分形城市研究进展：从几何形态到网络关联

城市是人类文明最主要的聚集地,也是一个开放复杂演化巨系统,认识其空间复杂性成为城市科学研究的热点和前沿。城市研究正呈现“从位置和场所向关联和流,从物质空间向城市网络空间”的转向。人类对城市的认识也从“空间是机器”转向“城市有机生命体”。分形是大自然的语言和地理学第四代语言,是挖掘城市空间自组织规律的有效工具,在揭示城市有机体复杂演化机制方面发挥重要作用。目前分形城市研究以指标构建和实证分析为主,缺乏系统的梳理和回顾;内容上侧重几何分形,复杂城市网络视角下的结构分形研究薄弱。本文简要回顾了近30余年来分形城市研究的发展历程,梳理了分形城市研究脉络：从城市形态的几何分形到城市结构与关联的网络分形,从静态分形特征到动态异速生长,并展望了分形城市未来研究方向。     

Fractal study of sustainable proportions of natural and artificial oases

The sustained development of an artificial oasis depends critically on the stability of the natural oasis associated with it. This work theoretically investigates the most suitable ratio of natural oasis area to artificial oasis area in oasis ecosystems, as quantified by the percentage of artificial oasis (PAO). Based on data from oases observed in Xinjiang Province, China, this paper analyzes the PAO distribution for these oases via fractal theory. The results allowed us to draw the following conclusions. (1) The PAO distribution possesses fractal characteristics, and the fractal dimension of the PAO decreases as the oasis evolves. (2) The interval of the fractal dimension of the PAO is 0–1.7068, and the interval of the expectation of the PAO is 0–85.01%. This indicates that the natural oasis should occupy at least around 15% of the total oasis area. (3) The fractal dimension and the expectation of the PAO for the ecosystem of oases in Xinjiang Province, China, are currently 0.5369 and 53.51%, respectively. These results show that the development of artificial oases in Xinjiang Province should continue, although the corresponding natural oases should also be maintained and developed at the same time.     

分形理论在深部粘土孔隙分布特征研究中的应用

针对深厚表土层对煤炭资源开采可能带来的安全生产及地表环境破坏问题,利用分形理论方法研究了鲁西南地区大埋深粘土的微孔隙发育规律。研究表明,该区深部粘土孔隙累计分布与孔径大小之间在双对数坐标下具良好的线性关系,相关系数在0.90以上。说明深部粘土中孔隙分布的分形结构是客观存在的,而分维值能真实地反映粘土孔隙特征,可作为一个综合指标,它也是土体孔隙定量描述的有效途径。这种粘土的孔径大于1μm左右时,其分维值在2.5~2.6。同时得出︰孔隙孔径2μm左右是该区深部粘土孔隙性质变化的界限。     

基于路网可达性的城市空间形态集聚分形研究

为将城市形态分形维数从平面空间拓展到交通网络系统,提出一种基于路网的分形集聚维数测算方法,探讨该维数的集聚—扩散性质。以郑州市中心城区为案例区,分别测算了各类功能用地半径集聚维数和路网集聚维数。结果表明：① 各类用地无论在平面中还是在路网中,密度从中心向外围的变化在特定区间内都是均匀的,符合分形特征。② 两种维数均呈现出商业用地<全部建设用地（不含道路与交通设施用地）<居住用地<工业及仓储用地的规律。③ 对于同类功能用地,相对于半径维数,路网集聚维数标度不变区尺度范围更广,对空间的划分也更为精细。④ 同类用地两种集聚维数的分形测量值存在差异,这体现出路网集聚维数对传统测度结果具有一定的延展—集聚修正作用。     

高光谱图像稀疏信息处理综述与展望

高光谱成像技术具有光谱连续、图谱合一,能够以较高的光谱诊断能力对地物目标进行精细化解译,可以大幅增强地物信息的提取能力。充分利用高光谱遥感图像丰富的空间、谱信息,进行观测目标地物的精细化解译,成为近年来遥感领域的研究热点和前沿领域,并在多个相关领域具有巨大的应用价值和广阔的发展前景。本文结合高光谱图像成像特点,对基于稀疏表示理论的高光谱图像处理与分析方法进行综述,概括了高光谱图像处理与分析主要研究,并对各个研究领域与方向进行分析和评价,最后对各研究领域发展提出建议和展望。     

