成矿元素品位有序数据集自仿射分形方法应用性评价

doi:10.11867/j.issn.1001-8166.2007.04.0357

地球科学进展 ›› 2007, Vol. 22 ›› Issue (4): 357 -361. doi: 10.11867/j.issn.1001-8166.2007.04.0357

万丽 ^1,2, 王庆飞 ^2,3

1.广州大学数学与信息科学学院，广东广州 510006；2.中国地质大学地质过程与矿产资源国家重点实验室，北京 100083；3.中国地质大学岩石圈构造、深部过程及探测技术教育部重点实验室，北京 100083

收稿日期:2007-01-20 修回日期:2007-03-01 出版日期:2007-04-10
通讯作者: 万丽（1961-），女，湖北武汉人，副教授，博士，现主要从事数学地质研究和教学工作.E-mail：wanli03100@21cn.com E-mail:wanli03100@21cn.com
基金资助:
国家自然科学基金项目“胶东中生代构造体制叠接与复合成矿系统的形成演化”（编号：40572063）；地质过程与矿产资源国家重点实验室开放基金项目“胶东大尹格庄金矿矿化网络分形研究”(编号：GPMR200626)；中国博士后科学基金项目“铜陵矿集区构造—岩浆—成矿系统复杂性解析”（编号：2005038361）资助.

Analysis on Application of the Self-affine Methods Dealing with the Dataset of Spatial Elementary Grade Distribution

WAN Li ^1,2, WANG Qing-fei ^2,3

1.School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006,China; 2.State Key Laboratory of Geological Processes and Mineral Resources，China University of Geosciences, Beijing 100083,China；3.Key Laboratory of Lithosphere Tectonics and Lithoprobing Technology of Ministry of Education , China University of Geosciences, Beijing 100083,China

Received:2007-01-20 Revised:2007-03-01 Online:2007-04-10 Published:2007-04-10

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自仿射分形的Hurst指数是分析地质剖面数据的有利参数。以大尹格庄金矿不同勘探线刻槽取样所得的金品位序列为例，评价Hurst指数的几种估算方法在地质剖面数据分析中的适用性。取相同尺度，全部数据集的增量标准偏差法统计散点呈波状变化，部分数据集的曲线长度变换法统计散点的后半部分呈波状变化,全部数据集的重标极差分析法统计散点线性拟合较好。结果显示增量标准偏差法对尺度要求较为苛刻，适于巨量数据的统计；曲线长度变换法应用性较广，所得Hurst指数反映品位的空间变化强度；重标极差分析法稳定性最好，其Hurst指数反映了品位变化相依性。 

关键词: 自仿射分形, Hurst指数, 相依性, 成矿元素, 胶东

Hurst parameter of self-affine fractal is the favorable parameters for studying the data of geological profiles. Hurst parameters of data series of gold grade, derived from notch grooves in different exploratory lines, are calculated by the methods of incremental standard deviation, curve length transform and rescaled range analysis(R/S), and the applicability of these methods is evaluated affectively. As uniform scaling analysis taken in the three methods, the plots by the first method show poor linear relationship in all the applications, the rear points obtained from the second method fluctuate in part of the applications, and the plots by the last method show good linear relationship in the most applications. Therefore, the restrictions of the dataset capacitance and the analysis scale for the incremental standard deviation method are more than those for the curve length transform method, and the R/S method can be applied widely than the two other methods and it is suitable for statistic analysis of small dataset. Moreover, the Hurst parameter received from the curve length transform method can reflect the spatial fluctuation intensity of gold grade, while the same parameterobtained by R/S analysis judges the persistence of grade distribution. 

Key words: Self-affine fractal, Hurst parameter, Persistence, Metallogenic element, Jiaodong peninsula.

中图分类号:

P628+.1

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