On the practice of estimating fractal dimension   总被引：11，自引：0，他引：11  

James R. Carr  William B. Benzer 《Mathematical Geology》1991,23(7):945-958

Coastlines epitomize deterministic fractals and fractal (Hausdorff-Besicovitch) dimensions; a divider [compass] method can be used to calculate fractal dimensions for these features. Noise models are used to develop another notion of fractals, a stochastic one. Spectral and variogram methods are used to estimate fractal dimensions for stochastic fractals. When estimating fractal dimension, the objective of the analysis must be consistent with the method chosen for fractal dimension calculation. Spectal and variogram methods yield fractal dimensions which indicate the similarity of the feature under study to noise (e.g., Brownian noise). A divider measurement method yields a fractal dimension which is a measure of complexity of shape.  相似文献   

Growth of the Mediterranean Gorgonian Lophogorgia ceratophyta (L., 1758)     

Michele Mistri  Victor Ugo Ceccherelli 《Marine Ecology》1993,14(4):329-340

Abstract. Growth of the shallow-water gorgonian Lophogorgia ceratophyta was investigated in an infralittoral station located in La Spezia Gulf, Ligurian Sea. Mean annual height growth rate was estimated to be 2.57 cm · a^-1. The fractal dimension of the colonies was found to gradually evolve in complexity, exhibiting a simpler branching pattern in younger specimens. The maintenance of a low, invariable ramification complexity as an optimal choice in managing relationships between water and the colony's living tissues is also discussed.  相似文献   

基于引力模型的城市空间互相关和功率谱分析——引力模型的理论证明、函数推广及应用实例   总被引：53，自引：7，他引：53  

陈彦光  刘继生 《地理研究》2002,21(6):742-752

空间相互作用是先于城市体系而存在的重要概念 ,引力模型是描述空间相互作用的基本函数之一 ,但引力模型的理论基础不明确而且实际应用有局限。本文首先从城市地理系统的广义分形假设出发 ,推导出引力模型的幂函数形式 ,使其从一个经验模型上升为理论模型 ;进而引入时变函数和时滞参数将引力模型推广为更为一般和更加实用的形式 ,为发展城市引力过程的空间互相关分析和功率谱分析方法奠定了理论基础。借助 194 9～ 1998年 5 0年的人口演化数据 ,以北京 -天津的空间相互作用为实例 ,对基于城市引力关系的空间作用进行了相关分析和波谱分析 ,从而提供了城市网络空间相互作用广义引力分析的典型范例。  相似文献   

Rescaled-range and power spectrum analyses on well-logging data   总被引：6，自引：0，他引：6  

Chun-Feng Li 《Geophysical Journal International》2003,153(1):201-212

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Crossover from Nonlinearity Controlled to Heterogeneity Controlled Mixing in Two-Phase Porous Media Flows     

Frederico Furtado  Felipe Pereira 《Computational Geosciences》2003,7(2):115-135

We use high resolution Monte Carlo simulations to study the dispersive mixing in two-phase, immiscible, porous media flow that results from the interaction of the nonlinearities in the flow equations with geologic heterogeneity. Our numerical experiments show that distinct dispersive regimes occur depending on the relative strength of nonlinearity and heterogeneity. In particular, for a given degree of multiscale heterogeneity, controlled by the Hurst exponent which characterizes the underlying stochastic model for the heterogeneity, linear and nonlinear flows are essentially identical in their degree of dispersion, if the heterogeneity is strong enough. As the heterogeneity weakens, the dispersion rates cross over from those of linear heterogeneous flows to those typical of nonlinear homogeneous flows.  相似文献   

Multifractal analysis of the spatial distribution of earthquakes in southern Italy     

C. Godano  M. L. Alonzo  A. Bottari 《Geophysical Journal International》1996,125(3):901-911

We evaluate the complete spectrum of the generalized fractal dimension of the spatial pattern of microearthquakes in Southern Italy, revealing a multifractal distribution structure. Our analysis is focused on the dependence of the multifractal distribution on the size of the selected area and the kind of seismicity in the area. As the size of the window varies, we observe that the capacity, information and correlation dimensions vary significantly, while both d _∞ and d _−infin; remain unchanged within their errors limits. We interpret this result in terms of the observation that our data are mainly clustered around a linear fault (the Sisifo fault). When we restrict the selected windows around the fault, clustering around a line (the fault) is highlighted. The capacity dimension changes from about 1.8 to about 1.4 and the correlation dimension decreases because we observe in detail the clustering of the seismicity along the fault, which approximates the maximum intense clustering of the whole data set. Although our results are strongly influenced by the fact that the data are dominated by the epicentres located on the fault, we can conclude that multifractal analysis can be a very useful tool to discriminate the seismicity linked to a particular fault in a given area.  相似文献   

Multifractal modeling and spatial statistics   总被引：9，自引：0，他引：9  

Qiuming Cheng  Frederik P. Agterberg 《Mathematical Geology》1996,28(1):1-16

In general, the multifractal model provides more information about measurements on spatial objects than a fractal model. It also results in mathematical equations for the covariance function and semivariogram in spatial statistics which are determined primarily by the second-order mass exponent. However, these equations can be approximated by power-law relations which are comparable directly to equations based on fractal modeling. The multifractal approach is used to describe the underlying spatial structure of De Wijs 's example of zinc values from a sphalerite-bearing quartz vein near Pulacayo, Bolivia. It is shown that these data are multifractal instead of fractal, and that the second-order mass exponent (=0.979±0.011 for the example) can be used in spatial statistical analysis.  相似文献   

Flexible spectral methods for the generation of random fields with power-law semivariograms     

Johannes Bruining  Diederik van Batenburg  Larry W. Lake  An Ping Yang 《Mathematical Geology》1997,29(6):823-848

Random field generators serve as a tool to model heterogeneous media for applications in hydrocarbon recovery and groundwater flow. Random fields with a power-law variogram structure, also termed fractional Brownian motion (fBm) fields, are of interest to study scale dependent heterogeneity effects on one-phase and two-phase flow. We show that such fields generated by the spectral method and the Inverse Fast Fourier Transform (IFFT) have an incorrect variogram structure and variance. To illustrate this we derive the prefactor of the fBm spectral density function, which is required to generate the fBm fields. We propose a new method to generate fBm fields that introduces weighting functions into the spectral method. It leads to a flexible and efficient algorithm. The flexibility permits an optimal choice of summation points (that is points in frequency space at which the weighting function is calculated) specific for the autocovariance structure of the field. As an illustration of the method, comparisons between estimated and expected statistics of fields with an exponential variogram and of fBm fields are presented. For power-law semivariograms, the proposed spectral method with a cylindrical distribution of the summation points gives optimal results.  相似文献   

Self-affine gravity covariance model for the Bay of Bengal     

Abhey Ram Bansal  Vijay P. Dimri 《Geophysical Journal International》2005,161(1):21-30

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Quantitative evidence for the fractal nature of the stratigraphie record: results and implications     

Robin J. Bailey 《Proceedings of the Geologists' Association. Geologists' Association》2005,116(2):129-138

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