城市地理研究中的单分形、多分形和自仿射分形   总被引：1，自引：0，他引：1  

陈彦光 《地理科学进展》2019,38(1):38-49

分形几何学在城市地理研究中具有广泛的应用,然而很多基本概念却让初学者感到迷惑。如何区分单分形、自仿射分形与多分形,是一个基本而重要的问题。简单分形容易理解,而真实的地理现象很少是单分形的。城市生长过程具有自仿射特征,而城市空间格局却具有多分形性质。作者发现,各种分形的共性在于三个方面：标度律、分数维和熵守恒。论文基于标度、分维和熵守恒公式,借助隐喻城市生长的规则分形来区分单分形、多分形和自仿射分形,讨论分形系统演化的机理、分形与空间自相关和空间异质性的联系,同时澄清一些在地理分形研究中的常见错误概念。最后以城市位序-规模分布为例,说明并对比单分形和多分形在城市地理研究中的建模与应用思路。  相似文献   

The Relationship between Fe Mineralization and Magnetic Basement Faults using Multifractal Modeling in the Esfordi and Behabad Areas (BMD), Central Iran     

Masoumeh NABILOU  Peyman AFZAL  Mehran ARIAN  Ahmad ADIB  Hassan KHEYROLLAHI  Mohammad FOUDAZI  Parviz ANSARIRAD 《《地质学报》英文版》2022,96(2):591-606

Multifractal modeling is a mathematical method for the separation of a high potential mineralized background from a non-mineralized background. The Concentration-Distance to Fault structures (C-DF) fractal model and the distribution of the known iron (Fe) deposits/mines seen in the Esfordi and Behabad 1:100,000 sheets from the Bafq region of central Iran are used to distinguish Fe mineralization based on their distance to magnetic basement structures and surface faults, separately, using airborne geophysical data and field surveys. Application of the C-DF fractal model for the classification of Fe mineralizations in the Esfordi and Behabad areas reveals that the main ones show a correlation with their distance from magnetic basement structures. Accordingly, the distances of Fe mineralizations with grades of Fe higher than 55% )43% < Fe ≤ 60%) are located at a distance of less than 1 km, whereas for surfacial faults with grades of 43% ≤ Fe ≤ 60%, the distances are 3162< DF ≤ 4365 m from the faults. Thus, there is a positive relationship between Fe mineralization and magnetic basement structures. Also, the proximity evidence of Precambrian high-grade Fe mineralization related to magnetic basement structures indicates syn-rifting tectonic events. Finally, this C-DF fractal model can be used for exploration of magmatic and hydrothermal ore deposits.  相似文献   

城市异速标度研究的起源、困境和复兴   总被引：5，自引：0，他引：5  

陈彦光 《地理研究》2013,32(6):1033-1045

系统总结了城市异速标度研究的学术源流、量纲困境和现状特征,重点探讨了城市化异速标度分析的前景和意义。异速标度是城市研究的基本理论方法之一,该方法起源于20世纪50年代的生物学和一般系统论。由于量纲难题,城市异速分析经过一段时间的研究热潮之后趋于冷落;由于分维概念的引入,异速标度关系摆脱了量纲困境;由于相关领域的推动,城市异速分析方法复兴。异速生长和异速标度分析在城市形态、城市生态、城市性态、城市动态以及城市体系等诸多领域都有应用。如今,异速生长正在与分形和自组织网络理论相互融合,发展成为基于一般标度律的城市过程和格局的集成分析方法。由于城市化与城市形态、城市体系等方面的密切相关,异速标度分析极有前景的一个发展方向可能是城市化研究。城市化异速分析可望将不同类型的城市异速标度研究成果组织成一个完整的逻辑框架。  相似文献   

作为CAS的复杂城市地理系统的SOC性质   总被引：1，自引：0，他引：1  

刘继生  陈彦光 《地理科学》2007,27(2):129-135

将城市作为复杂适应性系统(CAS)研究其自组织临界性(SOC)具有重要的理论意义和实践价值,这方面的探索工作刚刚开始。本文从城市的地理空间角度出发,论证城市是一种复杂适应性系统。城市在本质上是不可还原的,我们可以根据积木的机制将城市分解,但分解的结果对解释城市的复杂行为丝毫没有帮助。由于城市和城市体系都具有分形结构、服从Z ipf定律,且具有1/f噪声的特征,由此判断城市地理系统具有自组织临界性质。自组织临界性与复杂性适应性立论的视角不同,但可以统一于“混沌的边缘”这一概念。  相似文献   

