Fractally Invariant Distributions and an Application in Geochemical Exploration     

Wei Shen  D. R. Cohen 《Mathematical Geology》2005,37(8):895-913

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.  相似文献   

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   总被引：4，自引：1，他引：4       下载免费PDF全文

吴树仁  韩金良  石菊松  张永双  何锋  董诚 《地球学报》2005,26(5):455-460

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。  相似文献   

基于"3S"技术的于田绿洲湿地动态变化研究   总被引：7，自引：4，他引：7  

刘玉安  塔西甫拉提·特依拜  沈涛  张玉虎 《中国沙漠》2005,25(5):706-710

以极端干旱区典型绿洲———于田绿洲为研究区,采用遥感(RS)、地理信息系统(GIS)和全球定位系统(GPS)相结合的方法,进行了湿地资源调查,查明了于田绿洲湿地类型、区域分布及面积,应用模型和分形理论,探讨了于田绿洲湿地的动态变化特征,并分析了其发生动态变化的原因。研究结果对于干旱区绿洲湿地的合理开发和可持续发展有着重要现实意义。  相似文献   

Piecewise prediction model for watershed‐scale erosion and sediment yield of individual rainfall events on the Loess Plateau,China          下载免费PDF全文

Yu Guo‐Qiang  Zhang Mao‐Sheng  Li Zhan‐Bin  Li Peng  Zhang Xia  Cheng Sheng‐Dong 《水文研究》2014,28(21):5322-5336

Establishing a universal watershed‐scale erosion and sediment yield prediction model represents a frontier field in erosion and soil/water conservation. The research presented here was conducted on the Chabagou watershed, which is located in the first sub‐region of the hill‐gully area of the Loess Plateau, China. A back‐propagation artificial neural model for watershed‐scale erosion and sediment yield was established, with the accuracy of the model, then compared with that of multiple linear regression. The sensitivity degree of various factors to erosion and sediment yield was quantitatively analysed using the default factor test. On the basis of the sensitive factors and the fractal information dimension, the piecewise prediction model for erosion and sediment yield of individual rainfall events was established and further verified. The results revealed the back‐propagation artificial neural network model to perform better than the multiple linear regression model in terms of predicting the erosion modulus, with the former able to effectively characterize dynamic changes in sediment yield under comprehensive factor conditions. The sensitivity of runoff erosion power and runoff depth to the erosion and sediment yield associated with individual rainfall events was found to be related to the complexity of surface topography. The characteristics of such a hydrological response are thus closely related to topography. When the fractal information dimension is greater than the topographic threshold, the accuracy of prediction using runoff erosion power is higher than that of using runoff depth. In contrast, when the fractal information dimension is smaller than the topographic threshold, the accuracy of prediction using runoff depth is higher than that of using runoff erosion power. The developed piecewise prediction model for watershed‐scale erosion and sediment yield of individual rainfall events, which introduces runoff erosion power and runoff depth using the fractal information dimension as a boundary, can be considered feasible and reliable and has a high prediction accuracy. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

Hydrological impact of a reservoir network in the upper Gan River Basin,China     

Ningpeng Dong  Zhongbo Yu  Chuanguo Yang  Mingxiang Yang  Wenzhuo Wang 《水文研究》2019,33(12):1709-1723

  相似文献   

Size and spatial distribution of loess slides on the Chinese Loess Plateau     

Haijun Qiu  Sheng Hu  Xingang Wang  Dongdong Yang  Yanqian Pei  Shuyue Ma 《自然地理学》2020,41(2):126-144

ABSTRACT

The size and spatial distribution of loess slides are important for estimating the yield of eroded materials and determining the landslide risk. While previous studies have investigated landslide size distributions, the spatial distribution pattern of landslides at different spatial scales is poorly understood. The results indicate that the loess slide distribution exhibits a power-law scaling across a range of the size distribution. The mean landslide size and size distribution in the different geomorphic types are different. The double Pareto and inverse gamma functions can coincide well with the empirical probability distribution of the loess slide areas and can quantitatively reveal the rollover location, maximum probability, and scaling exponents. The frequency of loess slides increases with mean monthly precipitation. Moreover, point distance analysis showed that > 80% of landslides are located < 3 km from other loess slides. We found that the loess slides at the two study sites (Zhidan and Luochuan County) in northern Shaanxi Province, China show a significant clustered distribution. Furthermore, analysis results of the correlated fractal dimension show that the landslides exhibit a dispersed distribution at smaller spatial scales and a clustered distribution at larger spatial scales.  相似文献   

