分形理论在云南个旧锡矿遥感信息定量化分析中的应用

应用分形理论和方法对个旧锡矿遥感信息进行了定量化研究.结果显示,在格子边长为1.4～4.5 km的标度范围内,其遥感蚀变和断裂构造进入的总格子数的对数与格子边长的对数均具有很好的线性相关性,表明在研究标度范围内,各子区遥感线性与蚀变信息具有良好的统计自相似性和分形特征.在此基础上,以19号区和26号区为例,分析并进一步探讨了遥感信息分形特征的成矿意义.     

安阳矿区双全井田岩性结构与煤体变形的关系

煤体变形程度控制着煤与瓦斯突出和煤层气的可开发性,煤体结构空间展布预测是人们长期关注的焦点。以岩体力学和分形几何学基本理论为指导,以安阳矿区双全井田为例,通过计算岩体强度因子和分形维数,系统探讨了岩性结构对煤体变形的影响。研究表明,岩体强度因子和分形维数与断层和测井曲线判识的煤体结构之间存在密切关系:低强度因子和分形维数区,煤体易发生韧性变形,软煤发育;高强度因子和分形维数区,煤体(和岩体)以脆性变形为主,以断层发育为特征。这一结论为井田构造发育特征和软煤空间展布所证实。岩体力学和分形几何学的引入,为煤体结构空间展布区域预测提供了一种新途径。     

任楼矿井72煤层断层构造分形特征研究

利用分形理论,对安徽皖北任搂煤矿72煤层断层分形特征进行了研究,计算了不同构造分区的维数。研究发现构造复杂性不同及断裂性质的不同其分形维数也有所不同,构造简单,断层分维数小,而构造复杂区,断层分为数相对较大;剪切断裂带具有较低的分维值,张扭性断裂带分维值较高。     

泥石流堆积物的粒度分布及其分形结构

泥石流堆积物主要由砾石、砂砾、粉粒和粘粒组成,组成泥石流堆积物的颗粒级配变幅很大,从直径大于数十米的巨砾到肉眼难以看见的几微米的胶体微粒均有分布,大小颗粒粒径之比可达106—107。泥石流堆积物颗粒具有明显的自相似性和无标度区间。本文以小江流域多处泥石流堆积物为研究对象,采用图解法全面分析了泥石流堆积物的粒度组成特征,根据分形理论计算了泥石流堆积物颗粒的分维值,对泥石流堆积物的分形特征进行探讨,并与泥石流堆积物粒度特征相联系,发现分维很好的反映了泥石流堆积物颗粒组成及其粒度分布特征。将泥石流堆积物颗粒分维与泥石流的粘性、形成年代等性质相联系,以找出它们彼此之间的关系。     

一种基于小波域的分形遥感影像压缩方法

解决大数据量遥感影像传输和存储问题的方案之一,是对遥感影像进行高保真快速压缩。通过对遥感影像进行小波变换产生子带频域之间的相似性,再利用分形方法对具有相似性的相邻高频子带进行编码,由高一级的子影像构造低一级的子影像,然后采用分形迭代解码和小坡变换的逆变换重建影像。实验结果表明,该方法在一定程度上能够提高压缩比,在压缩时间上比传统的分形方法有明显的缩短,并且压缩后影像信息的损失量较少,影像恢复的质量较好。     

中强地震前后能量分布的自仿射特性

根据简化的地震波传播理论,“漫化”地震能量在空间的分配,减弱能量空间分布概率的极端情形及消除统计域为“空”的情形,由此构造类似于二维ｆＢｍ的地震能量空间分布概率曲面。与起伏不平的地形相似,由于基在水平方向及垂直方向的变化不是等比例的,因而这一分形曲面可能是统计自仿射的。     

Interpolation by regularized spline with tension: I. Theory and implementation

Bivariate and trivariate functions for interpolation from scattered data are derived. They are constructed by explicit minimization of a general smoothness functional, and they include a tension parameter that controls the character of the interpolation function (e.g., for bivariate case the surface can be tuned from a membrane to a thin steel plate), Tension can be applied also in a chosen direction, for modeling of phenomena with a simple type of anisotropy. The functions have regular derivatives of all orders everywhere. This makes them suitable for analysis of surface geometry and for direct application in models where derivatives are necessary. For processing of large datasets (thousands of data points), which are now common in geosciences, a segmentation algorithm with a flexible size of overlapping neighborhood is presented. Simple examples demonstrating flexibility and accuracy of the functions are presented.On leave from the Department of Physical Geography and Cartography, Comenius University, Mlynská dolina, Bratislava, Czechoslovakia.On leave from the Institute of Physics, Dúbravská cesta 9, Bratislava, Czechoslovakia.     

Experimental investigation of the elastic modulus of a fractal system—A model of fractured rocks

The elastic properties of a physical model representing a damaged rock matrix were studied using a square lattice deformed under tensile stress. The elastic modulusM of such a system varies in agreement with percolation theory as|x–x _c | ^f , wherex is the damage parameter andx _c the threshold value of the damage parameter,f3.6. Atxx _c the scale dependence ofM can be expressed asML ^–f/v , whereL is the size of the sample andv the correlation exponent in percolation theory.The experimental results are of interest in assessing elastic properties in earthquake focal zones and fault zones in general.     

Spatial analysis of elements in soils from Chengdu City

Three kinds of spatial analysis methods （geostatistics, concentration-area fractal model and the multifractal analysis called the moment method） were used for almost 50 elements, including heavy metals, disperse elements, rare elements and even others, in 6586 top soil （0-20 cm） samples and 1833 deep soil （150-200 cm） samples from Chengdu metropolitan area of 12400 km^2, southwestern China. The ranges of spatial correlation revealed by variograms are quite different for different kinds of elements in the top and deep soils. The most interest is the fact that the multifractal spectra of environmentally important elements such as Pb, Cr, Cd and Ni in top soils in the metropolitan area show systematic change from those in the deep soils, revealing a strong anthropogenic addition, while Hg, Zn, As, Cu and all common elements show no such kind of addition. In terms of multifractal properties based on the multifractal spectrum curves, those disperse and rare elements show great deviation from other major and trace elements, which is also of great interest.     

川中丘陵区土壤颗粒分形特征

分析了27个紫色土丘陵区土壤样品的机械组成，运用分形模型计算出土壤颗粒分形维数D（D=2．817—3．030），探讨了分形维数D与土壤粒度组成、土壤抗蚀性之间的关系，并分析了不同土地利用方式下土壤颗粒分形维数D与土壤有机质含量（O．M）、土壤容重（B.D）的相关关系。研究表明：土壤颗粒分形维数D能够很好的表征土壤质地，重点反映〈0．05mm的细颗粒物质，尤其是粘粒，其次是粉粒；与土壤有机质含量（O．M）、土壤容重（B．D）均达到极显著水平；其次分形维数D还能作为评价土壤水土流失和土壤生态恢复的指标。