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1.
The cumulative probability distributions for stream order, stream length, contributing area, and energy dissipation per unit length of channel are derived, for an ordered drainage system, from Horton's laws of network composition. It is shown how these distributions can be related to the fractal nature of single rivers and river networks. Finally, it is shown that the structure proposed here for these probability distributions is able to fit the observed frequency distributions, and their deviations from straight lines in a log-log plot. 相似文献
2.
Changing grading of soil: effect on critical states 总被引:6,自引:3,他引:3
Examples of situations are presented where the grading of a soil changes during its lifetime either by crushing of particles
leading to an increase of fine material or by slow transport of fine particles with seepage leading to a decrease of fine
material. Such grading changes influence the basic constitutive properties of the soil, in particular properties such as critical
states which are dependent on the available range of densities of packing. Discrete element modelling is used to show the
dependence of critical state conditions on grading and the way in which the particle assembly seeks out new critical state
conditions as the grading changes. 相似文献
3.
Upper Pollara eruption products (13 ka, Salina Island, Italy) include both homogeneous and heterogeneous pumices resulting from mixing/mingling processes between an HK andesite and a high-SiO2 rhyolite. Representative samples of heterogeneous pumices are collected and analyzed in order to check the correspondence between glass composition and morphological features of the mingling/mixing structures. Image analysis techniques are applied and eight grey color ranges (classes) are extracted from high-resolution scans of pumice. Class 1 (lighter colors) and class 8 (darker colors) show end-member glass compositions, i.e. HK andesite and high-SiO2 rhyolite, respectively. These two classes show spot- to cluster-like morphological structures. Intermediate classes show an HK dacitic to rhyolitic composition and a banding- to fold-like morphology. Fractal analysis by box-counting of the boundary pattern of eight grey classified images is performed over a length scale of 0.028–1.8 cm. Fractal dimension D is between 1.01 and 1.84. Coupled fractal analysis and geochemical data reveal that D increases as the degree of magma interaction (homogenization) increases. This feature well fits the results from numerical models on the convective mixing of fluids driven by thermal convection. We conclude that the increase of D observed in the Upper Pollara samples reflects the transition from fractal mixing to homogenization. End-member magmas (HK andesite and high-SiO2 rhyolite) represent isolated mixing regions, while homogenized magmas represent active mixing regions. In the analyzed pumices, isolated and active mixing regions coexist at scales between 10−4 and 10−2 m. Morphological and compositional features of the Upper Pollara pumices result from turbulence. 相似文献
4.
In order to model flow and transport in fractured rocks it is important to know the geometry of the fracture network. A stochastic approach is commonly used to generate a synthetic fracture network from the statistics measured at a natural fracture network. The approach presented herein is able to incorporate the structures found in a natural fracture network into the synthetic fracture network. These synthetic fracture networks are the images generated by Iterated Function Systems (IFS) as introduced by Barnsley (1988). The conditions these IFS have to fulfil to determine images resembling fracture networks and the effects of their parameters on the images are discussed. It is possible to define the parameters of the IFS in order to generate some properties of a fracture network. The image of an IFS consists of many single points and has to be suitably processed for further use. 相似文献
5.
The fractal geometry of flow paths in natural fractures in rock and the approach to percolation 总被引:2,自引:0,他引:2
The distributions of contact areas in single, natural fractures in quartz monzonite (Stripa granite) are found to have fractal dimensions which decrease fromD=2.00 to values nearD=1.96 as stress normal to the fractures is increased from 3 MPa up to 85 MPa. The effect of stress on fluid flow is studied in the same samples. Fluid transport through a fracture depends on two properties of the fracture void space geometry. the void aperture; and the tortuosity of the flow paths, determined through the distribution of contact area. Each of these quantities change under stress and contribute to changes observed in the flow rate. A general flow law is presented which separates these different effects. The effects of tortuosity on flow are largely governed by the proximity of the flow path distribution to a percolation threshold. A fractal model of correlated continuum percolation is presented which quantitatively reproduces the flow path geometries. The fractal dimension in this model is fit to the measured fractal dimensions of the flow systems to determine how far the flow systems are above the percolation threshold. 相似文献
6.
从信息论原理和分形几何学的观点出发,采用多种方法,分析研究1988年澜沧—耿马7.6级地震前地震活动的信息、信息熵和分维的变化特征表明,地震前1—2年内,中、小地震活动的信息熵、缺信量和容量维、信息维出现明显的低值变化过程,反映了地震前兆的减熵、降维特点,从一个侧面反映了大震前,一定区域内中、小地震活动的时空变化从无序向有序的演化过程。 相似文献
7.
分形与混沌理论在地震学中的应用与探讨 总被引:1,自引:2,他引:1
分形与混沌理论的研究与发展,揭示了自然界中一大类无规几何形体物理过程的内在规律性及其动力演化过程的内在随机性。这给我们探索自然界中分形客体的几何形态及其与内部物理本质的关系提供了一条暂新的途径。特别是这一理论给我们探讨地震问题,例如:探讨地震活动时空分布的确定性图像、地震演化过程的动力学行为、临界特征以及未来大地震的发生等问题,带来了某些希望。本文较详细地综述了近年来分形与混沌理论在地震学中的应用研究。全文共分5部分。第1部分是孕震过程的一般概述。第2部分描述单分形与多分形在地震学中的某些应用.文中第3部分介绍了混沌动力学中的某些研究在测震学与模型中的应用。第4部分综述了自组织临界现象和闪变噪声的研究.最后,第5部分是分形理论与混沌动力学在地球科学中的应用前景与展望. 相似文献
8.
Martin Laverty 《地球表面变化过程与地形》1987,12(5):475-480
The analysis of cave survey data is used to establish that cave length exhibits fractal (self-similar) behaviour, with dimensions in the range 1–1·5, over a range of measurement resolutions from 1 to 100 m. It is suggested that fractal dimensions, together with their range of applicability, will prove to be useful parameters for the study of caves. 相似文献
9.
复杂等高线自动综合是计算机辅助制图领域中一项重要且难度较大的任务。本文根据分形理论的基本原理,提出了一种基于量化等高线形状结构特征的复杂等高线自动综合的新方法。研究和实验表明,该方法充分顾及了地貌形态特征,能够对等高线图形进行客观、有效地概括。 相似文献
10.
Upscaling is a major issue regarding mechanical and transport properties of rocks. This paper examines three issues relative
to upscaling. The first one is a brief overview of Effective Medium Theory (EMT), which is a key tool to predict average rock
properties at a macroscopic scale in the case of a statistically homogeneous medium. EMT is of particular interest in the
calculation of elastic properties. As discussed in this paper, EMT can thus provide a possible way to perform upscaling, although
it is by no means the only one, and in particular it is irrelevant if the medium does not adhere to statistical homogeneity.
This last circumstance is examined in part two of the paper. We focus on the example of constructing a hydrocarbon reservoir
model. Such a construction is a required step in the process of making reasonable predictions for oil production. Taking into
account rock permeability, lithological units and various structural discontinuities at different scales is part of this construction.
The result is that stochastic reservoir models are built that rely on various numerical upscaling methods. These methods are
reviewed. They provide techniques which make it possible to deal with upscaling on a general basis. Finally, a last case in
which upscaling is trivial is considered in the third part of the paper. This is the fractal case. Fractal models have become
popular precisely because they are free of the assumption of statistical homogeneity and yet do not involve numerical methods.
It is suggested that using a physical criterion as a means to discriminate whether fractality is a dream or reality would
be more satisfactory than relying on a limited data set alone. 相似文献