构造-流体-成矿作用的分形与混沌动力学

系统分析总结了构造活动与裂隙-脉体系统的分形生长,构造活动、流体作用及矿物沉淀之间的非线性反馈作用以及具分形结构与混沌特征的矿物沉淀和矿床的形成过程。以湘西金矿、水口山铅锌金多金属矿田等典型矿床为例,研究发现,水口山铅锌金多金属矿田地层及岩体内的元素含量分布均呈单分形关系,而断裂带内动性较强的Cu、Pb、Zn等成矿元素的元素具有双分形关系,产生了新的元素分布规律,指示断裂活动促进了成矿元素富集,湘西金矿石英脉是通过分形生长向着脉体长度-厚度分维值a值先减小(对应着脉体的膨胀)然后增大(对应着脉体的伸长)的趋势发展演化的,且该矿床各中段金品位空间变化序列均为非线性演化序列,其成矿流体的演化及成矿元素的沉淀富集成矿过程为混沌动力学过程。这些结果表明,构造-流体-成矿作用具有分形结构特征,并具体表现为断裂体系的分形分布,矿床的分形分布,裂隙-脉体系的分形分布和品位分布的分形变化等。成矿元素活化、迁移及沉淀的复杂动力学过程中,构造活动控制了裂隙-脉体系统的分形生长与矿床的就位,且存在于构造活动、流体作用及矿物沉淀之间的非线性反馈作用最终导致了具分形结构与混沌特征的矿物沉淀和矿床的形成。     

基于分形理论的安徽省城市体系规模分布研究

文章通过测算安徽省近20年来城市体系规模分布的分维值，对该省城市体系规模现状及演化进行了具体分析，得出以下结论：现今安徽省城市规模分布较集中，人口分布呈现低水平均衡状态；1988年以来，就城市体系规模结构的演化特点来看可分为两个阶段：1988年-1999年，城市规模分布趋于集中；而进入2000年以来，城市规模分布趋于分散。并分析了这种现状及演化的原因，提出若干优化城市体系和促进经济发展的建议。     

用动态重结晶石英颗粒的分形确定变形温度及应变速率

韧性变形岩石中动态重结晶石英颗粒边界形态具有自相似性，表现出分形特征。动态重结晶石英颗粒边界的分形维数随温度的升高而减小，随应变速率的增加而增大，可作为韧性变形温度及应变速率的标度计。适合重结晶石英边界分维值的计算方法有封闭折线法和面积周长法。鲁西青邑韧性剪切带中糜棱岩动态重结晶石英颗粒边界具有自相似性，分维值为1.228～1.326，初步估算出古应变速率为10     

Numerical Modelling of Ore-forming Dynamics of Fractal Dispersive Fluid Systems

Based on an analysis of the fractal structures and mass transport mechanism of typical shear-fluid-ore formation system, the fractal dispersion theory of the fluid system was used in the dynamic study of the ore formation system. The model of point-source diffusive illuviation of the shear-fluid-ore formation system was constructed, and the numerical simulation of dynamics of the ore formation system was finished. The result shows that: (1) The metallogenic system have nested fractal structure. Different fractal dimension values in different systems show unbalance and inhomogeneity of ore-forming processes in the geohistory. It is an important parameter to symbolize the process of remobilization and accumulation of ore-forming materials. Also it can indicate the dynamics of the metallogenic system quantitatively to some extent. (2) In essence, the fractal dispersive ore-forming dynamics is a combination of multi-processes dominated by fluid dynamics and supplemented by molecule dispersion in fluids and     

利用稀土分布分形结构因子对碱性花岗岩稀土组成分类——以东准噶尔花岗岩为例

尝试用稀土分布的分形结构因子（FSF）值对我国碱性花岗岩的稀土组成进行了分类。可将我国碱性花岗岩的稀土分布分形结构因子划分为4种类型：（1）弱变异型（0．98－0．95）；（2）中变异型（0．95－0．92）；（3）强变异型（0．92－0．89）；（4）超强变异型（0．89－0．86）。其中前两种类型可很好地对应重稀土富集型和中稀土亏损型花岗岩，而后两种类型可对应轻稀土相对富集型和轻稀土特富型花岗岩。利用FSF值对新疆东准噶尔地区三带富碱花岗岩按稀土组成进行了归类。     

Changes in magnetic and fractal properties of fractured granites near the Nojima Fault, Japan

Abstract Anisotropy of magnetic susceptibility (AMS) has been used to infer finite strain fabrics in plastically deformed rocks, but there are few studies of magnetic properties in fractured fault rocks. Changes in magnetic and fractal properties of fractured granites from the Disaster Prevention Research Institute, Kyoto University (DPRI) 500 m drilling core towards the Nojima Fault and of the well-foliated fault gouge are described. Fractal analysis of fractured granites shows that the fractal dimension ( D ) increases linearly toward the gouge zone of the fault. In weakly fractured granites ( D = 1.05–1.24), it was found that the degree of AMS correlates positively with the fractal dimension, suggesting a fracture-related magnetic fabric due to fracturing. In strongly fractured granites ( D = 1.25–1.50), weaker, nearly isotropic AMS is found, suggesting erasure by the fragmentation of the magnetic minerals. Within the fault gouge zone, an isotropic AMS fabric was found, as well as twofold increases in magnetic intensity and susceptibility. These changes reflect the production of new magnetite grains, subsequently confirmed by hysteresis studies, which suggests that fault gouge might be regarded as the source of the regional geomagnetic field contrast along active faults. Thus, AMS is clearly a potentially useful tool for inferring the fracturing texture of magnetic minerals in fractured rocks and detecting active faults from the high susceptibility contrast of fault gouge.     

Fractal analysis of 2-D fracture networks of geothermal reservoirs in south-western Turkey

Natural fracture patterns of producing geothermal formations in south-western Turkey are mapped at different scales. The fractal dimensions of different fracture network properties, such as spatial distribution, density, connectivity, orientation, and length are measured by different methods. Analysis of the natural fracture patterns from giga to microscales identifies the descending behavior of box-counting fractal dimension with respect to the scale. It is observed that the fracture networks represent scale-invariant properties, but fractal dimensions might notably differ when the mass dimension is measured applying different methods. Anisotropic nature of fracture networks is also included in the fractal analysis.     

岩石破裂系分形及分维数测定

花岗岩在固体围压三轴压缩下破裂，然后沿主破裂面摩擦滑动（粘滑或稳滑），实际后我们将样品从围压介质铅中剥出来，做成显微薄片。在２０倍显微投影仪下观测其主破裂及裂纹系分布，用尺度法统计并计算裂纹系分维。结果表明，８个样品的无标度区（Ｒ）都相同，但是随尺度变化，分维值表现出分段线性的特征。当０．０５〈Ｒ〈０．１５ｍｍ时，裂纹系分维在１．１２－１．４１之间，主破裂分维在１．０８－１．１５之间；当０．１５〈     

Features of fractal dimension anomaly of radon content in underground water in North China before and after the 1976 Tangshan earthquake

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影像纹理的多标度分形分析

引入目前在分形几何中发展起来的多标度分形理论，发展了影像纹理的多标度分形分析，能够描述纹理结构更多的分形特征，反映影像纹理的局部分维差别，抑制目前仅基于整体分维计算存在的不同分形同分维之弊端，实现影像纹理的多分辨率分析。尽管分维测度是纹理的一个非常重要的特征，但单纯的仅基于分维测度的分析，并不足以表征所有的纹理信息。