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Assessing microstructures of pyrrhotites in basalts by multifractal analysis

机译：多重分形分析评价玄武岩中黄铁矿的微观结构

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Understanding and describing spatial arrangements of mineral particles and determining the mineral distribution structure are important to model the rock-forming process. Geometric properties of individual mineral particles can be estimated from thin sections, and different models have been proposed to quantify the spatial complexity of mineral arrangement. The Gejiu tin-polymetallic ore-forming district, located in Yunnan province, southwestern China, is chosen as the study area. The aim of this paper is to apply fractal and multifractal analysis to quantify distribution patterns of pyrrhotite particles from twenty-eight binary images obtained from seven basalt segments and then to discern the possible petrological formation environments of the basalts based on concentrations of trace elements. The areas and perimeters of pyrrhotite particles were measured for each image. Perimeter-area fractal analysis shows that the perimeter and area of pyrrhotite particles follow a power-law relationship, which implies the scale-invariance of the shapes of the pyrrhotites. Furthermore, the spatial variation of the pyrrhotite particles in space was characterized by multifractal analysis using the method of moments. The results show that the average values of the area-perimeter exponent (iDsubAP/sub/i), the width of the multifractal spectra (Δ(iD(0)−D(2)/i) and Δ(iD(q/isubmin/sub)−iD(q/isubmax/sub))) and the multifractality index (τ"(1)) for the pyrrhotite particles reach their minimum in the second basalt segment, which implies that the spatial arrangement of pyrrhotite particles in Segment 2 is less heterogeneous. Geochemical trace element analysis results distinguish the second basalt segment sample from other basalt samples. In this aspect, the fractal and multifractal analysis may provide new insights into the quantitative assessment of mineral microstructures which may be closely associated with the petrogenesis as shown by the bulk-rock geochemical analysis.
机译：了解和描述矿物颗粒的空间排列并确定矿物分布结构对于模拟岩石形成过程很重要。可以从薄片上估算单个矿物颗粒的几何特性，并且已经提出了不同的模型来量化矿物排列的空间复杂性。研究区位于中国西南部云南省的个旧锡多金属成矿区。本文的目的是应用分形和多重分形分析，从七个玄武岩段获得的二十八幅二值图像中量化黄铁矿颗粒的分布模式，然后根据痕量元素的浓度识别玄武岩可能的岩石形成环境。测量每个图像的黄铁矿颗粒的面积和周长。周边面积分形分析表明，黄铁矿颗粒的周长和面积遵循幂律关系，这暗示了黄铁矿形状的尺度不变性。此外，通过使用矩量法的多重分形分析来表征黄铁矿粒子在空间中的空间变化。结果表明，面积-周长指数（ D AP ）的平均值，多重分形谱的宽度（Δ（ D（0）＆减去; D（2））和Δ（ D（q min ）＆minus; D（q max < / sub>））），并且在第二玄武岩段中，黄铁矿粒子的多重分形指数（＆“（1））达到最小值，这意味着在2段中黄铁矿粒子的空间排列不均匀。分析结果将第二个玄武岩段样品与其他玄武岩样品区分开来，在这方面，分形和多重分形分析可为定量评估矿物微观结构提供新的见解，而矿物微观结构可能与成岩作用密切相关，如整体岩石地球化学分析所示。

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