Uncertainty Assessment for IDW Ore Grade Estimates
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摘要: 作为一种常用的矿石品位估值方法, 距离幂次反比(inverse distance weighting, 简称IDW)计算结果的可信度难以评估.对此, 提出了一种基于统计学理论的解决途径. 将参与IDW估值的样品品位视为指示化阈值, 推导得出估值过程中其分配到的权重, 即为待估点取这样品值的概率. 基于这一结论构建出IDW估计值对应的条件累计分布函数(conditional cumulative distribution function, 简称CCDF), 从而完成待估位置矿石品位不确定性的建模. 以一典型矿区的实际矿体勘探数据为基础进行了对比测试. 针对每个估值点的CCDF进行了中位数、期望、方差等信息的提取, 验证表明这一方法的计算结果与样品数据的实际情况之间存在较好的吻合度. 在一定程度上说明了它在IDW品位估值结果不确定性评价方面的有效性.Abstract: As a typical ore grade estimation method, inverse distance weighting (IDW) has a long-time standing deficiency in reliability evaluation for its estimates, which has seriously limited its practicability. A statistical solution is presented in this paper to address the issue. A key character of IDW, that weight of each participation sample is the probability that the current un-sampled value is equal to the corresponding sample value, is proposed and proved by considering the participation samples as cutoff values during an indicating process. Based on this character, the conditional cumulative distribution function (CCDF) models related to the points to be estimated are constructed to fully characterize the uncertainty of IDW estimates. At last, a case study is carried out using cross validation and a test dataset from exploration engineering of a real ore-body. It is found that the real character of test dataset has been successfully revealed by the medium, expected and variance drawing from the constructed CCDFs, showing that the theoretical analysis and practical application can prove the validity and practicability of the proposed method to some extent.
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图 1 实验样品数据的空间位置及品位分布情况
Fig. 1. Spatial distribution and summary statistics of the test dataset
图 2 期望估计值与真实值(a)和中位数估计值(b)之间的关系
ρ代表总体相关系数
Fig. 2. Scatter plots of expected estimates and true values (a) and medium estimates (b)
图 3 期望估计值与条件标准差(a)和估计标准差(b)之间的关系
ρ代表总体相关系数
Fig. 3. Scatter plots of expected estimates and conditional standard deviation (a) and estimation standard deviation (b)
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Achilleos, G., 2008. Errors within the Inverse Distance Weighted (IDW) Interpolation Procedure. Geocarto International, 23(6): 429-449. doi: 10.1080/10106040801966704 Ahrens, B., 2006. Distance in Spatial Interpolation of Daily Rain Gauge Data. Hydrology and Earth System Sciences, 10(2): 197-208. doi: 10.5194/hess-10-197-2006 Caers, J., 2011. Modeling Uncertainty in the Earth Sciences. John Wiley & Sons, Ltd., West Sussex, 246. Chilès, J., Delfiner, P., 1999. Geostatistics: Modeling Spatial Uncertainty. Wiley, New York, 695. Ellison, S.L.R., Rosslein, M., Williams, A., 2000. Quantifying Uncertainty in Analytical Measurement (Second Edition). CZTAC, Atlanta, 120. Goovaerts, P., 2001. Geostatistical Modelling of Uncertainty in Soil Science. Geoderma, 103(1-2): 3-26. doi: 10.1007/s00477-011-0496-2 Hohn, M.E., 1999. Geostatistics and Petroleum Geology. Kluwer Academic Publishers, Dordrecht, 235. Isaaks, E.H., Srivastava, R.M., 1989. An Introduction to Applied Geostatistics. Oxford University Press, Oxford, 592. Li, Z.L., Wang, P., Zhang, X.L., 2008a. Improvement and Application of Inverse Distance Weighted Method. Metal Mine, 328(4): 88-92 (in Chinese with English abstract). http://search.cnki.net/down/default.aspx?filename=JSKS200804024&dbcode=CJFD&year=2008&dflag=pdfdown Li, Z.L., Zhang, X.L., 2007. Designing and Realization of Mineral Resources