岩石材料微、细、宏观断裂机理尺度效应的分形研究

基于同一现场不同尺度的岩石材料,从大量三轴MTS试验岩石断口边痕、试样切割面或磨光面的节理痕迹和现场断裂迹线3个尺度层次,进行了岩石材料微、细、宏观断裂机理尺度效应的分形研究。提出圆与正方形相耦合的分形维数算法,探讨了其优越性并应用于岩石断裂的分形特征研究,得到岩石材料的微、细、宏观断裂机理存在无标度区域。在无标度区0.002 mm～4 000 mm内,岩石断裂构造的分布规律具有自相似性,是岩石材料的微、细、宏观断裂机理内在联系的外在反映,为跨越尺度界限研究岩石节理裂隙的破坏机理提供了可行途径。     

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。     

岩石声发射Kaiser点信号频带能量分布和分形特征研究

通过单轴加载岩石破坏全过程声发射试验,根据Kaiser效应原理采用参数法确定了Kaiser点.在此基础上,首先采用小波包频带分解方法,对岩石声发射Kaiser点信号的能量分布特征进行了研究,分析了砂岩声发射信号的不同频带能量分布规律,得到了Kaiser点特征频带能量百分比大于相邻点的重要结论.其次,采用G-P算法计算了声发射过程关联分维数,结果表明声发射过程不仅具有分形特征,而且Kaiser点声发射信号关联分维数小于其相邻点,其结论可作为通过波形分析识别Kaiser点的特征.     

三峡库区巴东县城附近主要滑坡边界轨迹分形分维特征与滑坡稳定性关系

为了探索复杂滑坡轨迹结构演化及其稳定性定量分析计算的新途径，本文利用分形分维理论，分析三峡库区巴东县城附近滑坡边界轨迹的几何分形结构，并采用盒维数法分别求得巴东县城附近11个滑坡边界轨迹的分维值，计算结果表明：每个滑坡的轨迹结构具有其特征性的分维值，轨迹结构越复杂，结构层次越清楚，分维值越高；其中，榨房坪滑坡和黄腊石滑坡的分维值最高，分别为1.50和1.483，西壤口和谭家湾滑坡的分维值最低，分别为0.925和0.732；而黄土坡和赵树岭滑坡的分维值介于二者之间，分别为1.111和1.091。结合典型滑坡边界轨迹结构演化与滑坡稳定性关系的定性分析及前期滑坡稳定性定量计算和模拟分析，初步揭示：滑坡边界轨迹结构与稳定性是密切相关的，滑坡边界轨迹宏观扩展增值越明显，轨迹结构越复杂，分维值越高，其稳定性条件也越差，因此，分数维可作为衡量滑坡轨迹结构复杂性和稳定性的重要标志；滑坡边界轨迹宏观扩展变形存在一个极限，超过这个极限滑坡的局部失稳就转化为整体滑动；而滑坡边界轨迹则记录了滑坡变形扩展现象和信息，因此，相对应地滑坡轨迹分形结构的分维值也应存在一个极值，在极值点滑坡体处于临滑状态；滑坡边界轨迹结构的极限分维值大致为1.4～1.5，此时滑坡接近于整体极限失稳状态，而分维值在1.1～1.3之间则表示滑坡处于整体稳定，局部存在潜在失稳状态，分维值小于1则表示滑坡处于相对稳定状态。     

Correlation Fractal and Multifractal Characteristics of Seismic Activity in the Taiwan Area, China

Based on the analysis of newly collected data of plate tectonics, distribution of active faults and crustal deformation, the Taiwan area is divided into two seismic regions and six seismic belts. Then, correlation fractal dimensions of all the regions and belts are calculated, and the fractal characteristics of hypocenteral distribution can be quantitatively analyzed. Finally, multifractal dimensions Dq and f(α) are calculated by using the earthquake catalog of the past 11 years in the Taiwan area. This study indicates that (1) there exists a favorable corresponding relationship between spatial images of seismic activity described with correlation fractal dimension analysis and tectonic settings; (2) the temporal structure of earthquakes is not single but multifractal fractal, and the pattern of Dq variation with time is a good indicator for predicting strong earthquake events.     

