空间模式的广义自相似性分析与矿产资源评价

尺度不变性(scale invariance)包括自相似性(各向同性)、自仿射性(成层结构)、广义自相似性(各向异性标度不变性)，是由各种地质过程和地质事件所产生的地质特征和模式的本质属性．尺度不变性可用分形和多重分形模型来表征．这些尺度特征的定量化可为刻画地质空问模式和模式识别提供有力的工具．例如。热液矿床的群聚现象可以用局部分形特征(局部奇异性)来刻画．通过在特征空问中(如频率空问)识别空问模式的广义自相似性．可以将空间混合模式进行分解或异常的识别．介绍了几种相关的分形模型和方法。包括度量空问模式广义尺度独立性(GSI)的线性模型；基于广义尺度独立性的异常分解S—A方法；度量空问模式的局部奇异性方法；以及如何利用分形特征预测未发现矿床的2种方法．有些方法已应用于许多矿产资源评价实例中．给出了对加拿大Nova Scotia省西南部湖泊沉积物样品中的4种元素As、Pb、Zn和Cu的地球化学数据处理分析结果。证明了局部奇异性分析和S—A异常分解方法对地球化学异常的增强和分离的有效性．研究表明：由S—A方法分解的异常往往具有多重分形的特点，而且普遍具有局部奇异性．研究区内具有明显奇异性的地区(元素含量富集区)是金矿异常区域。它们与金矿成矿作用和已知矿床的赋存密切相关．

Quantifying the Generalized Self-Similarity of Spatial Patterns for Mineral Resource Assessment

Scale invariance, including self-similarity (isotropic), self-affinity (stratification), and generalized self-similarity (anisotropy), is a common property of spatial patterns generated from various geological processes and events. Scale invariance can be described by means of fractal and multifractal models. Quantifying the scale invariance properties of spatial patterns may provide a powerful tool for characterizing geological processes and events. For example, the clustering distribution of hydrothermal mineral deposits can be characterized by means of local singularity analysis. The identification of distinct generalized self-similarity in the Fourier domain can be used to decompose spatial patterns into separate components such as anomalies from background patterns. The current paper introduces a number of relevant multifractal models and methods, including a linear model for generalized scale invariance (GSI); a spectrum-area method (S-A) for anomaly separation; a local singularity analysis method; and methods for predicting undiscovered mineral deposits on the basis of fractal and multifractal properties. Some of these methods have been applied in various case studies. The case study introduced in the current paper demonstrates the application of S-A anomaly separation and local anomaly enhancement in analyzing lake sediment geochemical data (As, Pb, Zn and Cu) for gold mineral resource prediction. It has been shown that the areas delineated by a strong singularity in As, Pb, Zn and Cu are spatially associated with the location of known gold mineral deposits.