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1.
Characterization of the Structure of River-Bed Gravels Using Two-Dimensional Fractal Analysis 总被引：7，自引：0，他引：7
This paper is concerned with the application of fractal analysis to understand the structure of water-worked gravel-bed river surfaces. High resolution digital elevation models, acquired using digital photogrammetric methods, allowed the application of two-dimensional fractal methods. Previous gravel-bed river studies have been based upon sampled profiles and hence one-dimensional fractal characterisation. After basic testing that bed elevation increments are Gaussian, the paper uses two-dimensional variogram surfaces to derive directionally dependent estimates of fractal dimension. The results identify mixed fractal behavior with two characteristic fractal bands, one associated with the subgrain scale and one associated with the grain scale. The subgrain scale characteristics were isotropic and sensitive to decisions made during the data collection process. Thus, it was difficult to differentiate whether these characteristics were real facets of the surfaces studied. The second band was anisotropic and not sensitive to data collection issues. Fractal dimensions were greater in the downstream direction than in other directions suggesting that the effects of water working are to alter the level of surface organisation, by increasing surface irregularity and hence roughness. This is an important observation as it means that water-worked surfaces may have a distinct anisotropic signal, revealed when using a fractal type analysis. 相似文献
2.
Complexity and scale in geomorphology: Statistical self-similarity vs. characteristic scales 总被引：3，自引：0，他引：3
Robert Andrle 《Mathematical Geology》1996,28(3):275-293
Two models of the relationship between complexity and scale of geomorphic lines are compared, one based on statistical self-similarity (in which complexity is invariant for some range of scale), and the other on the concept of characteristic scales (in which complexity changes continuously with scale). Two corresponding techniques are used in the comparison, fractal analysis utilizing the divider method, and an angle measure technique. These techniques are applied to three types of coastlines: fiord, volcanic, and tectonic, in order to ascertain which model, statistical self-similarity or characteristic scales, is more useful in understanding variations in coastline complexity for scale. Apparently linear log-log plots of number of steps against steplength produced by fractal analysis display slight but significant curvature. Upon closer examination, it is determined that using fractal dimension to compare even the same types of features is unreliable because of the dependency of fractal dimension on scale of measurement, even if the same steplengths are used throughout the study. These results are corroborated by the use of the angle measure technique, a method based on measuring angles between points along a digitized line. It is concluded that the coastlines examined display no evidence of statistical self-similarity and that the characteristic scales model is more useful in investigating complexity and scale in geomorphology. 相似文献
3.
基于岩体不连续面三维分形维岩体质量评价研究 总被引：1，自引：0，他引：1
岩体内部不连续面分布具有随机性、不规则性,但又具有统计自相似性。基于三维随机不连续面网络模拟技术,对岩体结构统计均质区内的不连续面进行计算机模拟,并应用分形理论计算岩体不连续面分布的分形维数。岩体不连续面分布分维数具有尺寸效应,随着岩体尺寸增大分维数减小,到一定程度趋于稳定。这一稳定的分维值称之为表征分维数,用此值描述不连续面分布特征。将岩体不连续面分布的表征分维数与按传统岩体分类标准所得岩体质量等级进行对比,提出以岩体不连续面分布表征分维数为指标的岩体质量分类方法。在岩体分类基础上,提出基于表征分维数的岩体等效抗剪强度指标的折减计算。 相似文献
4.
地表的分形测量及其大地构造学意义 总被引：5，自引：1，他引：4
以湖北红安地区为例,采用投影覆盖法(projectivecoveringmethod)对地表进行了二维分形测量,结果表明,地表面积具有双分形(bifractal)关系,即具有小尺度的结构分形(texturalfractal)和大尺度的构造分形(structuralfractal),分叉点(breakpoint)的尺度为3610m,分维值都在2～3之间且结构分维值大于其构造分维值。可见,地表形态具有分形性质,分维值可以指示地表形态的复杂程度。构造分维值可作为构造活动强度的一个指标,可为大地构造单元的划分提供定量依据。复杂地表形态主要是由构造活动(内营力作用)和各种复杂表生地质作用(外营力作用)引起的,前者主要控制大尺度的地形起伏,后者则塑造小尺度的地表形态。地表分维值可以指示地表的发育成熟度,该地区小尺度的结构分维值大于大尺度的构造分维值表明其处于地表形态的发育晚期。此外,地表的分形尺度可以来用确定构造活动尺度,从而指导构造地质与找矿勘探研究。 相似文献
5.
