求多重分形谱的滑动格子法在深浅地表元素分布中的应用研究  

Study of the Application of the Gilding-box Method for Calculate Multifracial Spectrum in the Distribution of Surface Layer and In-depth Elements

作　　者：安聪沛[1] 吴堑虹[2] 

机构地区：[1]中南大学数学科学与计算技术学院,湖南长沙410083 [2]中南大学地学与环境工程学院,湖南长沙410083

出　　处：《数学的实践与认识》2007年第13期66-72,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(40473029)

摘　　要：在多重分形理论和特征判定法的基础上,构造了求多重分形谱的滑动格子计算法,计算出了研究区域4种元素深、浅层的多重分形谱f(α)的图像.结果显示浅层元素的分布不具备多重分形特征;深层元素分布符合多重分形特征.就三种分形维数——格子维数、信息维数、关联维数对深层元素的分布做出了大小排序解释;后就多重分形谱f(α)的跨度、对称性和两端差值Δf做出了对应于深层元素分布概率分布集中差异、高低浓度分布差异、稳定性的解释.最后根据上述分析的结果指出应用求多重分形谱的滑动格子法研究深浅地层元素分布是一快速、实用、有效的方法,具有良好的应用前景.Based on the prerequisite of a multifractal set. This paper constructs the gildingbox algorithm to calculate multifractal spectrum of the 4 elements in deep and superficial crust. Judging out the in-depth all elements distribution all tallies, the surface layer all elements distribution does not conform to the multifractal distributed characteristics. Putting forward the ordering explanation of the 3-fractal dimensiont box-dimension, information-dimension, and correlation-dimension, latter explain the span, the symmetry, △f of the multifractal spectrum into probability distribution-discrepancy, concentratlon-discrepancy, and stability, At last paper points out the application of the gilding-box method for calculate multiracial spectrum in the distribution of surface layer and in-depth elements is a fast, practical, soundly method. Application of this method will be extended.

关 键 词：多重分形谱 滑动格子法 元素分布 

分 类 号：P595[天文地球—地球化学]