MULTIFRACTAL AND GEOSTATISTIC METHODS FOR CHARACTERIZING LOCAL STRUCTURE AND SINGULARITY PROPERTIES OF EXPLORATION GEOCHEMICAL ANOMALIES
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摘要: 勘查地球化学和地球物理场的局部空间结构变化性应包括空间自相关性以及奇异性.前者可通过地质统计学中常用的变异函数来实现; 后者可用多重分形模型进行刻划.具有自相似性或统计自相似性的多重分形分布(multifractal distributions)的奇异性(α)可以反映地球化学元素在岩石等介质中的局部富集和贫化规律.而多重分形插值和估计方法可以同时度量以上两种局部结构性质(空间自相关性以及奇异性), 因而, 它不仅能够进行空间数据插值, 同时还能保持和增强数据的局部结构信息, 这对于地球化学和地球物理异常分析和识别是有益的.应用该方法处理加拿大Nova Scotia省西南部湖泊沉积物地球化学砷等元素数据表明, 地球化学数据的局部奇异性在该区能够反映局部金和钨-锡-铀矿化蚀变带或岩相变化以及构造交汇等局部成矿有利部位.Abstract: Spatial textural analysis of exploration geochemical and geophysical data includes spatial association and singularity. Spatial variability and association can be measured using variogram, which has been commonly used in geostatistics. The singularity can be analyzed in multifractal modeling. Singularity in the application to geochemical data can reflect the regularity of enrichment and dispersion of elements due to mineralization. The method introduced in the paper can take into account both spatial variability and singularity in data estimation and data interpolation. It can be used to conduct data interpolation as well as retain local texture information, which is essential for analyzing and interpreting geochemical data for mineral exploration. The case study of identification of Au and Sn-W-U mineralization-related alterations from lake sediment geochemical data in the southwestern Nova Scotia, Canada, has demonstrated that the singularity exponent involved in the multifractal interpolation method may characterize the alteration or other local areas favourable for mineralization.
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图 1 加拿大北部Nova Scotia省西南部地区地质简图
1.花岗杂岩; 2.Halifax组浅变质碎屑沉积岩; 3.Goldenville组浅变质碎屑沉积岩; 4.金矿床和矿点分布
Fig. 1. Simplified geology of the southwestern Nova Scotia, Canada
图 5 估计奇异性指数(α) 所涉及的线性相关系数(R > 0.97)
Fig. 5. Correlation coefficients involved in estimation of singularity index (α)
图 6 由多重分形方法所计算的砷的分布
Fig. 6. Results obtained using the multifractal interpolation method for As
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[1] Cheng Q. Multifractal interpolation [A]. In: Lippard S J, Naess A, Sinding-Larsen R, eds. Proceedings of the Fifth Annual Conference of the International Association for Mathematical Geology[C]. Trondheim, Norway: [s.n.], 1999.245-250. [2] Herzfeld U C. A method for seafloor classification using directional variogram, demonstrated for data from the western flank of the Mid-Atlantic Ridge[J]. Mathematical Geology, 1993, 25(7): 901-924. doi: 10.1007/BF00891050 [3] Journel A G, Huijbregts C H J. Mining geostatistics [M]. New York: Academic Press, 1978.600. [4] Cheng Q. Interpolation by means of multifractal, kriging and moving average techniques [A]. In: Proceedings of GAC/MAC meeting GeoCanada 2000[C]. Canada: Geological Association of Canada, 2000. [5] Cheng Q. Multifractality and spatial statistics[J]. Computers & Geosciences, 1999, 25(9): 949-961. doi: 10.1016/S0098-3004(99)00060-6 -
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