Variations in surface morphology and lithology provide an opportunity to study lithologic and morphologic influences on the spatial pattern of stream-sediment geochemistry within two contrasting environments of the Eastern Alps (Hohe Tauern Range and Gurktaler Alpen Range). The fractal dimension, a measure of surface roughness over a variety of scales, is used to model the dissipation of erosive products due to climatic controlled denudation and fluvial mass transport. Based on a spatial correlation analysis, specific elemental concentrations are used as indicators for a dominant lithotype. Fractal geometry of these elements has been estimated by sequential Gaussian simulation of the area/perimeter relationship (Dal) and by the estimation of multifractal spectra. It is shown that within a 510–780 km2 survey area the spatial variations of Al, Ga, Ni and Ca can be approximated by single fractals but for those of Ag and Sn multifractal models must be used. Fractal properties derived from simulated surfaces are explainable by the process controlling the spatial structure of the data. Climatic and tectonic parameters apparently influences Dal at large scales. At smaller scales rock-type variation exert an additional influence on Dal. 相似文献
6.
Fractal models for predicting soil hydraulic properties: a review 总被引：33，自引：0，他引：33
Modern hydrological models require information on hydraulic conductivity and soil-water retention characteristics. The high cost and large spatial variability of measurements makes the prediction of these properties a viable alternative. Fractal models describe hierarchical systems and are suitable to model soil structure and soil hydraulic properties. Deterministic fractals are often used to model porous media in which scaling of mass, pore space, pore surface and the size-distribution of fragments are all characterized by a single fractal dimension. Experimental evidence shows fractal scaling of these properties between upper and lower limits of scale, but typically there is no coincidence in the values of the fractal dimensions characterizing different properties. This poses a problem in the evaluation of the contrasting approaches used to model soil-water retention and hydraulic conductivity. Fractal models of the soil-water retention curve that use a single fractal dimension often deviate from measurements at saturation and at dryness. More accurate models should consider scaling domains each characterized by a fractal dimension with different morphological interpretations. Models of unsaturated hydraulic conductivity incorporate fractal dimensions characterizing scaling of different properties including parameters representing connectivity. Further research is needed to clarify the morphological properties influencing the different scaling domains in the soil-water retention curve and unsaturated hydraulic conductivity. Methods to functionally characterize a porous medium using fractal approaches are likely to improve the predictability of soil hydraulic properties. 相似文献
7.
Recent studies have shown that internal surfaces of porous geological materials, such as rocks and lignite coals, can be described by fractals down to atomic length scales, In this paper, the basic properties of self-similar and self-affine fractals are reviewed and how fractal dimensions can be measured by small-angle scattering experiments are discussed.This paper was presented at Emerging Concepts, MGUS-87 Conference, Redwood City, California, 13–15 April 1987. 相似文献
8.
