MML-EM Algorithm and Its Application on Mixed Distributions of Geochemical Data
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摘要: 概率图法在筛分混合分布的问题上，只能对混合分布的各项参数作出粗略的估计.为了解决这一问题，引入了MML-EM法.模拟研究表明，在混合分布参数估计上，该方法比概率图法有更高的精度.以江西大吉山钨矿石英脉原生晕数据为例，经过该方法的筛分，得到钨、钽和铌的含量服从由2个子分布组成的混合对数正态分布，即双峰分布.结合前人的地质研究，可以初步得出结论：钨的高值总体代表了岩浆期后热液成矿期的热液充填石英脉型矿化，低值总体可能代表其他成矿期的事件，其中高值部分可能构成岩浆晚期浸染型的弱钨矿化.钽和铌的高值总体代表岩浆晚期的浸染型富矿化，低值总体代表其他成矿期的叠加矿化.该方法为化探数据中混合分布的筛分以及解释多地质成因总体提供了一种良好的定量化工具.Abstract: When separating the mixed distributions of element abundance, probability graphs can only make a rough estimate of parameters. To solve this problem, we introduce a method of Minimum Message Length Criterion-Expectation-Maximization Algorithm (MML-EM). Simulation studies have shown that the method has higher accuracy than probability graphs in estimating the parameters of mixed distributions of element abundance. It is applied to dealing with the geochemical data of quartz vein, sampled from tungsten ore in Dajishan, Jiangxi Province. The research shows that the concentrations of W, Ta and Nb are mixed pairs of log-normal distributions, biomodel distributions. Referring to the previous geological results, the conclusion is as follows. For W, the component with high average value represents the high-grade ore formed by hydrothermal filling type in ore-forming processes, and the one with low average value represents the mineralization in other stages, high-value parts of which may indicate that there is a weak disseminated tungsten mineralization at late magmatic stage. For Ta and Nb, the situation is similar. So the method provides a good quantitative tool that can help separate the mixed distributions of geochemical data and explain the multiple geological events.
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图 1 钨的混合分布筛分(对数变换后)
Fig. 1. Tungsten concentration data partitioned into two-components
图 2 钽的混合分布筛分(对数变换后)
Fig. 2. Tantalum concentration data partitioned into two-components
图 3 铌的混合分布筛分(对数变换后)
Fig. 3. Niobium concentration data partitioned into two-components
表 1 MML-EM方法模拟
Table 1. Simulation of the algorithm of MML-EM
试验号 α真值 α估计值 μ真值 μ估计值 σ真值 σ估计值 1 0.5 0.51 0 -0.04 1 0.93 0.5 0.49 3 3.00 1 0.86 2 0.9 0.9 0 0 1 1.03 0.1 0.1 6 5.88 1 0.95 
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表 2 概率图法模拟
Table 2. Simulation of the probability graphs
试验号 α真值 α估计值 μ真值 μ估计值 σ真值 σ估计值 1 0.5 0.6 0 0.7 1 1.2 0.5 0.4 3 2.3 1 1.08 2 0.9 0.67 0 -0.9 1 4.25 0.1 0.33 6 5.1 1 3.8
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表 3 大吉山矿床成矿期与成矿阶段
Table 3. Metallogenetic epoches and metallogenetic stages of Dajishan deposit
成矿期 成矿阶段 矿物共生组合 蚀变特征 温度(℃) 岩浆期 I1含TR矿化花岗闪长岩 斜长石、微斜长石、条纹长、黑云母、石英、榍石、磁铁矿、独居石、锆石、褐帘石 弱钾长石化 成岩：640 I2含Nb-Ta-TR矿化二云母二长花岗岩 斜长石、微斜长石、条纹长、石英黑云母、白云母、独居石、磷钇矿 钾长石化
弱钠长石化成岩：550；成矿：334 I3含Nb-Ta-Be-W白云母花岗岩 斜长石、微斜长石、白云母、石英、钠长石、石榴子石、绿柱石、硅铍石、铌钽铁矿、细晶石、黑钨矿、白钨矿 钠长石化
白云母化
云英岩化成岩：526；成矿：309 伟晶期 I4含Be-(Rb)-W矿化似伟晶岩 白云母、微斜长石、绿柱石、石英、黑钨矿 无 成岩：503~455；成矿：280~255 岩浆期
后热液
成矿期I5含W-Be-(Rb)长石石英脉 白云母、微斜长石、绿柱石、石英、黑钨矿 白云母化
硅化成矿：290 I6含W-Be-Mo石英脉 白云母、电气石、石英、微斜长石、绿柱石、含铍石榴子石、黑钨矿、辉钼矿 白云母化
电气石化
萤石化成矿：287 I7含W-Mo-Bi石英硫化物脉 白云母、石英、黑钨矿、白钨矿、雌黄铁矿、黄铁矿、毒砂、闪锌矿、方铅矿 白云母化
硅化
萤石化
绢云母化成矿：260 I8含W-碳酸盐脉 白云母、碳酸盐、萤石、黑钨矿、白钨矿、黄铁矿 白云母化碳酸盐化绿泥石化 成矿：130
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表 4 钨的分布参数
Table 4. Estimated statistical parameters of tungsten
分支 权重 均值(10-6) 方差 1 0.21 26.1 12.6 2 0.79 297.7 403
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表 5 钽的分布参数
