基于ArcGIS的DEM水系盒维数的计算

水系分形维数的计算与分析,有助于深入理解其与地貌发育、流域径流和侵蚀产沙等过程之间的关系。本文从分形维数的计算原理出发,结合目前最流行的GIS软件,提出了新的水系盒维数计算方法,并以安塞纸坊沟流域为例,说明该方法能较好地反映流域地貌特征。     

DEM在构造地貌定量分析中的应用与展望

作为一种描述地形起伏特征的数据模型,数字高程模型（Digital Elevation Model,DEM）通过有限的地形高程数据实现对地形曲面的数字化模拟（即地形表面形态的数字化表示）,为研究地表的演化过程提供了数据基础。文章归纳梳理了DEM在基本地形因子、流域地貌特征、古地貌面的重塑、构造地貌发育模式、地貌分类与制图以及地形特征提取算法等领域的应用现状。总的来看,DEM研究对象以陆地为重点,以河流地貌和山地地貌为主要内容;研究过程从早期对地貌形态的定性描述向多种地貌参数的半定量、定量分析转变;研究尺度空间上从某个小流域到整个造山带,时间上从数小时向百万年扩展。构造地貌演化时间序列的不确定性、地貌参数获取的复杂性、地形模型算法的多样化以及DEM生成过程中的误差因素,这些均影响构造地貌定量分析结果的准确度,因此在归纳梳理已有研究成果的同时,对DEM在构造地貌研究领域的应用进行了一些思考。      

基于DEM的典型地貌区河流形态特征分析

为分析不同地貌类型区的河流形态特征差异,遴选了川中丘陵区、黄土高原、辽河平原三个不同地貌类型区,选择西江河、清水川及沙河的代表性小流域,基于数字地形分析方法,计算了三个样区的分形维数、地形起伏度、平均坡度,对比了丘陵、高原、平原三种地形条件下中小起伏山地河网形态的差异。研究表明:三个小流域河网的分支比分别为3.46、4.45、4.20,长度比分别为1.87、2.48、2.05;河网分形维数为1.99、1.64、1.99。Horton参数能够较好地刻画流域发育状况,可以为不同地貌类型河流形态特征分析提供参考。     

基于高分辨率DEM数据的分形几何岩性识别方法初探

多重分形理论的建立为研究自然地物带来了新的方法。自然地物由于其独特的分形特征,适合采用多重分形等非线性方法来进行定量描述。文章利用遥感重点实验室机载激光雷达测量生成的DEM数据,对不同类型岩石进行了分形几何特征研究,发现不同岩性分布区的DEM多重分形谱存在差异性。多重分形谱f(ɑ)值随ɑ值变化出现大小差异体现了纹理在不同尺度的差异,此特征对于遥感纹理分类和岩性信息提取有重要意义。     

红层软岩遇水作用的孔隙结构多重分形特征

红层软岩内部孔隙具有随机、多样化的分布特点,孔隙结构的变化是影响其宏观力学性能的关键所在。由SEM扫描电镜获取岩样不同饱水时间下的细观结构图像,根据盒维数法计算出孔隙的分形维数,发现随着饱水时间的加长,孔隙的分形维数呈现增大趋势。同时对孔隙的数量、大小进行统计分析,得出不同饱水时间下岩样内部孔隙的分布特征。基于多重分形理论,采用统计矩的方法对孔隙结构进行定量表征。结果表明,孔隙结构的分配函数与q阶次趋于线性关系,验证了该结构的自相似性与无标度性,由广义分形维数D(0)>D(1)>D(2)说明了孔隙具有多重分形特征,由多重分形谱参数分析了孔隙结构的不规则性与复杂程度,更好地表征孔隙大小各异的分布情况。结合孔隙结构的多重分形特征与岩样抗压强度,建立起孔隙结构变化与其力学性能的关联性,对研究红层软岩的损伤过程具有一定的指导意义。     