Reserve Calculation Module Using Inverse Distance Square Method. Geology and Prospecting, 43(6): 92-97 (in Chinese with English abstract). doi: 10.3969/j.issn.0495-5331.2007.06.017 Li, Z.L., Zhang, X.L., Weng, Z.P., 2008b. Research and Application of Indicator Kriging Method in Ore Body Reserves Calculation. Express Information of Mining Industry, 24(1): 11-15 (in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-KYKB200801006.htm Lin, L.B., 2003. Assessment and Development of Deposit Resource in Zijinshan Gold Mine. Nonferrous Metals (Mine Section), 55(4): 19-21 (in Chinese with English abstract). doi: 10.3969/j.issn.1671-4172.2003.04.007 Manchuk, J., Leuangthong, O., Deutsch, C., 2009. The Proportional Effect. Mathematical Geosciences, 41(7): 799-816. doi: 10.1007/s11004-008-9195-z Niu, W.J., 2011. Inverse Distance Weighting Method Based on Variogram. Journal of Donghua University (Natural Science), 37(3): 362-367 (in Chinese with English abstract). doi: 10.3969/j.issn.1671-0444.2011.03.020 Shepard, D., 1968. A Two-Dimensional Interpolation Function for Irregularly-Spaced Data. Proceedings of the 23rd ACM National Conference, New York, 517-524. Tan, Z.H., Jing, Y.B., Wang, L.G., et al., 2011. Improved IDW Method for Ore Grade Estimation Based on Spatial Variation. Journal of China University of Mining & Technology, 40(6): 928-932 (in Chinese with English abstract). http://www.cqvip.com/QK/93316X/201106/40318280.html Tomczak, M., 1998. Spatial Interpolation and Its Uncertainty Using Automated Anisotropic Inverse Distance Weighting (IDW)-Cross-Validation/Jackknife Approach. Journal of Geographic Information and Decision Analysis, 2(2): 18-30. Wu, C.L., Tian, Y.P., Zhang, X.L., et al., 2011. Discuss on the Theory and Method about Construction of the Digital Mine. Geological Science and Technology Information, 30(2): 102-108 (in Chinese with English abstract). doi: 10.3969/j.issn.1000-7849.2011.02.017 Yamamoto, J.K., 2000. An Alternative Measure of the Reliability of Ordinary Kriging Estimates. Mathematical Geology, 32(4): 489-509. doi: 10.1023/A:1007577916868 Zhang, J., Goodchild, M.F., 2002. Uncertainty in Geographical Information. Taylor & Francis Ltd., London, 288. Zhang, X.L., Wu, C.L., Weng, Z.P., et al., 2010. Research and Application of the Digital Mine Software Quanty Mine. Earth Science—Journal of China University of Geosciences, 35(2): 302-311 (in Chinese with English abstract). doi: 10.3799/dqkx.2010.031 李章林, 王平, 张夏林, 2008a. 距离幂次反比法的改进与应用. 金属矿山, 328(4): 88-92. https://www.cnki.com.cn/Article/CJFDTOTAL-JSKS200804024.htm 李章林, 张夏林, 2007. 距离平方反比法矿产资源储量计算模块设计与实现. 地质与勘探, 43(6): 92-97. https://www.cnki.com.cn/Article/CJFDTOTAL-DZKT200706016.htm 李章林, 张夏林, 翁正平, 2008b. 指示克里格法在矿体储量计算方面的研究与应用. 矿业快报, 24(1): 11-15. https://www.cnki.com.cn/Article/CJFDTOTAL-KYKB200801006.htm 林连宝, 2003. 紫金山金矿资源的评价与开发利用. 有色金属(矿山部分), 55(4): 19-21. https://www.cnki.com.cn/Article/CJFDTOTAL-YSKU200304007.htm 牛文杰, 2011. 基于变异函数的距离加权反比法. 东华大学学报(自然科学版), 37(3): 362-367. https://www.cnki.com.cn/Article/CJFDTOTAL-DHDZ201103021.htm 谭正华, 荆永滨, 王李管, 等, 2011. 基于空间变异性的IDW矿石品位估值改进方法. 中国矿业大学学报, 40(6): 928-932. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGKD201106016.htm 吴冲龙, 田宜平, 张夏林, 等, 2011. 数字矿山建设的理论与方法探讨. 地质科技情报, 30(2): 102-108. https://www.cnki.com.cn/Article/CJFDTOTAL-DZKQ201102018.htm 张夏林, 吴冲龙, 翁正平, 等, 2010. 数字矿山软件(Quanty Mine)若干关键技术的研发和应用. 地球科学——中国地质大学学报, 35(2): 302-311. https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX201002015.htm -
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