Stroke构造、移位一体化的道路网示意化方法     

付仲良  翁宝凤  胡玉龙 《测绘学报》2016,45(9):1115-1121

针对当前常用示意性地图生成方法中往往存在简化程度不够、未考虑长度信息以及时间效率低等问题,提出了stroke构造、移位一体化的道路网示意化方法。该方法在对道路网进行stroke划分构造的同时,直接对其进行渐进式的移位示意化及拓扑检查。同时本文还提出利用相似分形维数来定量比较并验证不同示意化方法的有效性。试验表明,本算法在考虑原始线形的基础上,示意化过程简单,时间效率较高,减少了拓扑冲突问题,保证了拓扑一致性及路网的均衡分布,具有较好的清晰度和认知度。  相似文献   

广义残差地形模型及其在局部重力场逼近中的应用     

吴怿昊  罗志才  周波阳 《测绘学报》2016,45(5):531-537

研究了残差地形模型中的非调和性问题,比较了基于棱柱体和球冠体的积分模型,提出了基于球冠体积分的广义残差地形模型。以泊松小波径向基函数为构造基函数,结合广义残差地形模型,融合多源实测重力数据构建了局部区域重力场模型。研究结果表明:基于棱柱体积分的残差地形模型精度较低,在山区可能引入毫伽级以上的误差,建议采用更为接近真实地形表面的球冠体积分模型。相比于原始的残差地形模型,基于球冠体积分的广义残差地形模型能更为精确地逼近局部重力场模型中地形因素引起的高频效应。  相似文献   

基于规则格网的DEM插值实验     

张一帆  王青山 《测绘工程》2016,25(2)

通过地形建模,将6个地形隶属函数按照101×101,112×112,126×126,144×144,168×168,201×201,257×257 7种格网密度生成6种局部地形单元的规则格网DEM;使用反距离加权(IDW)等7种插值算法,将前6种格网密度下的DEM插值成257×257规格;从原始257×257DEM中随机抽取检查点计算残差,并对残差中误差进行分析。通过分组插值实验,运用控制变量法、方差分析等方法研究地貌类型、采样密度和插值算法对DEM插值精度的影响。  相似文献   

华北克拉通基底花岗质片麻岩变形和流变学研究——以辽西寺儿堡地区为例   总被引：2，自引：0，他引：2  

李婧  刘永江  李伟民  金巍  梁琛岳  温泉波  张媛媛 《大地构造与成矿学》2016,(5):891-907

辽西寺儿堡镇新太古代花岗质片麻岩内发育的宏观、微观构造变形特征表明该地区曾遭受了强烈的韧性变形改造。花岗质岩石变形程度在初糜棱岩–糜棱岩之间,岩石经历了SWW向左行剪切作用改造。岩石中石英有限应变测量判别结果表明,构造岩类型为L-S型,为平面应变。岩石的剪应变平均值为1.43,运动学涡度值为0.788~0.829,指示岩石形成于以简单剪切为主的一般剪切变形中。此外,石英颗粒以亚颗粒旋转重结晶和颗粒边界迁移重结晶作用为主,长石颗粒塑性拉长,部分发生膨凸式重结晶作用;石英组构特征(EBSD)揭示石英以中–高温柱面滑移为主;石英颗粒边界具有明显的分形特征,分形维数值为1.151~1.201,指示了中高温变形条件。综合石英、长石的变形行为、石英组构特征以及分形法Kruhl温度计的判别结果,推断辽西寺儿堡镇新太古代花岗质片麻岩经历过480~600℃的中高温变形,其同构造变质相为高绿片岩相-低角闪岩相。花岗质岩石的古差异应力为10.62~12.21 MPa,估算的应变速率为10~(–11.67)~10~(–13.34) s~(–1),即缓慢的变形,可能记录早期中高温、低应变速率的韧性变形过程,反映华北克拉通基底中下部地壳变形特征。  相似文献