限制性克立格法在矿产资源储量估算中的应用
|
摘要
本文针对资源评价中储量估算问题,在深入研究几种矿业生产中广泛使用的克立格方法的基础之上,提出了限制性克立格法的优点,通过当前国际流行的地质统计学软件Micromine实现了地质建模以及储量估算的可视化操作,并解决了储量估算过程中一些参数的设置问题,同时利用Fortran语言编写并实现了限制性克立格法的计算。通过Micromine软件与Fortran程序的结合,建立了有效的储量评估系统。解决了实际生产中地质建模和储量计算的可视化、模块化、自动化,并通过实例分析了限制性克立格法当中阂值的选取问题,比较了各种克立格方法的储量计算结果,实现了限制性克立格法在实际工作中的应用。实践证明该方法是有效的、可行的、可操作的,为今后储量估算工作提供了一种可行的方法。
Reserves estimation is an important thing in geology mineral resource field, while geostatistics is one of the most effective tools for reserves estimation. It is a significance issue for geology works to improve the technology level of reserves estimation and its result's creditability and reliability. The research which is facing to the application of spatial 3D mineral resource modeling and reserves estimation, mainly base on two aspects: one is to interpret mineral correctly into solid model; the other one is to select the appropriate spatial interpolation methods in the process of reserves estimation, in the short time to complete accurate reserves estimation. With the update and development, geostatistics provides an path for resoling the questions.
In the exploring of geology resource, there are kinds of estimation methods, for example Inverse Distant Weight, Section, Geostatistics and so on, it is more advance for geostatistics. In geostatistics, it is divided into ordinary kriging, cokriging, indicator kriging and restricted kriging and so on. Kriging is a most popular method in reserves estimation, and restricted kriging has obvious advantages, it can control the configuration of different sample values to reduce the effect for estimator which caused by smooth effect, is a bridge link between sample value and sample configuration.
The article discusses the development situation of kriging method applied in reserves estimation, explains the theory of kriging mathematic model, which include regional variable, variogram, the determination of cutoff and the pre-probability, and it also describes the working steps and working flow which based on the software of Micromine, discusses the question of setting parameters and many problems to which we must pay attention.
The article introduces some related conceptions about kriging, compares between different kriging methods and others (e.g. Inverse Distance Weight). From the point of ore type and ore form, analyzes the using range of kriging, provides a reference base for choosing appropriate methods in actual works.
The emphases of this article is to study the application of kriging methods in actual mine reserves estimation, from the point of view of application, takes restricted kriging as an typical method, spreads the research on the various kriging methods. Most methods which concerned by this article is most basic and mature in geostatistics, the application has been discussed both in national and international magazines. But we still think that it is important to regard these methods as an effective solution by using clearly mathematic concept, combining with the requirement of reality produce, giving systemic, rigorous and concise discussion. The application of rigorous mathematic concepts and 3D visual geology software, which can enable us using mathematic model to solve reality works and get some new conclusions.
(1) Chapter one is the fundament of geostatistics, discussing regional variable, covariance's conceptions and properties and their mathematic models. Deeply discussing the spherical model which is often used in actual works. In Chapter two, describing 5 kinds of Kriging methods strictly by the tools of matrix, probes into the theory and mathematic model of kriging, summarizes the meaning and the properties of various kriging methods.
(2) Chapter three analyzes the mathematic meaning of restricted kriging, radically discovers its physical meaning. As a combination of ordinary kriging and indicator kriging, it links a bridge between data magnitude and data configuration, and can eliminate "smooth effect" which caused by ordinary kriging's property "weight independences its data values". Chapter four describes the using range of restricted kriging, analyze the effects which caused by different deposits. Giving the process of restricted kriging combined with actual examples, deeply discusses the mean that is how to determine the pre- probability of different grade segments.
(3) Chapter five describing and analyzing the results by using different kriging, which provides a basis for finding most appropriate kriging method in reality works. Chapter six, in the platform of 3D visual geology software, discussing how to use the kriging methods and set the parameters in reality works.
Reserves estimation is an important thing in geology mineral resource field, while geostatistics is one of the most effective tools for reserves estimation. It is a significance issue for geology works to improve the technology level of reserves estimation and its result's creditability and reliability. The research which is facing to the application of spatial 3D mineral resource modeling and reserves estimation, mainly base on two aspects: one is to interpret mineral correctly into solid model; the other one is to select the appropriate spatial interpolation methods in the process of reserves estimation, in the short time to complete accurate reserves estimation. With the update and development, geostatistics provides an path for resoling the questions.
