多维分形理论和地球化学元素分布规律

成秋明

多维分形理论和地球化学元素分布规律

成秋明

York大学地球大气科学和地理系, 加拿大多伦多 M3J1P3

基金项目:

加拿大自然科学基金项目 NSERC—OGP0183993

详细信息

中图分类号: P595
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出版历程
- 收稿日期: 1999-12-07
- 刊出日期: 2000-05-25

MULTIFRACTAL THEORY AND GEOCHEMICAL ELEMENT DISTRIBUTION PATTERN

CHENG Qiuming

Department of Earth Atmospheric Science and Geography, York University, Toronto M3J1P3, Canada

摘要

摘要: 多维分形模型不仅采用常规的低阶矩统计, 而且采用高阶矩统计对多维分形分布进行度量, 从而能较细致地刻划正常值以及异常值.地球化学元素的正常值往往服从统计学中的大数定量, 即满足正态分布或对数正态分布, 然而异常值会服从分形分布(Preato).介绍了多维分形领域中的最新发展以及在地球化学研究中特别是研究超常元素空间分布和富集规律中的应用.结果表明, 通常的统计方法只对应于多维分形围绕均值周围的局部特征.为了有效地研究异常值的分布和富集规律, 建议采用高阶矩统计方法和多维分形方法, 并给出了两种分析地球化学元素, 并突出异常值贡献的方法.这些方法不仅可应用于研究微量元素的空间分布和富集规律, 而且可以区分地球化学背景与矿化有关的异常值.还介绍了该方法在对加拿大B.C.省西北部Mitchell-Sulphurets地区金铜矿化蚀变带研究中的应用.
- 多维分形模型 /
- 元素异常分形分布 /
- 金铜矿化 /
- 加拿大B.C.省
Abstract: Multifractal model is used to measure the multifractal distribution by means of not only the conventional low-order moment statistics but also the high-order moment statistics. Therefore, this model can be used to measure the statistical properties of the anomalous values as well as the background geochemical values. The background geochemical values usually follow normal or lognormal distributions, but the anomalous values may follow fractal (Preato) distributions. This paper introduces some recent developments of multifractal modeling and their applications to geochemistry, in particular to the spatial distribution and concentration pattern of trace elements. The results show that the ordinary statistical methods are effective only for the understanding of local properties of the values surrounding the multifractal mean value. In order to characterize effectively the distribution and concentration pattern of the anomalous values, this paper proposes the high-order moment statistical method and multifractal method. Furthermore, two methods have been given in this paper for the analyses of geochemical elements and anomalous values: concentration-area (C—A) fractal method and high-order correlation coefficient. The former method is used for separating anomalies from their background values and the latter is for enhancing the correlation coefficient between anomalous values of multiple elements. A case study is used to illustrate the application of these methods to the detection of Au/Cu-associated alteration zones in the Mitchell-Sulphurests mineral district, northwest of B.C. Province, Canada.
- multifractal modeling /
- fractal distribution of anomalous values /
- Au/Cu mineralization /
- B. C. Province, Canada

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图 2 多维分形对1 030岩石样品Au质量分数分析结果

(a) Q—Q图表明Au质量分数背景值基本服从对数正态分布; (b) 多维分形谱函数; (c) Au质量分数等值线值与等值线包围的面积之间的关系.两条直线分别为最小二乘拟合直线.由两条直线的交点所对应的Au的分界值w (Au) =200×10^-9可区分异常与背景的值; (d) 阴影范围表示Au异常(w (Au) ≥200×10^-9) 范围; 黑点表示已知地表出露的蚀变带范围

Fig. 2. Results obtained by multifractal modelling to the Au

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图 1 研究区地质图及地表岩石取样位置

(a) 简化地质图, 包括蚀变带轮廓^①. (b) 岩石取样位置.Mitchell侵入岩: 1.正长岩, 二长岩, 闪长岩, 二长闪长岩; 2.Bowser湖组Hazelton群.3.Mount Dilworth建造; 4.Untik河建造和Betty溪建造; 5.Jack建造Stuhint群; 6.沉积岩; 7.火山岩; 8.黄铁矿蚀变岩; 9.冰川、湖泊和未知区

Fig. 1. Geology of the study area and the locations of rock samples

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