基于分形分维和数学函数的南流江流域河网信息提取

利用南流江流域30 m分辨率的DEM数据,介绍了Arc GIS中进行河网提取的一系列过程,并利用其图解建模工具,提取南流江流域的不同汇流累积面积的水系河网,实现了提取过程的流程化处理。分别统计河源密度和沟壑密度,并分别计算它们与汇流累积面积的几何函数关系,并对其进行二阶求导,确定其二阶导数关系,得到合适的汇流累积阈值,并借助分形分维理论对河网的分维值进行了验证。利用函数关系和分形分维确定汇流累积面积提取水系河网的方法有效地避免了人工选择汇流累积面积的主观性,提高了研究结果的准确性和可靠性,在知道研究流域河网分维值的前提下,可快速获取准确的汇流累计面积阈值。     

基于DEM的南水北调中线水源区水系分维估算

分形理论是现代数学的一个分支,常被用来研究自然界中具有自相似性的复杂地理对象。本文以丹江水库的DEM为数据源,利用ArcGIS 9.3软件提取流域水系,根据集水面积阈值与水系分维的相互关系,将分形理论、GIS技术相结合,用基于网格法的分维估算方法计算了南水北调中线水源区水系分形维数,经计算得出该流域水系分维值为1.253。与传统方法相比,这种方法计算水系分维具有简便、高效等优点。     

Qualitative and Quantitative Characterization of Shale Microscopic Pore Characteristics Based on Image Analysis Technology

In order to evaluate the shale microscopic pore characteristics more economically and effectively in limited circumstances, the pore characteristics of Longmaxi Formation in Pengshui area, Sichuan Basin, were qualitatively observed and analyzed with Scanning Electron Microscopy (SEM) and Field Emission Scanning Electron Microscopy (FESEM) with argon ion polishing method at the same time. Pore quantitative information were extracted from shale SEM and FESEM images with the help of a professional image analysis software IamgeJ2x, and combined with statistical methods, the whole pore size distribution as well as shale pore fractal dimension and the relevance between fractal dimension and organic matter content, mineral composition and pore adsorption capacity and the corresponding pore structure characteristics of Longmaxi Formation in Pengshui area were analyzed. The study shows that under SEM, there are mostly micro pores of Longmaxi Formation in Pengshui area. The main pore types include intergranular pore, clay mineral layer pore, intragranular pore and micro cracks, etc. Through argon ion polishing FESEM, there mainly develop nanoscale pores. The main pore types contain organic pore, inorganic mineral pore (pyrite intergranular pore, intragranular pore, clay mineral layer pore and intergranular pore, etc.) and micro cracks. The use of both of the two methords is more advantageous to qualitatively analyze shale pore. The whole pore size distribution of shale pore has four main peaks and the main distribution range is 3~10 nm, 10~40 nm, 100~400 nm, 1~4 μm, respectively. The shape factor of shale organic matter pore is distributed between 0.9~1 and inorganic mineral pore is distributed between 0.5~0.7. It shows that the organic matter pore is circular, nearly circular and inorganic mineral pore shape is triangle, polygon, slit shape and so on. The inorganic mineral pore shape is relativly complex because of the different pore causes. The shale pore of Longmaxi Formation in Pengshui area conforms to the fractal features, and the organic pore fractal dimension is smaller than that of inorganic mineral pore, showing that the organic matter pore structure is relatively simple. There is a certain relevance between fractal dimension and organic matter content, mineral composition, porosity, and adsorbed gas content. With the increase of the organic matter content, the shale pore fractal dimension increase, the pore structure characteristics become complicated. With the shale pore fractal dimension increasing, the biggest gas adsorption quantity increases and the ability of pore adsorption strengthens.     

从时间序列中提取维数信息

作者介绍了分形和分维的概念、性质和意义，重点讨论了从一维序列中提取维数信息的，并给出了一些在天气了气候中的应用。     

河北平泉地区中元古界长城群高于庄组风暴浊积岩及其分形特征

河北平泉中元古界长城群高于在组地层中发育风暴浊积岩。在沉积序列、结构构造、矿物成分及显微组构的研究基础上，采用分数维函数理论研究了该区风暴浊积岩的形成规律，发现地质历史上的风暴作用强度与其频率之间存在着一种分数维函数关系，显示了灾变事件的内在规律性，即自相似性。