In the exploring of geology resource, there are kinds of estimation methods, for example Inverse Distant Weight, Section, Geostatistics and so on, it is more advance for geostatistics. In geostatistics, it is divided into ordinary kriging, cokriging, indicator kriging and restricted kriging and so on. Kriging is a most popular method in reserves estimation, and restricted kriging has obvious advantages, it can control the configuration of different sample values to reduce the effect for estimator which caused by smooth effect, is a bridge link between sample value and sample configuration.
The article discusses the development situation of kriging method applied in reserves estimation, explains the theory of kriging mathematic model, which include regional variable, variogram, the determination of cutoff and the pre-probability, and it also describes the working steps and working flow which based on the software of Micromine, discusses the question of setting parameters and many problems to which we must pay attention.
The article introduces some related conceptions about kriging, compares between different kriging methods and others (e.g. Inverse Distance Weight). From the point of ore type and ore form, analyzes the using range of kriging, provides a reference base for choosing appropriate methods in actual works.
The emphases of this article is to study the application of kriging methods in actual mine reserves estimation, from the point of view of application, takes restricted kriging as an typical method, spreads the research on the various kriging methods. Most methods which concerned by this article is most basic and mature in geostatistics, the application has been discussed both in national and international magazines. But we still think that it is important to regard these methods as an effective solution by using clearly mathematic concept, combining with the requirement of reality produce, giving systemic, rigorous and concise discussion. The application of rigorous mathematic concepts and 3D visual geology software, which can enable us using mathematic model to solve reality works and get some new conclusions.
(1) Chapter one is the fundament of geostatistics, discussing regional variable, covariance's conceptions and properties and their mathematic models. Deeply discussing the spherical model which is often used in actual works. In Chapter two, describing 5 kinds of Kriging methods strictly by the tools of matrix, probes into the theory and mathematic model of kriging, summarizes the meaning and the properties of various kriging methods.
(2) Chapter three analyzes the mathematic meaning of restricted kriging, radically discovers its physical meaning. As a combination of ordinary kriging and indicator kriging, it links a bridge between data magnitude and data configuration, and can eliminate "smooth effect" which caused by ordinary kriging's property "weight independences its data values". Chapter four describes the using range of restricted kriging, analyze the effects which caused by different deposits. Giving the process of restricted kriging combined with actual examples, deeply discusses the mean that is how to determine the pre- probability of different grade segments.
(3) Chapter five describing and analyzing the results by using different kriging, which provides a basis for finding most appropriate kriging method in reality works. Chapter six, in the platform of 3D visual geology software, discussing how to use the kriging methods and set the parameters in reality works.
引文
[1]陈永清,王世称.综合信息成矿系列预测的基本原理和方法[J].山东地质,1995,11(1):55-62.
[2]揣援援,范继璋.MapInfo综合信息矿产资源评价系统及应用[J].地球物理学进展,2005,20(4):1155-1159.
[3]邓明国,李文昌,秦德先.克立格方法在个旧矿区芦塘坝10-9矿体储量计算中的应用[J].地质与勘探,2006,42(6):67-70.
[4]邓明国,王巨民,秦德先.对数Kriging在矿体储量计算中的应用[J].金属矿山,2006,10:49-52.
[5]冯超东,杨鹏,胡乃联.克立格法在Surpac软件中的实现及应用[J].金属矿山,2007,4:55-58.
[6]傅佩红,刘耀林,李雪飞.指示克立格法及其在城市地价评估中的应用[J].2004,21(4):65-67.
[7]甘建胜,洪伟.基于时空数据的线性组合插值模型及其应用[J].福建林学院学报,2006,26(4):318-323.
[8]甘建胜.区域城镇化空间统计分析模型及其应用[J].福建论坛,2006,11:46-49.
[9]郭妮.中条山铜矿峪4#矿体矿床模型的建立及其研究[J].矿产与地质,2003,17(2):183-187.
[10]侯景儒,尹镇南,立维明,等.实用地质统计学[M].北京:地质出版社:1998:31_44.
[11]韩燕.多种Krige方法的数学模型:博士学位论文[D].长春:吉林大 学,2004.
[12]韩燕.一种协克立格法的矩阵分析[J].长春科技大学学报,2003,30(4):413-414.
[13]贺华中,代侦勇.克立格估值方法中权系数空间相关性研究[J].华中师范大学学报,2007,41(3):477-479.
[14]何清杭,张镇西,王晶.基于指示克立格法的最佳激发波长和最佳发射波长的确定[J].光谱学与光谱分析,2007,27(8):1476-1479.
