分形结构因子及其在地质学上的应用  

FRACTAL STRUCTURE FACTOR AND ITS APPLICATION IN GEOLOGY

作　　者：沈步明[1] 

机构地区：[1]中国科学院地质研究所,北京100029

出　　处：《岩石学报》1993年第3期267-276,共10页Acta Petrologica Sinica

基　　金：中国科学院地质研究所所长基金

摘　　要：本文以分形理论为基础,提出了一个频率分布的分形结构因子,用以表征频率分布的结构性,即表征物质在空间分布的均匀性或测量值之间的相关性。本文列举了五个实例,说明了分形结构因子是定量地表征矿物、岩石和矿床中各种组分变化特征的强有力的工具。In this paper, the fractal structure factor is proposed to represent the detailed structure of frequency distribution, i. e. the homogeneity of space distribution of matter and interrelation between data. The calculation method can be described as follows. (1) Firstly these observations are arranged again according to the sequence from small to large, and the total interval of data is divided into r small intervals. If the probability of the data point entered in the i-th interval is expressed as P(r), the total quantity of information I(r) can be calculated by the following formula: I(r)=—sum from i=1 to r (P(r)·log P(r)) (1) (2) If r is changed, a serial values of I(r) can be obtained. (3) D can be calculated by the following formula: I (r)=I_0+D_Ⅰlog(r) (2) where D is fractal dimension of information content, i.e. the changed rate of information content, I(r) is the total information content and is an entropy in a system. Because the entropy is an expression of order-disorder degree in a system, it is reasonable to define D as 'fractal structure factor'. To distinguish them, the fractal structure factor is expressed as FSF. The fractal structure factor has been proved to be a strong approach to express the changing character of every component in mineral, rock and ore deposit by five examples in this paper. By using the differences of FSF between samples or components,it is possible to carry out the classification and comparison for them and to investigate the reasons for this difference in FSF. Therefore, it will deepen the research in these fields.

关 键 词：分形结构因子 矿物学 地质学 

分 类 号：P571[天文地球—矿物学]