Table 5. Estimated statistical parameters of tantalum
分支 权重 均值(10-6) 方差 1 0.25 0.01 0.01 2 0.75 1.60 28.0
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表 6 铌的分布参数
Table 6. Estimated statistical parameters of niobium
分支 权重 均值(10-6) 方差 1 0.95 1.43 3.13 2 0.05 13.38 4.29
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Allegre, C.J., Lewin, E., 1995. Scaling laws and geochemical distributions. Earth and Planetary Science Letters, 132(1-4): 1-13. doi: 10.1016/0012-821X(95)00049-I Cheng, Q.M., Agterberg, F.P., Ballantyne, S.B., 1994. The separation of geochemical anomalies from background by fractal methods. Journal of Geochemical Exploration, 51(2): 109-130. doi: 10.1016/0375-6742(94)90013-2 Figueiredo, M.A.F., Jain, A.K., 2002. Unsupervised learning of finite mixture models. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(3): 381-396. doi: 10.1109/34.990138 Hsu, Y.S., Walker, J.J., Ogren, D.E., 1986. A stepwise method for determining the number of component distributions in a mixture. Mathematical Geology, 18(2): 153-160. doi: 10.1007/BF00898280 Lian, J.Y., 2006. Improved EM algorithm and its application on the parameter estimation in mixed distribution models (Dissertation). University of Chang'an, Xi'an (in Chinese with English abstract). Shen, W., 2008. Fractal invariable distribution and its application in gold mineral deposits in Shandong Province, China. Earth Science Frontiers, 15(4): 65-70 (in Chinese with English abstract). http://search.cnki.net/down/default.aspx?filename=DXQY200804009&dbcode=CJFD&year=2008&dflag=pdfdown Sinclair, A.J., 1976. Applications of probability graphs in mineral exploration. Translated by Zhao, P.D., Hu, W.L., Li, Z.J., et al., 1981. Geological Publishing House, Beijing (in Chinese). Sinclair, A.J., 1991. A fundamental approach to threshold estimation in exploration geochemistry: probability plots revisted. Journal of Geochemical Exploration, 41(1-2): 1-22. doi: 10.1016/0375-6742(91)90071-2 Teng, J.D., 1990. Vertical zoning distribution of mineralization in the Dajishan mine. Mining Geology, 11(2): 13-24 (in Chinese). Wang, J.K., Gai, J.Y., 1995. Mixture distribution and its application. Journal of Biomathematics, 10(3): 87-92 (in Chinese with English abstract). http://europepmc.org/abstract/CBA/568584 Zhang, C.S., Manheim, F.T., Hinde, J., et al., 2005. Statistical characterization of a large geochemical database and effect of sample size. Applied Geochemistry, 20(10): 1857-1874. doi: 10.1016/j.apgeochem.2005.06.006 Zhang, S.F., 2004. EM algorithm and its application in parameter estimation for Gussian mixture. Journal of Spacecraft TT & C Technology, 23(4): 47-52 (in Chinese with English abstract). Zhao, P.D., 1990. The statistical analysis of geological exploration. Geological Publishing House, Beijing (in Chinese). Zhao, P.D., Hu, W.L., Li, Z.J., 1983. Statistical prediction of mineral deposit. Geological Publishing House, Beijing (in Chinese). 连军艳, 2006. EM算法及其改进在混合模型参数估计中的应用研究(硕士学位论文). 西安: 长安大学. 申维, 2008. 分形不变分布及其在山东地区金矿床中的应用. 地学前缘, 15(4): 65-70. doi: 10.3321/j.issn:1005-2321.2008.04.008 Sinclair, A.J., 1976. 概率图在矿床勘探中的应用. 赵鹏大, 胡旺亮, 李紫金, 等译, 1981. 北京: 地质出版社. 滕建德, 1990. 大吉山矿区矿化垂直带状分布. 矿山地质, 11(2): 13-24. 王建康, 盖钧镒, 1995. 混合分布理论及应用. 生物数学学报, 10(3): 87-92. https://www.cnki.com.cn/Article/CJFDTOTAL-SWSX199503016.htm 张士峰, 2004. 混合正态分布参数极大似然估计的EM算法. 飞行器测控学报, 23(4): 47-52. 赵鹏大, 1990. 地质勘探中的统计分析. 北京: 地质出版社. 赵鹏大, 胡旺亮, 李紫金, 1983. 矿床统计预测. 北京: 地质出版社. -
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