[15]黄勇,郭庆荣,任海.地统计学在土壤重金属研究中的应用及展望[J].生态环境,2004,13(4):681-684.
[16]贾福聚,秦德先,黎应书.都龙锡矿曼家寨矿段品位模型的建立[J].矿业研究与开发,2007,27(4):54-56.
[17]金宝轩.网格计算环境下的3维空间信息应用研究[D],武汉:武汉大学,2005.
[18]李岭.地质统计学及其在某铜矿山储量计算中的应用[J].矿业研究与开发,2004,24(5):21-23.
[19]李庆斌,王山东,陈佩富.《固体矿产资源/储量分类》应用软件的研究与运用[J].矿业快报,2004,20(9):7-11.
[20]李笑吟,毕华兴,张志.晋西黄土区土壤水分有效性分析的克立格法[J].土壤学报,2006,43(6):1004-1010.
[21]李颖,杨永强,范云芳.阿尔泰成矿区金矿预测图形库及属性库的建立方法[J].长春科技大学学报,2000,30(3):293-295.
[22]刘洪,夏立显.应用弹性BP算法预测贵州金矿储量[J].地球物理学进展,2005,20(2):399-401.
[23]刘鑫,毕华兴,李笑吟.晋西黄土区土壤水分时空异质性分析[J].水土保持研究,2006,13(6):51-54.
[24]罗周全,刘晓明,吴亚斌.地质统计学在多金属矿床储量计算中的应用研究[J].地质与勘探,2007,43(3):83_87.
[25]吕连宏,张征,迟志淼.地质统计学在环境科学领域的应用进展[J].地球科学与环境科学,2006,28(1),101_105.
[26]马建超,李佳林.克立格法在数字地层创建中的应用[J].核工程研究与设计,2007,2:45-49.
[27]秦涛.Geostatists Analyst中空间内插方法的介绍[J].化工矿产地质,2005,27(4):235-240.
[28]史舟,金辉明,李艳.地统计软件包的开发及在土壤空间变异中的应用[J].水土保持学报,2005,19(5):170-173.
[29]孙刚,徐兵,韩燕.限制性克立格法在阿舍勒铜矿储量计算中研究与应用[J].世界地质,2007,26(4):409-412.
[30]孙刚,徐兵,韩燕.限制性克立格法在地学中的研究与应用[J].2008,23(2):617-621.
[31]孙洪泉.岩层模拟的地质统计学方法[J].苏州科技学院学报:工程技术版,2007,20(4):12-15.
[32]孙立双,王恩德,王井利.基于空间分布权系数Kriging邻域选点算法[J].沈阳建筑大学学报,2007,23(3):423-426.
[33]王家华,高海余,周叶,等.克里金地质绘图技术[M].北京:石油工业出版社:1999:50-55.
[34]王世称,陈永良,夏立显.综合信息矿产预测理论与方法[M].北京:科学出版社,2000.
[35]王世称,范继璋,杨永华.矿产资源评价[M].吉林:科学技术出版社,1990.
[36]王岩,尹海丽,窦在祥.蒙特卡罗方法应用研究[J].青岛理工大学学报,2006,27(2):111-113.
[37]王银宏,严光生,翟裕生.三部式潜在矿产资源定量评价与蒙特卡罗模拟[J].中国矿业,2006,15(6):14-17.
[38]王银宏,彭润民,王建平.克立格算法的若干思考[J].地质与勘探,2004,40(2):77-79.
[39]吴蓉,周志芳.基于指示克立格方法的裂隙介质渗透性参数空间分布规律分析[J].水利学报,2004,6:104-107.
[40]肖克炎,丁建华,刘锐.美国“三步式”固体矿产资源潜力评价方法评述[J].地质论评,2006,52(6):793-798.
[41]杨蕊.克立格法在储量预测中的应用[J].内蒙古石油化工,2007,33(4):103-105.
[42]杨永华.蒙特卡罗方法与矿产资源评价[J].地质与勘探,1985,21(1):45-50.
[43]叶天竺.固体矿产预测评价技术方法[M].武汉:中国地质大学出版社,2006.
[44]易彬樘,张治英,徐德忠.协同克立格和标化植被指数在广东省登革热分布特征研究中的应用[J].西安交通大学学报,2003,24(5):448-451.
[45]尹增谦,管景峰,张晓宏,等.蒙特卡罗方法及应用[J].物理与工程,2002,12(1):45-49.
[46]张仁铎.空间变异理论及应用[M].北京:科学出版社:2005:23-40.
