Assessing Microstructures of Ore-Minerals by Multifractal
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摘要:
分形与多重分形已广泛地应用于不同领域, 不同尺度下的各种分布特征研究更是受到广泛关注.以云南个旧松树脚矿田中2件含矿矽卡岩样品中黄铁矿颗粒为研究对象, 通过分形与多重分形方法研究了黄铁矿颗粒在二维空间上的分布特征.结果显示, 黄铁矿在微观尺度空间上的分布不均一, 具有明显的分形与多重分形分布特征.所选研究区外接触带黑绿色含硫化物矿石矽卡岩和接触带矽卡岩型块状硫化物矿石显微照片分析结果显示, 前者黄铁矿颗粒分布的盒子维数D0、信息维数D1、关联维数D2及广义多重分形维数Dq的变化范围均较小, 而后者较大; 前者外接触带黑绿色含硫化物矿石矽卡岩含矿性相对较弱, 而后者矿石矿物相对富集.从这个意义上说, 分形与多重分形维数与样品含矿性有一定的对应关系, 因此, 分形与多重分形分析有望进一步为岩石含矿性的定量化评价提供微观尺度上的证据.
Abstract:Fractal and multifractal concepts have been increasingly applied in various scientific and engineering fields.The distribution patterns of different objects at different scales have attracted more and more attention as well.This paper focuses on the investigation of the spatial heterogeneity of ore-forming minerals at micro-scales.Two ore-bearing skarn samples have been selected and the corresponding light-thin sections have also been prepared.The first sample, taken from the external contact zone between the skarn and the granite, is the blackish green ore-bearing skarn, and the second is the skarn-type ore sample which was taken from the skarn contact zone.Through MATLAB platform, the pyrites have been digitally recognized from the microphotographying images of the thin sections.The box-counting dimensions, generalized fractal dimensions and multifractal spectra have been calculated to characterize the spatial structure of the pyrites.The corresponding fractal and multifractal dimensions of the first sample are relatively lower, whereas those of the second sample are higher.The results show that there is a coressponding relationship between the multifractal parameters and the ore-forming potentials of the rocks under consideration, which can provide new indication for the quantitative assessment of ore-bearing potentials of rocks.
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Key words:
- microstructure of mineral /
- multifractal /
- fractal dimension
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图 1 矽卡岩中黄铁矿矿石的光学显微照片
a, b.外接触带黑绿色含硫化物矿石矽卡岩样品Sk1-2中黄铁矿显微照片P1和P2;c, d.对应接触带矽卡岩型块状硫化物矿石样品Sk1-3中的胶状黄铁矿显微照片P3和P4
Fig. 1. Photographs of pyrites in skarn rocks
图 2 数字图像识别技术处理黄铁矿的显微图像过程
a为图 1a的灰度图像; b为提取黄铁矿颗粒矢量图
Fig. 2. The image recognition processes of the photographs of pyrites based on MATLAB
图 3 分形维数D0估计
图a—d分别为图 1中对应矿石矿物空间分布分维估计结果
Fig. 3. Estimations of fractal dimension D0 using the multifractal analysis
图 4 广义分形维数Dq估计结果示意图
Fig. 4. Sketch map of Dq in the calculated spectra obtained with regression
图 5 黄铁矿颗粒分布的多重分形谱示意图
Fig. 5. Sketch map of multifractal spectra for the space distribution of pyrites at microscales
表 1 黄铁矿颗粒微观分布特征的分形参数
Table 1. Fractal parameters describing the spatial microstructures of pyrite particles
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