John C. Gallant Ian D. Moore Michael F. Hutchinson Paul Gessler 《Mathematical Geology》1994,26(4):455-481
This paper examines the characteristics of four different methods of estimating the fractal dimension of profiles. The semi-variogram, roughness-length, and two spectral methods are compared using synthetic 1024-point profiles generated by three methods, and using two profiles derived from a gridded DEM and two profiles from a laser-scanned soil surface. The analysis concentrates on the Hurst exponent H,which is linearly related to fractal dimension D,and considers both the accuracy and the variability of the estimates of H.The estimation methods are found to be quite consistent for Hnear 0.5, but the semivariogram method appears to be biased for Happroaching 0 and 1, and the roughness-length method for Happroaching 0. The roughness-length or the maximum entropy spectral methods are recommended as the most suitable methods for estimating the fractal dimension of topographic profiles. The fractal model fitted the soil surface data at fine scales but not at broad scales, and did not appear to fit the DEM profiles well at any scale. 相似文献
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Recent analyses of geographical data have shown that mountains can be well described in terms of fractals, which raises the fundamental question about the mechanisms producing fractal surfaces in geomorphological evolution. Because the formation of mountain ranges takes place over an extremely long period of time, direct observations of erosion mechanisms are hardly feasible. Therefore, we expect that model experiments on the erosion of mountain ridges taking place on a limited time scale should contribute significantly to our understanding of the emergence of fractal structures in geomorphological phenomena. During the watering of an initially smooth ridge made of a mixture of silica sand and earthy soil the surface evolves into a shape analogous to actual mountain profiles with self-affine geometry. For the exponents describing, respectively, the spatial and the temporal scaling of the surface width, α=0.78±0.05 and β=0.8±0.06 have been obtained. The former value is in a very good agreement with α=0.8±0.1 calculated for genuine transect profiles. The processes in our micromodel can be well described in terms of self-organized criticality: The system evolves into a critical state, where surface roughening takes place due to power-law distributed landslides. 相似文献
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The study of septal patterns in ammonoids has been centered on functional and/or constructional issues. Complexly fluted septa have been considered as complementary structures that reinforce the ammonite shell, their frilled sutures possibly manifesting the demand for strength. Ammonitic sutures display features that denote typical fractal behavior, since they can present very long perimeters relative to the contiguous shell areas, and most provide evidence of statistical self-similarity when observed at varying scales of magnification. However, there is a lower limit of scale measurements below which the fractal behavior of the curve no longer holds, and the perimeter length/step size relationship approaches an Euclidean geometry. This paper describes a new methodology that allows the accurate characterization of suture complexity in ammonoids using the technique of fractal analysis (step-line procedure). The proposed methodology helps to fix the position of this cut-off point, allowing for independent estimates of the fractal dimensions of the curve for both large and small measurement scales (i.e., first and second orders of suture complexity). This approach improves the resolution of fractals in the analysis of suture complexity, thus facilitating the potential interpretation of suture patterns in functional/constructional, evolutionary and paleoecological terms. 相似文献
13.
传统上研究含气页岩宏观缝网特征的方法多是基于小样品开展,通过观察小样品的裂缝展布特征来了解页岩的裂缝发育的宏观特性。但是这类方法因尺度过小,缺乏代表性,不能获取连续面上的裂缝特征,难以分析裂缝发育和地应力方向之间的关系。为获取更详细的大尺度含气页岩的宏观裂缝特征,本文从重庆市涪陵地区石柱县采样获取2m×3m×0.7m完整大尺度岩块,并采用有序标号切割来获取30cm3规格岩样,在此基础上提取小岩样的表面裂缝并按照大尺度岩样切割的相对顺序构建三维裂缝网络。分析观测大尺度的三维裂缝网络可以发现,含气页岩的裂缝分布具有明显的规律性:水平主应力方向上的裂缝发育度普遍高于最小水平主应力方向;垂直方向上的裂缝与最小水平主应力的夹角为-62°。分维研究表明所有不同面上的裂缝均符合分维特性,说明小尺度裂缝特征和大尺度裂缝特征具有相似的规律性。此外,研究还表明最大水平主应力上的裂缝密度和分形维数最大,缝网结构最为复杂,最小水平主应力方向缝网结构次之,垂直主应力方向的裂缝结构最为简单;水平应力方向上主要以层理裂缝为主,垂直方向上以剪切缝为主,且与最小水平主应力的夹角为-62°。在掌握宏观裂缝分布特征基础上,研究可为页岩显微观测实验提供相应的理论依据。 相似文献
14.