[47]周智勇,陈建宏,张涛.基于三维稳健克立格法的品位建模[J].金属矿山,2007,10:78-80.
[48]Armstrong M.,Problems with universal kriging[J].Math.Geol.,1984,16(1):101-108.
[49]Agterberg F P,Bonham-Carter G F,Wright D F.Statistical pattern integration for mineral exploration.In:Gaal G,Merriam D F(Eds.).Computer Applications in Resource Exploration and Assessment for Minerals and Petroleum.Pergamon,Oxford,1990.
[50]Agterberg,F P.Combing indicator patterns for mineral resources evaluation,in China University of Geosciences(Eds.),Proceedings of International Workshop on Statistical Prediction of Mineral Resources,Wuhan,China,1990.
[51]Ballin P.,Journel,A.and Aziz K.,Prediction of uncertainty inreservoir performance forecasting[J].JCPT,1992,31(4):52-62.
[52]Bardossy A.Notes on the robustness of the Kriging system[J].Math. Geol., 1988,20(3): 189-204.
[53]Borgman L., New advances in methodology for statistical test useful in geostatistical studies [J]. Math. Geol., 1988, 20(4):383-403.
[54]Boufassa A. and Armstrong M., Comparison between different kriging estimators [J]. Math. Geol., 1989,21(3):331-345.
[55]Bourgault G. and Marcotte D., Multivariate variogram and its application to the linear model of coregionalization [J]. Math. Geol.,1991,23(7):899-927.
[56]Carr J. and Mao N., A general form of probability kriging for estimation of the indicator and uniform transforms [J]. Math. Geol.,1993, 25(4):425-438.
[57]Carr J R. On visualization for assessing Kriging outcomes [J]. Math.Geol., 2002,34(4): 421-433.
[58]Chiles J. P. and Delfiner P., Geostatistics: Modeling spatial uncertainty [M]. Wiley, New York, 1999, 680-695.
[59]Christakos, G., On the problem of permissible covariance and variogram models [J]. Water Resources Research, 1984,20(2):251-265.
[60]Cressie N., Fitting variogram models by weighted least squares [J].Math. Geol., 1985,17(5):563-586.
[61]Cressie N., The origin of kriging [J]. Math. Geol., 1990,22(3):239-252.
[62]Cressie N., Statistics for spatial data [M]. 1993, Wiley, New York,623-900.
[63]Cressie N. and Hawbcins D. H., Robust estimation of the variogram [J]. Math. Geol, 1980,12(2):115-126.
[64]Davis B. M., Uses and abuses of cross-validation in geostatistics [J].Math. Geol., 1987, 19(3)
[65]Deutsch C, DECLUS: A Fortran 77 program for determining optimum spatial declustering weights [J]. Computers & Geosciences,1989,15(3):325-332.
[66]Deutsch C, Correcting for negative weights in ordinary kriging [J].Computers & Geosciences, 1996,22(7):765-773.
[67]Diamond P. and Armstrong M., Robustness of variograms and conditioning of kriging matrices [J]. Math. Geol., 1984,16(8):809-822.
[68]Dietrich C. R. and Osborne M. R., Estimation of covariance parameters in kriging via restricted maximum likelihood [J]. Math.Geol., 1991,23(1):119-135.
[69]Dowd P., Lognormal kriging-the general case [J]. Math. Geol., 1982,14(5):474-500.
[70]Doyen P., Porosity from seismic data: A geostatistical approach [J].Geopysics, 1988, 53(10):1263-1275.
[71]Dubrule O. and Kostov C., An interpolation method taking into account inequality constraints [J]. Math. Geol., 1986, 18(1):33-51.
[72]Gao Haiyu and Wang Jiahua, The updated kriging variance and optimal sample design [J]. Math. Geol., 1996,28(2).
[73]Goldberger A., Best linear unbiased prediction in the generalized linear regression model [J]. JASA, 1962, 57:369-375.
[74]Goovaerts P., Comparative performance of indicator algorithms for modeling conditional probability distribution functions [J]. Math.Geol, 1994,26(3):385-410.
[75]Goovaerts P, Geostatistics for Natural Resources Evaluation [M].Oxford University Press, 1997, New York.
[76]Herzfeld U. C., A note on programs performing kriging with nonnegative weights [J]. Math. Geol, 1989,21(3):391-393.
[77]Isaaks E. H. and Srivastava R. M, An introduction to applied geostatistics [M]. Oxford University Press, 1990, New York.
