Box fractal dimension as a measure of statistical homogeneity of jointed rock masses

A written computer programme to estimate the box fractal dimension (D_B) is verified by estimating D_B of the triadic Koch curve for which the theoretical D is known. The influence of a number of input parameters of the box-counting method on the accuracy of estimated D_B is evaluated using the same Koch curve. The employed size range of the applied box networks was found to be the parameter which has the strongest influence on the accuracy of estimated D_B. This indicated the importance of finding the range of self-similarity or self-affinity for the object considered to select the proper range for the box sizes and, in turn, to obtain accurate estimates of D_B. By calculating D_B for different block sizes sampled from three generated two-dimensional joint patterns, it is shown that D_B can capture the combined effect of joint-size distribution and joint density on the statistical homogeneity of rock masses. The spatial variation of D_B along a 350 m stretch of a tunnel in the shiplock area of the Three Gorges dam site is computed using the joint data mapped on the walls and the roof of the tunnel. This spatial variation of D_B is used, along with the visual geological evaluation of the joint trace maps of the tunnel, in making decisions about statistical homogeneity of the rock mass around the tunnel. The results obtained on statistically homogeneous regions were found to be quite similar to the results obtained from a previous statistical homogeneity investigation which incorporated the effect of number of joint sets and their orientation distributions, but not the spatial variation of D_B. It is recommended that the spatial variation of D_B is used, along with the results of other methods such as contingency table analysis and equal area plots, which incorporate the effect of joint orientation distribution, in addition to the geology of the site, in determining the statistically homogeneous regions of jointed rock masses.     

人工冻土破碎块度分布的分形性质

从分形几何的观点出发，通过对冻土模型的爆破试验，着重对试样爆后破块块度分析进行了统计分析。结果表明，冻土爆后块度分布是个分形，分形维数不仅是反映冻土破碎程度恰当的统计特征量，而且与试样冻结温度密切相关，还探讨了分维值与冻土抗压强度的关系。     

构造因素对半地堑盆地的层序充填的影响

运用平衡剖面分析和构造物理模拟实验方法研究了典型铲式正断层模型上盘盆地的发育过程．研究表明，铲式正断层的产状以及断层上盘的变形方式直接影响上盘盆地的形态和沉积层序结构．简单铲式正断层的上盘发育相对简单的半地堑盆地，复杂铲式（坡坪式）正断层的上盘则发育包含有内部次级背斜凸起和向斜凹陷的复式半地堑，而且半地堑盆地的宽度与拆离断层面深度成正比．在沉积物补偿充填的情况下，渐进伸展将使半地堑的宽度也保持不变，从而使半地堑构造斜坡上产生“视水退”的层序结构现象，并且使盆地中“垂向加积”的沉积层序演变为宏观上“侧向加积”的沉积层序．这种由构造因素对半地堑盆地的层序充填的影响在渤海湾盆地的部分老第三纪断陷中得到印证．     

西北地区城市规模分形结构的研究

本文利用分形理论和相空间概念，从理论的角度演绎推导出城市规模分形结构的一般模式，并以此为基础，结合西北地区自然，经济，社会状况，对五省萄城市规模分形结构进行初步分析，为深入研究其城市体系，制定城市，区域发展战略提供一定的参考。     

泥石流的分形特征及其意义

分析了泥石流流体和堆积物粒度分布的分形结构特征，其分维值介于２￣３之间，平均值分别为２．７１和２．６５左右。研究了泥石流沟水系的分形特征及其在不同观察尺度下分维的变化特征，结果表明，分维可作为描述泥石流粒度成分和泥石流沟水系的参数，反映了泥石流活动的形成演化特征，在此基础上，论述了分维的研究意义。     

岩石断面的分形测量及其分维的计算

在实验室内使岩石单轴压缩直至破裂,用位移传感器测量其断面高度,用显微镜观测断面切片的剖线,所得数据用尺度法计算其分维,各种岩石的不同曲线的分维在1.002-1.028之间,与野外断层主迹线分维值相同.用切岛法计算整个断面的分维约为2.05左右.有关分析和计算认为,分维的大小与岩石破裂时所受力的方向有关,与采样步长有关,而与岩石样品的大小无关.     

模糊分维及其在地震研究中的某些应用

在模糊集理论与分形理论的基础上,引进了模糊分维的概念;给出了模湖容量维D₀与模糊关联维D₂的定义与确定方法;讨论了模糊分维与常用的分维（清晰分维）的关系.给出了模糊分维在地震研究中的应用结果: 1.根据模糊容量维D₀随时间的上升趋势变化,可以划分出大地震活动的高潮期;由模糊容量维D₀与模糊关联维D₂随时间变化的曲线,可以分析识别大地震前的中长期前兆异常. 2.根据模糊容量维D₀随空间和时间的变化,可以划分出未来大震所在的地区,并可发现大震前数年D₀呈现增大或减小的趋势. 3.根据前兆数据的模糊时间分维D₀随时间的变化,可以发现大地震的短期前兆异常.     

初探地震活动的时间分维特征

本文运用分维的概念和方法,对我国部分强震前地震活动时间分维,前震震群活动时间分维,7级以上大地震的余震活动时间分维和小震群活动时间分维进行了计算。初步结果表明,同一类型的地震活动(如强震前较大时空范围内地震活动、强震的余震、前震震群、小震群等类型)的时间分维十分相近,而不同类型地震活动的时间分维存在着差异,一般说来,强震前的地震活动比较普遍地存在降维现象,表现出临近强震时,震源及附近地区地震活动时间结构的有序性增强。这为地震预报开辟了一个新的途径。     

Fractal Method for Statistical Analysis Geological Data

This paper establishes the phase space in the light of spacial series data,discussesthe fractal structure of geological data in terms of correlated functions and studies thechaos of these data.In addition,it introduces the R/S analysis for time series analysisinto spacial series to calculate the structural fractal dimensions of ranges and standard de-viation for spacial series data,and to establish the fractal dimension matrix and the proce-dures in plotting the fractal dimension anomaly diagram with vector distances of fractal di-mension.At last,it has examples of its application.     

Lyapunov exponent and dimension of the strange attractor of elastic frictional system

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