京津冀城市用地形态的双分形特征及其演化   总被引：1，自引：1，他引：1  

赵静湉  陈彦光  李双成 《地理科学进展》2019,38(1):77-87

区域城乡一体化的标志之一是城镇体系结构的一体化,这个过程可以从标度的角度进行描述和评价。分形是标度分析的重要方法,地理空间无尺度分布特征的典型参数是分维。论文以京津冀城镇体系为例,利用遥感图像的解译数据和人口普查数据开展分形分析、位序-规模分布分析和异速标度分析,用以解释1995—2013年间京津冀城镇体系演化的过程。结果表明,京津冀城镇体系及其演化的特征有：①京津冀空间结构和位序-规模分布都表现为自仿射双分形结构;②京津冀区域的城市人口-城区面积异速标度退化为假线性关系;③随着城镇体系的演化,自仿射的双分形结构逐步向自相似分形结构演化。由此得出结论：其一,京津冀城镇体系存在结构性的不协调因素。其空间结构和等级结构具有二元化特征,但演化方向却呈现内在结构一体化的显著趋势。其二,大城市用地不够集约。城市边缘区的无序扩张导致土地利用铺张浪费。地方政府和规划专家可以有意识地利用城镇体系演化的这种特征和趋势制定管理措施和优化规划方案。  相似文献   

Cascade model for fluvial geomorphology   总被引：3，自引：0，他引：3  

W. I. Newman  D. L. Turcotte 《Geophysical Journal International》1990,100(3):433-439

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Deep borehole log evidence for fractal distribution of fractures in crystalline rock   总被引：7，自引：0，他引：7  

Peter Leary 《Geophysical Journal International》1991,107(3):615-627

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Stochastic behaviour and scaling laws in geoelectrical signals measured in a seismic area of southern Italy     

Vincenzo Cuomo  Vincenzo Lapenna  Maria Macchiato  Carmine Serio  & Luciano Telesca 《Geophysical Journal International》1999,139(3):889-894

We explore the inner dynamics of daily geoelectrical time series measured in a seismic area of the southern Apennine chain (southern Italy). Autoregressive models and the Higuchi fractal method are applied to extract maximum quantitative information about the time dynamics from these geoelectrical signals. First, the predictability of the geoelectrical measurements is investigated using autoregressive models. The procedure is based on two forecasting approaches: the global and the local autoregressive approximations. The first views the data as a realization of a linear stochastic process, whereas the second considers the data points as a realization of a deterministic process, which may be non-linear. Comparison of the predictive skills of the two techniques allows discrimination between low-dimensional chaos and stochastic dynamics. Our findings suggest that the physical systems governing electrical phenomena are characterized by a very large number of degrees of freedom and can be described only with statistical laws. Second, we investigate the stochastic properties of the same geoelectrical signals, searching for scaling laws in the power spectrum. The spectrum fits a power law P (  f )∝  f  ^−α , with the scaling exponent α a typical fingerprint of fractional Brownian processes. In this analysis we apply the Higuchi method, which gives a linear relationship between the fractal dimension D _Σ and the spectral power law scaling index α : D _Σ=(3− α )/2. This analysis highlights the stochastic nature of geoelectrical signals recorded in this seismic area of southern Italy.  相似文献   

Electrical spectroscopy of porous rocks: a review—I.Theoretical models     

T. L. Chelidze  & Y. Gueguen 《Geophysical Journal International》1999,137(1):1-15

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Numerical Method for Conditional Simulation of Levy Random Fields   总被引：2，自引：0，他引：2  

Scott Painter 《Mathematical Geology》1998,30(2):163-179

Stochastic simulations of subsurface heterogeneity require accurate statistical models for spatial fluctuations. Incremental values in subsurface properties were shown previously to be approximated accurately by Levy distributions in the center and in the start of the tails of the distribution. New simulation methods utilizing these observations have been developed. Multivariate Levy distributions are used to model the multipoint joint probability density. Explicit bounds on the simulated variables prevent nonphysical extreme values and introduce a cutoff in the tails of the distribution of increments. Long-range spatial dependence is introduced through off-diagonal terms in the Levy association matrix, which is decomposed to yield a maximum likelihood type estimate at unobserved locations. This procedure reduces to a known interpolation formula developed for Gaussian fractal fields in the situation of two control points. The conditional density is not univariate Levy and is not available in closed form, but can be constructed numerically. Sequential simulation algorithms utilizing the numerically constructed conditional density successfully reproduce the desired statistical properties in simulations.  相似文献