[78]Isaaks E. H. and Srivastava R. M, Spatial continuity measures for probabilistic and deterministic geostatistics [J]. Math. Geol, 1988,20(4):313-341.
[79]Jaquet O, Factorial kriging analysis applied to geological data from petroleum exploration [J]. Math. Geol, 1989,21(7).
[80]Journel A. G, Kriging in terms of projections [J]. Math. Geol, 1977,9(6):563-586.
[81]Journel A. G, Lognormal approach to predicting local distribution [J]. Math. Geol., 1980, 12(4):285-303.
[82]Jorunel A. G., Nonparametric estimation of spatial distribution [J].Math. GeoL, 1983,15(3):445-468.
[83]Journel A. G., Geostatistics: models and tools for the earth sciences [J]. Math. GeoL, 1985,18(1):119-140.
[84]Journel A. G., Constrained interpolation and qualitative information-the soft kriging approach [J]. Math. GeoL, 1986,18(3):269-286.
[85]Journel A. G., Geostatistics and petroleum Geol. [J]. Math. Geol.,1989,21(6):803-804.
[86]Journel A. G. and Huijbrechts C. J., Mining geostatistics [M].Academic Press 1978, London.
[87] Journel A. G. and Posa D., Characteristic behavior and order relations for indicator variograms [J]. Math. GeoL, 1990,22(8): 1011-1025.
[88]Journel A. G. and Rossi M., When do we need a trend model in kriging? [J]. Math. GeoL, 1989,21(7):715-739.
[89]Matheron G., Principles of geostatistics [J]. Economic Geol., 1963,58:1246-1266.
[90]McCammon R B, Briskey J A. A proposed national mineral-resource assessment. Nonrenewable Resources, 1992, 1(4):259-265.
[91]Moyeed R. A. and Papritz A., An empirical comparison of Kriging methods for nonlinear spatial point prediction [J]. Math. GeoL, 2002, 34(4):365-386.
[92]Myers D. E., Matrix formulation of Co-Kriging [J]. Math. Geol., 1982,14(3):249-257.
[93]Myers D. E., Estimation of linear combinations and cokriging [J].Math. Geol., 1983,15(6):633-637.
[94]Myers D. E., Interpolation with positive definite functions [J].Sciences de la Terre, 1988,28:251-265.
[95]Pan G. C., Practical issues of geostatistical reserve estimation in the mining industry [J]. CIM Bull, 1995, 88:31-37.
[96]Pan G. C. and Moss K. etc, Afortran program for three dimensional cokriging with case demonstration [J]. Computers & Geosciences,1992,18:557-578.
[97]Pawlowsky V., Cokriging of regionalized compositions [J]. Math.Geol., 1989,21(5):519-522.
[98]Pawlowsky V., Estimation of regionalized compositions: A comparison of three methods [J]. Math. Geol., 1995,27(1):105-127.
[99]Shlomo P. Neuman, Elizabeth A. Jacobson. Analysis of nonintrinsic spatial variability by residual kriging with application to regional groundwater levels [J]. Math. Geol.,1984,16 (5):433-466.
[100] Singer D A. Basic concepts in three part quantitative assessments of undiscovered mineral resources [J]. Nonrenewable Resources, 1993,2(2): 69-81.
[101] Singer D A. Some suggested future directions of quantitative resources assessment [J]. Journal of China University of Geosciences, 2001,12(1): 40-44.
[102] Pan Guocheng. Restricted Kriging for mixture of grade models [J].Math. Geol., 1993,25 (6): 713-736.
[103] Pan Guocheng. Restricted Kriging: A Link Between Sample Value and Sample Configuration [J]. Math. Geol., 1994,26 (1): 135-155.
[2]揣援援,范继璋.MapInfo综合信息矿产资源评价系统及应用[J].地球物理学进展,2005,20(4):1155-1159.
[3]邓明国,李文昌,秦德先.克立格方法在个旧矿区芦塘坝10-9矿体储量计算中的应用[J].地质与勘探,2006,42(6):67-70.
[4]邓明国,王巨民,秦德先.对数Kriging在矿体储量计算中的应用[J].金属矿山,2006,10:49-52.
[5]冯超东,杨鹏,胡乃联.克立格法在Surpac软件中的实现及应用[J].金属矿山,2007,4:55-58.
[6]傅佩红,刘耀林,李雪飞.指示克立格法及其在城市地价评估中的应用[J].2004,21(4):65-67.
[7]甘建胜,洪伟.基于时空数据的线性组合插值模型及其应用[J].福建林学院学报,2006,26(4):318-323.