基于DEM的单沟泥石流危险性定量评价

DEM(Digial Elevaion Model)是地貌景观高程信息的数字表达,能够直观的反应地形地貌条件。泥石流形成和运动受其流域地貌条件的制约,流域系统信息是地貌发育状态的定量描述;故其值能够作为描述泥石流危险性的一种定量化指标。该研究在对甘肃南部地区白龙江流域的252条泥石流沟的基本参数统计分析基础上,选取其中45条泥石流单沟;通过DEM数据拟合其沟谷高程—面积抛物线方程,计算单沟泥石流流域面积—高程函数积分S;在缺乏流域其他环境因子参数的情况下,定量化描述泥石流危险性。     

基于DEM的单沟泥石流危险性定量评价

DEM(Digial Elevaion Model)是地貌景观高程信息的数字表达,能够直观的反应地形地貌条件。泥石流形成和运动受其流域地貌条件的制约,流域系统信息是地貌发育状态的定量描述;故其值能够作为描述泥石流危险性的一种定量化指标。该研究在对甘肃南部地区白龙江流域的252条泥石流沟的基本参数统计分析基础上,选取其中45条泥石流单沟;通过DEM数据拟合其沟谷高程—面积抛物线方程,计算单沟泥石流流域面积—高程函数积分S;在缺乏流域其他环境因子参数的情况下,定量化描述泥石流危险性。     

基于多重分形的花岗岩结构区分方法初探——以蓝田铀矿花岗岩样品为例

自然地物表面复杂,难以用普通的数学参量进行表达,多重分形理论提供了一种对自然地物进行定量描述的新方法。花岗岩型铀矿床是我国4大铀矿床类型之一,因而研究花岗岩结构的定量特征,能为遥感找矿提供信息。文章通过对花岗岩的手标本照片进行分形几何特征研究,介绍了使用盒维数和多重分形谱对手标本照片进行计算的方法,计算结果表明对于成分相同粒度结构不同的花岗岩,盒维数和多重分形谱均存在与粒度结构相关的差异,这些差异对于遥感岩性识别具有重要意义。     

云贵高原北盘江流域构造地貌特征分析

云贵高原位于青藏高原东南侧,新生代以来伴随着青藏高原的隆升而发生了一系列构造抬升运动。北盘江发源于滇东,自西北向东南流经云贵高原向广西丘陵过渡的斜坡地带。选取北盘江作为研究区,通过提取流域河流地貌参数来研究新构造运动,定量化分析研究区的构造地貌特征。利用30 m分辨率的数字高程模型(DEM)数据,通过GIS技术提取北盘江水系流域的河流地貌参数,包括子流域的面积高程积分(HI)、流域盆地倾斜指数(AF)、河长阶梯指数(SL)、谷底宽度与谷肩高度比(VF)等,并综合分析区域地质构造背景、断层及地震分布等特征。分析表明:4种地貌参数能很好地反映区域构造运动和地貌特征;垭都—紫云断裂在内的一系列断层系统对北盘江中游地区的河流地貌、水系格局、河谷形态等起到了控制性的作用;北盘江流域的地貌演化过程受地质构造作用影响较大,且区域差异明显。     

不同类型地貌的各向异性分形与多重分形特征研究

利用标准偏差法和固定质量法，研究了新疆天山地区3种不同构造地貌单元地形剖线的自仿射分形和多重分形特征。结果表明，在所研究的标度范围内，不同构造地貌单元剖线分维值总体上呈现出高山区大于中低山区大于盆地区特点，同一个地貌研究区不同方向的剖线呈现不同程度的各向异性。多重分形谱Dq的形态和值域范围也呈现出不同特征。研究认为，地貌表面形态并不是完全随机的，而是一种各向异性的分形布朗运动，分维值表征了内外营力作用的方向和强度，渡越长度是自仿射分形研究中的另一个重要参量。利用上述分形特征可定量研究地貌的发展阶段和地貌动力学。     