Fred J. Molz Tomasz J. Kozubowski Krzysztof Podgórski James W. Castle 《Hydrogeology Journal》2007,15(4):809-816
In order to generalize the fractal/facies concept, a new stochastic fractal model for ln(K) increment probability density functions (PDFs) is presented that produces non-Gaussian behavior at smaller lags and converges to Gaussian at larger lags. The model is based on the classical Laplace PDF. The new stochastic fractal family is called fractional Laplace motion (fLam) having stationary increments called fractional Laplace noise (fLan). This fractal is different from other fractals because the character of the underlying increment PDFs changes dramatically with lag size, which leads to lack of self-similarity. Data also appear to display this characteristic. In the larger lag size ranges, approximate self-affinity does hold. The basic field procedure for further testing of the fractional Laplace theory is to measure ln(K) increment distributions along transects, calculate frequency distributions from the data, and compare results to appropriate fLan family members. The variances of the frequency distributions should also change with lag size (scale) in a prescribed manner. There are mathematical reasons such as the geometric central limit theorem, for surmising that fLam/fLan may be more fundamental than other approaches that have been proposed for modeling ln(K) frequency distributions. 相似文献
15.
Two-dimensional Hurst Index of Joint Surfaces 总被引：2，自引：1，他引：2
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JRC分形估测方法的实用性 总被引：2，自引：0，他引：2
基于分形几何的码尺法分维数与岩石节理粗糙度系数的物理意义剖析，认为Ｄ－ＪＲＣ之间不存在必然的相关性．分析标准轮廓曲线的分维数，发现其分维数差级微小，难以实行粗糙度系数分级．根据实测资料阐述了岩石节理表面轮廓曲线的“自相似”是统计意义而不是绝对的，它要求ＪＲＣ分形估测应统计求取，而过繁的分维数测量步骤削弱了ＪＲＣ的分形统计估测的可行性．建立在实测资料统计分析基础上的ＪＲＣ尺寸效应分形模型ＪＲＣｎ＝ＪＲＣ０（Ｌｎ／Ｌ０）－Ｄ客观而真实地刻画了粗糙度系数随取样长度增大而降低的规律，其中，ＪＲＣ尺寸效应分维数（Ｄ）具明确的物理意义，它描述了ＪＲＣ随结构面规模增大而降低的衰减速率．最后，运用ＪＲＣ尺寸效应分维数（Ｄ）探讨了岩石节理粗糙度系数尺寸效应的各向异性规律． 相似文献
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钙质砂是远洋地区港口、机场和民用建筑等构筑物的天然地基材料。通过钙质砂一维压缩蠕变试验和微观结构测试,发现了蠕变前后表面孔隙面积减小且呈分散分布的规律以及试验过程中试样瞬时变形、快速变形和衰减变形特征与粒径的高度相关性;利用基于分形理论改进的相对颗粒破碎率和质量分形维数描述了蠕变前后颗粒破碎程度,得到了分形维数和蠕变与时间的衰减形态曲线关系以及宏观质量分形维数和微观表面分形维数的线性关系,并在此基础上对单一粒径组钙质砂蠕变过程中的分形破碎行为进行了多尺度分析和宏微观跨尺度关联性研究,获得了蠕变过程中颗粒破碎发展以及微观孔隙变化规律,证明了钙质砂蠕变过程中的颗粒重组排列、破碎和研磨行为,揭示了钙质砂蠕变机制。 相似文献
19.
On the practice of estimating fractal dimension 总被引：11，自引：0，他引：11
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
20.
根据Ramberg的纵弯褶皱粘性力学实验,在褶皱形态的分形分析基础上,利用分形理论和褶皱的流变学理论导出了褶皱的分数维(D)与岩层厚度(h)和粘度(μ)间的关系式,并探讨了褶皱复杂性对褶皱分数维的影响,从中获得有关复杂褶皱的流变学信息。影响分形褶皱复杂程度的因素很多,主要因素包括岩层的厚度和粘度。因此,对褶皱的分形测量和岩层厚度及粘度的分析,可以定量分析分形褶皱形成的流变机理。这一研究是褶皱的非线性流变学理论研究的一个尝试。 相似文献