[8]甘建胜.区域城镇化空间统计分析模型及其应用[J].福建论坛,2006,11:46-49.
[9]郭妮.中条山铜矿峪4#矿体矿床模型的建立及其研究[J].矿产与地质,2003,17(2):183-187.
[10]侯景儒,尹镇南,立维明,等.实用地质统计学[M].北京:地质出版社:1998:31_44.
[11]韩燕.多种Krige方法的数学模型:博士学位论文[D].长春:吉林大 学,2004.
[12]韩燕.一种协克立格法的矩阵分析[J].长春科技大学学报,2003,30(4):413-414.
[13]贺华中,代侦勇.克立格估值方法中权系数空间相关性研究[J].华中师范大学学报,2007,41(3):477-479.
[14]何清杭,张镇西,王晶.基于指示克立格法的最佳激发波长和最佳发射波长的确定[J].光谱学与光谱分析,2007,27(8):1476-1479.
[15]黄勇,郭庆荣,任海.地统计学在土壤重金属研究中的应用及展望[J].生态环境,2004,13(4):681-684.
[16]贾福聚,秦德先,黎应书.都龙锡矿曼家寨矿段品位模型的建立[J].矿业研究与开发,2007,27(4):54-56.
[17]金宝轩.网格计算环境下的3维空间信息应用研究[D],武汉:武汉大学,2005.
[18]李岭.地质统计学及其在某铜矿山储量计算中的应用[J].矿业研究与开发,2004,24(5):21-23.
[19]李庆斌,王山东,陈佩富.《固体矿产资源/储量分类》应用软件的研究与运用[J].矿业快报,2004,20(9):7-11.
[20]李笑吟,毕华兴,张志.晋西黄土区土壤水分有效性分析的克立格法[J].土壤学报,2006,43(6):1004-1010.
[21]李颖,杨永强,范云芳.阿尔泰成矿区金矿预测图形库及属性库的建立方法[J].长春科技大学学报,2000,30(3):293-295.
[22]刘洪,夏立显.应用弹性BP算法预测贵州金矿储量[J].地球物理学进展,2005,20(2):399-401.
[23]刘鑫,毕华兴,李笑吟.晋西黄土区土壤水分时空异质性分析[J].水土保持研究,2006,13(6):51-54.
[24]罗周全,刘晓明,吴亚斌.地质统计学在多金属矿床储量计算中的应用研究[J].地质与勘探,2007,43(3):83_87.
[25]吕连宏,张征,迟志淼.地质统计学在环境科学领域的应用进展[J].地球科学与环境科学,2006,28(1),101_105.
[26]马建超,李佳林.克立格法在数字地层创建中的应用[J].核工程研究与设计,2007,2:45-49.
[27]秦涛.Geostatists Analyst中空间内插方法的介绍[J].化工矿产地质,2005,27(4):235-240.
[28]史舟,金辉明,李艳.地统计软件包的开发及在土壤空间变异中的应用[J].水土保持学报,2005,19(5):170-173.
[29]孙刚,徐兵,韩燕.限制性克立格法在阿舍勒铜矿储量计算中研究与应用[J].世界地质,2007,26(4):409-412.
[30]孙刚,徐兵,韩燕.限制性克立格法在地学中的研究与应用[J].2008,23(2):617-621.
[31]孙洪泉.岩层模拟的地质统计学方法[J].苏州科技学院学报:工程技术版,2007,20(4):12-15.
[32]孙立双,王恩德,王井利.基于空间分布权系数Kriging邻域选点算法[J].沈阳建筑大学学报,2007,23(3):423-426.
[33]王家华,高海余,周叶,等.克里金地质绘图技术[M].北京:石油工业出版社:1999:50-55.
[34]王世称,陈永良,夏立显.综合信息矿产预测理论与方法[M].北京:科学出版社,2000.
[35]王世称,范继璋,杨永华.矿产资源评价[M].吉林:科学技术出版社,1990.
[36]王岩,尹海丽,窦在祥.蒙特卡罗方法应用研究[J].青岛理工大学学报,2006,27(2):111-113.
[37]王银宏,严光生,翟裕生.三部式潜在矿产资源定量评价与蒙特卡罗模拟[J].中国矿业,2006,15(6):14-17.
[38]王银宏,彭润民,王建平.克立格算法的若干思考[J].地质与勘探,2004,40(2):77-79.
[39]吴蓉,周志芳.基于指示克立格方法的裂隙介质渗透性参数空间分布规律分析[J].水利学报,2004,6:104-107.