Discrete multifractals

The concept of multifractal modeling has been used intensively in various fields of science for characterizing measures with self- similarity. It has been shown that multifractal modeling provides powerful tools for characterizing patterns in the spatial distribution of geological quantities and objects. Existing multifractal models were proposed for the purpose of handling spatially intertwined fractals with continuous fractal spectrum f(α) (or continuous codimension function C(γ)). In this paper, these conventional multifractals are termed “continuous multifractals” whereas multifractals with discrete fractal dimensions are termed “discrete multifractals.” The properties of discrete multifractals are investigated. It is shown by various artificial examples and a case study of stratigraphy of Ocean Drilling Program (ODP) site 645 that spatially intertwined fractals/multifractals indeed can have discrete fractal dimensions. Histogram-and moment-based techniques are proposed for discrete multifractal modeling and illustrated using the artificial examples. The new concept of discrete multifractals and associated multifractal modeling yields not only techniques for characterizing multifractals with discrete fractal dimensions but it also provides insight into the relationships between fractals, bifractals, and multifractals.     

Discrete multifractals

The concept of multifractal modeling has been used intensively in various fields of science for characterizing measures with self- similarity. It has been shown that multifractal modeling provides powerful tools for characterizing patterns in the spatial distribution of geological quantities and objects. Existing multifractal models were proposed for the purpose of handling spatially intertwined fractals with continuous fractal spectrum f(α) (or continuous codimension function C(γ)). In this paper, these conventional multifractals are termed “continuous multifractals” whereas multifractals with discrete fractal dimensions are termed “discrete multifractals.” The properties of discrete multifractals are investigated. It is shown by various artificial examples and a case study of stratigraphy of Ocean Drilling Program (ODP) site 645 that spatially intertwined fractals/multifractals indeed can have discrete fractal dimensions. Histogram-and moment-based techniques are proposed for discrete multifractal modeling and illustrated using the artificial examples. The new concept of discrete multifractals and associated multifractal modeling yields not only techniques for characterizing multifractals with discrete fractal dimensions but it also provides insight into the relationships between fractals, bifractals, and multifractals.     

分形统计模型的理论研究及其在地质学中的应用

本文提出了一般分形模型和一般分维数的概念,认为许多地质模型是一般分形模型的特例,指出幂函数分布和帕累托分布是分形统计模型的数学基础,论证了幂函数分布在高端截尾条件下具有尺度不变的分形性质,根据非线性回归模型参数估计的方法,提出了求分维数的新方法,该方法具有许多优点。通过在计算机上产生随机数对分形统计模型进行模拟研究,以及通过实例说明分形统计模型应用的方法及步骤,并解释了分维数的实际意义。     

Time-Varying Multifractal Characteristics and Formation Mechanism of Loaded Coal Electromagnetic Radiation

Dynamic collapses of deeply mined coal rocks are severe threats to miners. To predict the collapses more accurately using electromagnetic radiation (EMR), we investigate the time-varying multifractal characteristics and formation mechanism of EMR induced by underground coal mining. A series of uniaxial compression and multi-stage loading experiments with coal samples of different mechanical properties were carried out. The EMR signals during their damage evolution were monitored in real-time; the inherent law of EMR time series was analyzed by fractal theory. The results show that the time-varying multifractal characteristics of EMR are determined by damage evolutions process, the dissipated energy caused by damage evolutions such as crack propagation, fractal sliding and shearing can be regard as the fingerprint of various EMR micro-mechanics. Based on the Irreversible thermodynamics and damage mechanics, we introduced the damage internal variable, constructed the dissipative potential function and established the coupled model of the EMR and the dissipative energy, which revealed the nature of dynamic nonlinear characteristics of EMR. Dynamic multifractal spectrum is the objective response of EMR signals, thus it can be used to evaluate the coal deformation and fracture process.     