Fractally Invariant Distributions and an Application in Geochemical Exploration

Fractal modelling has been applied extensively as a means of characterizing the spatial distribution of geological phenomena that display self-similarity at differing scales of measurement. A fractal distribution exists where the number of objects exhibiting values larger than a specified magnitude displays a power-law dependence on that magnitude, and where this relationship is scale-invariant. 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. Population limits, derived from fractal modelling using a summation method, are compared with those derived from more conventional probability plot modelling of stream sediment geochemical data from north-eastern New South Wales. Despite some degree of subjectivity in determining the number of populations to use in the models, both the fractal and probability plot modelling have assisted in isolating anomalous observations in the geochemical data related to the occurrence of mineralisation or lithological differences between sub-catchments. Thresholds for the main background populations determined by the fractal model are similar to those established using probability plot modelling, however the summation method displays less capacity to separate out anomalous populations, especially where such populations display extensive overlap. This suggests, in the geochemical data example provided, that subtle differences in the population parameters may not significantly alter the fractal dimension.     

http://www.sciencedirect.com/science/article/pii/S1674987110000320

The self-similar is a common phenomena arising in the field of geology.It has been shown that geochemical element data,mineral deposits,and spacial distribution conform to a fractal structure.A fractal distribution requires that the number of objects larger than a specified size have a power-law dependence on size.This paper shows that a number of distributions,including power-function,Pareto, lognormal,and Zipf,display fractal properties under certain conditions and that this may be used as the mathemat...     

基于分形几何理论的DFN模型构建方法研究

以重庆梁-忠（梁平县-忠县）高速公路礼让隧道为工程研究背景,通过测线法调查现场节理,获得了节理产状分布概率密度函数,并从分形几何学的角度分析了节理间距及迹长的分形分布规律,推导出能反映节理间距及迹长分布状态的分形维数D及分形分布概率密度函数。在该基础上采用Matlab软件以及Monte-Carlo随机分析方法,产生节理参数随机数,结合3DEC中最新模块离散裂隙网络(DFN)技术,建立了能反映节理裂隙分布特征的离散裂隙网络模型并验证了模型的有效性,结果表明,分形分布比负指数分布包含更多的间距、迹长分布信息,更接近于实际分布;分形维数D反映了节理间距、迹长在其变化范围内的分布特征,分形维数的大小取决于小间距、小迹长部分数量在总节理数量中的比例,为节理裂隙岩体网络模型构建提供了一种新方法。     

Selection of Less Biased Threshold Angles for SAM Classification Using the Real Value–Area Fractal Technique

The accuracy of classification of the Spectral Angle Mapping (SAM) is warranted by choosing the appropriate threshold angles, which are normally defined by the user. Trial‐and‐error and statistical methods are commonly applied to determine threshold angles. In this paper, we discuss a real value–area (RV–A) technique based on the established concentration–area (C–A) fractal model to determine less biased threshold angles for SAM classification of multispectral images. Short wave infrared (SWIR) bands of the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) images were used over and around the Sar Cheshmeh porphyry Cu deposit and Seridune porphyry Cu prospect. Reference spectra from the known hydrothermal alteration zones in each study area were chosen for producing respective rule images. Segmentation of each rule image resulted in a RV–A curve. Hydrothermal alteration mapping based on threshold values of each RV–A curve showed that the first break in each curve is practical for selection of optimum threshold angles. The hydrothermal alteration maps of the study areas were evaluated by field and laboratory studies including X–ray diffraction analysis, spectral analysis, and thin section study of rock samples. The accuracy of the SAM classification was evaluated by using an error matrix. Overall accuracies of 80.62% and 75.45% were acquired in the Sar Cheshmeh and Seridune areas, respectively. We also used different threshold angles obtained by some statistical techniques to evaluate the efficiency of the proposed RV–A technique. Threshold angles provided by statistical techniques could not enhance the hydrothermal alteration zones around the known deposits, as good as threshold angles obtained by the RV–A technique. Since no arbitrary parameter is defined by the user in the application of the RV‐A technique, its application prevents introduction of human bias to the selection of optimum threshold angle for SAM classification.     

岩层厚度对碳酸盐岩构造裂缝面密度和分形分布的影响

岩层厚度对于碳酸盐岩构造裂缝的发育起到重要作用.新疆柯坪大湾沟、青松和蓬莱坝构造性质比较稳定,剖面的构造裂缝测量结果统计分析表明,碳酸盐岩构造裂缝面密度与层厚呈负相关关系,层厚越大,构造裂缝面密度越小,但裂缝规模较大;随着层厚减薄,构造裂缝面密度线性增大,但裂缝规模较小.碳酸盐岩构造裂缝具有良好的分形特征,统计结果显示...