[40]肖克炎,丁建华,刘锐.美国“三步式”固体矿产资源潜力评价方法评述[J].地质论评,2006,52(6):793-798.
[41]杨蕊.克立格法在储量预测中的应用[J].内蒙古石油化工,2007,33(4):103-105.
[42]杨永华.蒙特卡罗方法与矿产资源评价[J].地质与勘探,1985,21(1):45-50.
[43]叶天竺.固体矿产预测评价技术方法[M].武汉:中国地质大学出版社,2006.
[44]易彬樘,张治英,徐德忠.协同克立格和标化植被指数在广东省登革热分布特征研究中的应用[J].西安交通大学学报,2003,24(5):448-451.
[45]尹增谦,管景峰,张晓宏,等.蒙特卡罗方法及应用[J].物理与工程,2002,12(1):45-49.
[46]张仁铎.空间变异理论及应用[M].北京:科学出版社:2005:23-40.
[47]周智勇,陈建宏,张涛.基于三维稳健克立格法的品位建模[J].金属矿山,2007,10:78-80.
[48]Armstrong M.,Problems with universal kriging[J].Math.Geol.,1984,16(1):101-108.
[49]Agterberg F P,Bonham-Carter G F,Wright D F.Statistical pattern integration for mineral exploration.In:Gaal G,Merriam D F(Eds.).Computer Applications in Resource Exploration and Assessment for Minerals and Petroleum.Pergamon,Oxford,1990.
[50]Agterberg,F P.Combing indicator patterns for mineral resources evaluation,in China University of Geosciences(Eds.),Proceedings of International Workshop on Statistical Prediction of Mineral Resources,Wuhan,China,1990.
[51]Ballin P.,Journel,A.and Aziz K.,Prediction of uncertainty inreservoir performance forecasting[J].JCPT,1992,31(4):52-62.
[52]Bardossy A.Notes on the robustness of the Kriging system[J].Math. Geol., 1988,20(3): 189-204.
[53]Borgman L., New advances in methodology for statistical test useful in geostatistical studies [J]. Math. Geol., 1988, 20(4):383-403.
[54]Boufassa A. and Armstrong M., Comparison between different kriging estimators [J]. Math. Geol., 1989,21(3):331-345.
[55]Bourgault G. and Marcotte D., Multivariate variogram and its application to the linear model of coregionalization [J]. Math. Geol.,1991,23(7):899-927.
[56]Carr J. and Mao N., A general form of probability kriging for estimation of the indicator and uniform transforms [J]. Math. Geol.,1993, 25(4):425-438.
[57]Carr J R. On visualization for assessing Kriging outcomes [J]. Math.Geol., 2002,34(4): 421-433.
[58]Chiles J. P. and Delfiner P., Geostatistics: Modeling spatial uncertainty [M]. Wiley, New York, 1999, 680-695.
[59]Christakos, G., On the problem of permissible covariance and variogram models [J]. Water Resources Research, 1984,20(2):251-265.
[60]Cressie N., Fitting variogram models by weighted least squares [J].Math. Geol., 1985,17(5):563-586.
[61]Cressie N., The origin of kriging [J]. Math. Geol., 1990,22(3):239-252.
[62]Cressie N., Statistics for spatial data [M]. 1993, Wiley, New York,623-900.
[63]Cressie N. and Hawbcins D. H., Robust estimation of the variogram [J]. Math. Geol, 1980,12(2):115-126.
[64]Davis B. M., Uses and abuses of cross-validation in geostatistics [J].Math. Geol., 1987, 19(3)
[65]Deutsch C, DECLUS: A Fortran 77 program for determining optimum spatial declustering weights [J]. Computers & Geosciences,1989,15(3):325-332.
[66]Deutsch C, Correcting for negative weights in ordinary kriging [J].Computers & Geosciences, 1996,22(7):765-773.
[67]Diamond P. and Armstrong M., Robustness of variograms and conditioning of kriging matrices [J]. Math. Geol., 1984,16(8):809-822.
[68]Dietrich C. R. and Osborne M. R., Estimation of covariance parameters in kriging via restricted maximum likelihood [J]. Math.Geol., 1991,23(1):119-135.
[69]Dowd P., Lognormal kriging-the general case [J]. Math. Geol., 1982,14(5):474-500.
[70]Doyen P., Porosity from seismic data: A geostatistical approach [J].Geopysics, 1988, 53(10):1263-1275.
[71]Dubrule O. and Kostov C., An interpolation method taking into account inequality constraints [J]. Math. Geol., 1986, 18(1):33-51.