新疆阿尔泰地区断裂控矿的多重分形机理

新疆阿尔泰地区断裂构造非常发育并对热液成矿有重要控制作用。分形分析表明该区断裂和矿床的空间分布均为多重分形分布,断裂的奇异指数为1.597～2.403,多重分维谱值为0.551～1.706;矿床的奇异指数为0.925～2.287,分维谱值为0.138～1.363。断裂的高的奇异指数和分维谱值表明该区断裂构造具有较高的成熟度和连通性,有利于提高岩石渗透性、促进流体流动和热液矿床的形成。断裂构造的多重分形分布导致该区热液成矿作用的多重分形分布。断裂体系演化过程中不同断裂部位变形和渗透性存在明显差异,数值模拟表明断裂与岩性和流体之间存在强烈的耦合作用并导致不同岩性的断裂具有明显不同的断裂渗透率。断裂-脉体系演化是一个自组织过程,元胞自动机模拟表明只有在分形渗透临界以上连通性较好的脊骨断裂部位是最有利于流体流动和成矿作用的。因此只有在部分有利的断裂部位才能形成矿床,并导致了断裂构造的奇异指数和多重分维谱值明显高于矿床。     

一种求地震记录多重分形谱的改进算法

通过分析地震记录多重分形谱的不同计算方法，引入一种新的多重分形概率测度概念，同时也提出了一种时间序列多重分形分析的改进方法。该方法具有计算量小、计算时间短的特点，并同时也可以快速、有效地求出地震记录的多重分形谱。     

基于数字图像灰度相关性的类岩石材料损伤分形特征研究

通过类岩石材料石膏试件单轴压缩试验,获得材料在荷载作用下从损伤到破坏的整个时间序列的数字图像。以试件表面数字图像的灰度相关性的变化为依据,建立损伤量度来表征材料表面损伤和破坏的发展。通过图像处理,建立损伤演化的二值图,并采用分形和多重分形谱理论对材料表面损伤的演化进行描述。研究结果表明,图像灰度相关性系数分布的演化与试件表面的变形局部化在空间和时间上都存在对应关系。随着试件表面损伤量增加,分形维数与应变之间有很好的线性关系,多重分形谱图的曲线形状从开始的对称光滑单峰形式,逐渐向左侧集中发展,其谱宽逐渐减小。     

Effects of watershed and estuarine characteristics on the abundance of submerged aquatic vegetation in Chesapeake Bay subestuaries

Watershed land use can affect submerged aquatic vegetation (SAV) by elevating nutrient and sediment loading to estuaries. We analyzed the effects of watershed use and estuarine characteristics on the spatial variation of SAV abundance among 101 shallow subestuaries of Chesapeake Bay during 1984–2003. Areas of these subestuaries range from 0.1 to 101 km², and their associated local watershed areas range from 6 to 1664 km². Watershed land cover ranges from 6% to 81% forest, 1% to 64% cropland, 2% to 38% grassland, and 0.3% to 89% developed land. Landscape analyses were applied to develop a number of subestuary metrics (such as subestuary area, mouth width, elongation ratio, fractal dimension of shoreline, and the ratio of local watershed area to subestuary area) and watershed metrics (such as watershed area). Using mapped data from aerial SAV surveys, we calculated SAV coverage for each subestuary in each year during 1984–2003 as a proportion of potential SAV habitat (the area < 2 m deep). The variation in SAV abundance among subestuaries was strongly linked with subestuary and watershed characteristics. A regression tree model indicated that 60% of the variance in SAV abundance could be explained by subestuary fractal dimension, mean tidal range, local watershed dominant land cover, watershed to subestuary area ratio, and mean wave height. Similar explanatory powers were found in wet and dry years, but different independent variables were used. Repeated measures ANOVA with multiple-mean comparison showed that SAV abundance declined with the dominant watershed land cover in the order: forested, mixed-undisturbed, or mixed-developed > mixed-agricultural > agricultural > developed. Change-point analyses indicated strong threshold responses of SAV abundance to point source total nitrogen and phosphorus inputs, the ratio of local watershed area to subestuary area, and septic system density in the local watershed.     

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.