分形不变分布及其在山东地区金矿床中的应用

Fractal invariable distribution and its application in gold mineral deposits in Shandong Province,China

自相似性(标度不变性)是地学中的一个普遍现象。研究表明,地球化学元素含量、矿床储量规模及其空间分布具有分形结构。分形不变分布的特点要求大于某一尺度物体的数目与物体大小之间存在幂指数关系。论证了幂函数分布、帕累托分布、对数正态分布和齐波夫定律在一定条件下具有分形不变性质,它们是分形模型的数学基础。基于分形模型,用求和方法确定中国山东省金地球化学元素异常值范围。等值线大于或等于金地球化学元素临界值(200×10-9)围成的异常面积包含了已知的大型、超大型金矿床。

The self-similarity is a common phenomenon in geology. It has been shown that geochemical element data, mineral deposit and its space distribution have fractal structures. A fractal distribution requires that the number of objects larger than a specified size has a power-law dependence on the size. This paper shows that a number of distributions, including power-function, Pareto, log-normal and Zipf, display fractal properties under certain conditions and that this may be used as the mathematical basis for developing fractal models for data exhibiting such distributions. The summation method is developed on the basis of fractal models to determine thresholds for Au data in Shandong Province, China. The anomalous area enclosed by contours which have contour values greater than or equal to threshold（200×10^-9） contain the known large-sized and super largesized gold mineral deposits.