[72]Gao Haiyu and Wang Jiahua, The updated kriging variance and optimal sample design [J]. Math. Geol., 1996,28(2).
[73]Goldberger A., Best linear unbiased prediction in the generalized linear regression model [J]. JASA, 1962, 57:369-375.
[74]Goovaerts P., Comparative performance of indicator algorithms for modeling conditional probability distribution functions [J]. Math.Geol, 1994,26(3):385-410.
[75]Goovaerts P, Geostatistics for Natural Resources Evaluation [M].Oxford University Press, 1997, New York.
[76]Herzfeld U. C., A note on programs performing kriging with nonnegative weights [J]. Math. Geol, 1989,21(3):391-393.
[77]Isaaks E. H. and Srivastava R. M, An introduction to applied geostatistics [M]. Oxford University Press, 1990, New York.
[78]Isaaks E. H. and Srivastava R. M, Spatial continuity measures for probabilistic and deterministic geostatistics [J]. Math. Geol, 1988,20(4):313-341.
[79]Jaquet O, Factorial kriging analysis applied to geological data from petroleum exploration [J]. Math. Geol, 1989,21(7).
[80]Journel A. G, Kriging in terms of projections [J]. Math. Geol, 1977,9(6):563-586.
[81]Journel A. G, Lognormal approach to predicting local distribution [J]. Math. Geol., 1980, 12(4):285-303.
[82]Jorunel A. G., Nonparametric estimation of spatial distribution [J].Math. GeoL, 1983,15(3):445-468.
[83]Journel A. G., Geostatistics: models and tools for the earth sciences [J]. Math. GeoL, 1985,18(1):119-140.
[84]Journel A. G., Constrained interpolation and qualitative information-the soft kriging approach [J]. Math. GeoL, 1986,18(3):269-286.
[85]Journel A. G., Geostatistics and petroleum Geol. [J]. Math. Geol.,1989,21(6):803-804.
[86]Journel A. G. and Huijbrechts C. J., Mining geostatistics [M].Academic Press 1978, London.
[87] Journel A. G. and Posa D., Characteristic behavior and order relations for indicator variograms [J]. Math. GeoL, 1990,22(8): 1011-1025.
[88]Journel A. G. and Rossi M., When do we need a trend model in kriging? [J]. Math. GeoL, 1989,21(7):715-739.
[89]Matheron G., Principles of geostatistics [J]. Economic Geol., 1963,58:1246-1266.
[90]McCammon R B, Briskey J A. A proposed national mineral-resource assessment. Nonrenewable Resources, 1992, 1(4):259-265.
[91]Moyeed R. A. and Papritz A., An empirical comparison of Kriging methods for nonlinear spatial point prediction [J]. Math. GeoL, 2002, 34(4):365-386.
[92]Myers D. E., Matrix formulation of Co-Kriging [J]. Math. Geol., 1982,14(3):249-257.
[93]Myers D. E., Estimation of linear combinations and cokriging [J].Math. Geol., 1983,15(6):633-637.
[94]Myers D. E., Interpolation with positive definite functions [J].Sciences de la Terre, 1988,28:251-265.
[95]Pan G. C., Practical issues of geostatistical reserve estimation in the mining industry [J]. CIM Bull, 1995, 88:31-37.
[96]Pan G. C. and Moss K. etc, Afortran program for three dimensional cokriging with case demonstration [J]. Computers & Geosciences,1992,18:557-578.
[97]Pawlowsky V., Cokriging of regionalized compositions [J]. Math.Geol., 1989,21(5):519-522.
[98]Pawlowsky V., Estimation of regionalized compositions: A comparison of three methods [J]. Math. Geol., 1995,27(1):105-127.
[99]Shlomo P. Neuman, Elizabeth A. Jacobson. Analysis of nonintrinsic spatial variability by residual kriging with application to regional groundwater levels [J]. Math. Geol.,1984,16 (5):433-466.
[100] Singer D A. Basic concepts in three part quantitative assessments of undiscovered mineral resources [J]. Nonrenewable Resources, 1993,2(2): 69-81.
[101] Singer D A. Some suggested future directions of quantitative resources assessment [J]. Journal of China University of Geosciences, 2001,12(1): 40-44.
[102] Pan Guocheng. Restricted Kriging for mixture of grade models [J].Math. Geol., 1993,25 (6): 713-736.
[103] Pan Guocheng. Restricted Kriging: A Link Between Sample Value and Sample Configuration [J]. Math. Geol., 1994,26 (1): 135-155.