R/S analysis of earthquake time interval

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城市分形中心与占优标度区选择

用回转半径法研究城市分形特征时,中心点位置的选择至关重要。以反映城市基础设施情况的兴趣点(point of interest,POI)作为基础数据,分析中心点位置对标度区识别的影响。将POI几何中心、重心、密度中心、中心城区几何中心和重心5种统计中心作为待选中心,给出辐射范围、核心密度与分形维数、中心漂移度等标度区相关指标,提出判断占优标度区的POI数量最大化原则。通过统计中心与地标中心标度区对比,确定城市分形中心和占优标度区。省会城市及直辖市标度区分析结果显示:统计中心各有优劣,占优中心总体上更倾向于POI几何中心和密度中心,地标中心有时优于统计中心;密度中心对应的占优标度区半径维数较低,若半径维数太低则容易陷入局部密度中心;中心漂移度指标表明可能存在更好的分形中心选择方案。     

Influences of different surveying and mapping methods on fractal characteristics of gully-head shoulder lines

Abstract

Accurate quantification of gully shoulder lines (gully borderlines) will help better understand gully formation and evolution. Surveying and mapping are the most important ways to obtain precise morphology. To evaluate the influences of different steps of surveying and of curve-fitting methods of mapping on the morphology of the shoulder line characterized by fractal dimensions, 13 shoulder lines at gully heads were surveyed using a total station and then mapped with different methods of curve fitting, with the fractal dimensions calculated by maps compared with those measured in the field. Fractal dimensions by field measurement ranged from 1.185 to 1.456. Compared with field measurements, the average absolute errors of polygonal line, quadratic B-spline, and arc-fitting methods are 0.045, 0.040, and 0.046, respectively; the average relative errors are 3.48, 3.13, and 3.59%. Therefore, the quadratic B-spline method has a higher accuracy. The standard error of the fractal dimension tends to be larger as average step length increases. The error is ~5% when the step length is 0.7 m, which is advisable for field surveying. This study will help promote the efficiency of field surveying and mapping, and thus promote the accuracy and credibility of gully morphology.     

高密度电阻率法成像

介绍在地质大学电法科研组“高密度电阻率法正、反演软件”的基础上,研制高密度电阻率法2.5维电阻率成像系统;讨论不平地形条件下高密度电阻率法2.5维电阻率成像的算法和软件,可用于九种常用电极装置观测结果的电阻率成像。对理论和实测数据的成像结果表明,该成像系统程序运行稳定,成像效果很好。     

能源生产的分形研究——以新疆为例

根据能源生产的实际领域年产量观测值带有一定的延续性而非随机性的特点,利用分形理论的基本原理,将不确定的非线性系统数量化,构造新疆能源生产领域时间序列,通过计算能源生产的分形结构特征和分维值,在无规则中找到秩序。并分析其代表的实际意义,以便更好地为能源生产方面的决策提供依据。     

Failure Process after Peak Strength of Artificial Joints by Fractal Dimension

Because lack of information when the joints exhibit strain softening behavior, the transition from peak to residual values is assumed to decrease either linearly or exponentially. Also, displacement of slide side after peak is much larger than the peak displacement and the stress approaches the residual state, thus studying failure process after peak strength is very important. In this research, three types of artificial joints with tooth-shaped asperity under repeated direct-shear were tested. Continuously movement of slide side after peak strength was monitored during shearing test. Reduction of shear parameters was examined according to two failure criteria (Barton and Patton). JRC value (Joint Roughness Coefficient) for a given profile was estimated by fractal dimension. One of the results of this study is that Barton’s criterion predicts a good estimation of residual strength and the second result is when the amount of fractal dimension of a joint surface increases, the JRC amount also increases, and with having value of h (height average) and l (base average) of a tooth-shaped asperity can determine the JRC of joint surface. M. Askari is a M.Sc Student of Engineering Faculty, Mining Engineering Department, Tarbiat Modares University, Tehran.     

度量映射方法在河流分维测算中的应用

应用TM卫星图像数据，根据对黑龙江省阿什河约80km河段、松花江及嫩江约2300km河段的分维研究。证明了在度量数列满足持邻性和等比收敛性的条件下。可以应用度量映射方法计算随机分形集的分维。研究表明，黑龙江省阿什河河段（约80km）的分维比松花江和嫩江河段（约2300km）的分维高；曲线的分维一定要与标度的变化区间联系起来，否则分维将失去可比性；河流的分维不仅与标度有关，还与矢量化时原图像的分辨率有关。     

分形在下庄铀矿田中的应用

本文运用分形理论对下庄地区铀矿床(矿点)的空间分布进行了研究。结果表明,铀矿床(矿点)的空间分布具有统计自相似性的分形特征,分数维可以用来定量描述铀矿床(矿点)的分布规律;应用盒计维数的统计方法计算了铀矿床(矿点)空间分布的分数维D值,并对西、中、东成矿活动区的分数维D值进行了比较,探讨了分数维D值的地质意义。实际资料计算结果显示网格数与标度之间具很好的相关性,其相关系数均达0.98以上。     

基于孔隙分形维数的土壤大孔隙流水力特征参数研究

根据数字图像制备分析技术得到大孔隙数目、大小和形状等特征数据,用分形理论计算孔隙分形维数,并对两类不同质地土壤的孔隙分形维数进行分析比较,应用基于孔隙分形维数的大孔隙分形模型,建立了土壤水分特征曲线和非饱和导水率的预测模型。结果表明,孔隙分形维数D_v可定量描述不同质地土壤结构,其模型预测精度优于颗粒大小分布估计的分形模型,可用于实际问题的研究。     

Dimensional parameters of columnar stromatolites as a result of stromatolite ecosystem evolution

Columnar stromatolites representing more than a half of species described in Precambrian stromatolite assemblages reveal a regular trend of size variations during the Proterozoic and Early Paleozoic. Their dimensional parameters grew gradually during the Paleoproterozoic to attain peak values in the Early Riphean and to decline steadily afterward during the Middle-Late Riphean, Vendian, and Cambrian. Size variations are established based on statistically averaged maximum diameters of columns calculated for 230 taxa and on percentages of large, medium and small species occurring in successive units of stratigraphic scale. The units correspond to three Paleoproterozoic subdivisions (time span from 2.3 to 1.65 Ga) and to five subdivisions of the Riphean, Vendian and Early Paleozoic jointly spanning a comparable period of geologic time. The results of calculation depict a unimodal variation curve with one infliction point designating inversion of ascending and descending trends in the Early Riphean time. The inversion and cardinal changes in taxonomic composition of the entire stromatolite community across the Riphean lower boundary appear to be interrelated. Abiotic events, which certainly influenced diversity of all, especially columnar stromatolites, have no manifestation however in the size-variation curve lacking perceptible oscillations in both the ascending and descending branches. Consequently, dimension parameters of columnar stromatolites appear to be independent of direct influence of abiotic events.