大学报(自然科学版).2007,30(1):112-116.
[27]唐咸远.应用MATLAB进行地理三维地貌可视化和地形分析[J].广西工学院学报,2006,17(2):17-19.
[28]颜辉武,祝国瑞.地下水的体视化研究[M].武汉大学出版社,2004.8
[29]孟庆生,樊玉清,孔庆馥.地质模型中离散数据点的等值线绘制方法[J].山东轻工业学院学报,2002,16(2):6-9.
[30]Franke R.Scattered Data Interpolation:Test of Some Methods[J].Mathematics of Computation,1982,38(157):181-200.
[31]Franke R,Hagen H.Least Squares Surface Approximation using Multiquadrics and Parameter Domain Distortion[J].Computer Aided Geometric Design,1999,16(3):177-196.
[32]Lee S,Wolberg G,Shin S Y.Scattered data interpolation with multilevel B-splines[J].IEEE Trans on Visualization and Computer Graphics,1997,3(3):228-244.
[33]Cressie N.Statistics for spatial data[M].New York:John Wiley&Sons,1991.
[34]Dubrule O.Comparing splines and Kriging[J].Computer&Geosciences,1984,10(2):327-328.
[35]LOPHAVEN S N,NIELSEN H B,SANDERGAARD J.DACE-A Matlab Kriging toolbox,Version2.0[R]. Denmark: Technical University of Denmark,2002.
[36]Levoy M. Display of Surfaces from Volume Data[J].IEEE CG and A,1988,8(3):29-37.
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