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1.
The stratified structure of Koch curves limits their value as models of nonstratified curves typical in nature, which may nevertheless have statistically self-similar character. Richardson plots for basic and randomized Koch curves are marked by strong, scale-periodic disruptions, and compare poorly with the smoothly sloping, compact Richardson plots derived for some natural, irregular curves. These disruptions relate to the heirarchies of dominant element sizes created in the discrete steps of Koch curve construction, with element vertices acting as attractors for divider steps. We have developed a curve-generation algorithm that adds individual bend elements to a line segment in a nonstratified manner, explicitly following the self-similar limit relation of curve length (L) to added line segment length (r). Values that may be specified include curve fractal dimension (D) and bend element shape (angle of inclination for the added segments). The procedure allows combinations of fractal dimension and element shape, which encompass the range of D values encountered for natural fractal curves. The nonstratified construction method provides useful standard curves for testing and norming of geometric analysis methods commonly applied to complex natural features. In a preliminary test of a multisampling divider method algorithm, the resulting Richardson plots consistently diverge from linear form, and are likely to lead to an overapproximation of D value. 相似文献
2.
The use of the fractal dimension to quantify the morphology of irregular-shaped particles 总被引：3，自引：0，他引：3
For several decades, sedimentologists have had difficulty in obtaining an efficient index of particle form that can be used to specify adequately irregular morphology of sedimentary particles. Mandelbrot has suggested the use of the fractal dimension as a single value estimate of form, in order to characterize morphologically closed loops of an irregular nature. The concept of fractal dimension derives from Richardson's unpublished suggestion that a stable linear relationship appears when the logarithm of the perimeter estimate of an irregular outline is plotted against the logarithm of the unit of measurement (step length). Decreases in step length result in an increase in perimeter by a constant weight (b) for particles whose morphological variations are the same at all measurement scales (self-similarity). The fractal dimension (D) equals 1.0-(b), where b is the slope coefficient of the best-fitting linear regression of the plot. The value of D lies between 1.0 and 2.0, with increasing values of D correlating with increasing irregularity of the outline. In practice, particle outline morphology is not always self-similar, such that two or possibly more fractal elements can occur for many outlines. Two fractal elements reflect the morphological difference between micro-scale edge textural effects (D1) and macro-scale particle structural effects (D2) generated by the presence of crenellate-edge morphology (re-entrants). Fractal calibration on a range of regular/irregular particle outline morphologies, plus examination of carbonate beach, pyroclastic and weathered quartz particles indicates that this type of analysis is best suited for morphological characterization of irregular and crenellate particles. In this respect, fractal analysis appears as the complementary analytical technique to harmonic form analysis in order to achieve an adequate specification of all types of particles on a continuum of irregular to regular morphology. 相似文献
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On the basis of results of simple box-counting analysis, it has been suggested in several recent publications that natural fracture patterns are fractal. Fractal patterns are characterized by self-similarity of structure on a range of scales and provide straight-line distributions on box-counting plots. New analysis of a fracture pattern that provided the most convincing straight-line box-counting curve previously published, shows that the curve is non-linear and, therefore, that the fracture pattern is not fractal. Non-linear box-counting curves are also characteristic of other natural fracture patterns analysed but spurious linear curves can be obtained if the area analysed extends beyond the mapped area. 相似文献
4.
成矿元素品位有序数据集自仿射分形方法应用性评价 总被引：1，自引：0，他引：1
自仿射分形的Hurst指数是分析地质剖面数据的有利参数。以大尹格庄金矿不同勘探线刻槽取样所得的金品位序列为例，评价Hurst指数的几种估算方法在地质剖面数据分析中的适用性。取相同尺度，全部数据集的增量标准偏差法统计散点呈波状变化，部分数据集的曲线长度变换法统计散点的后半部分呈波状变化,全部数据集的重标极差分析法统计散点线性拟合较好。结果显示增量标准偏差法对尺度要求较为苛刻，适于巨量数据的统计；曲线长度变换法应用性较广，所得Hurst指数反映品位的空间变化强度；重标极差分析法稳定性最好，其Hurst指数反映了品位变化相依性。
相似文献
5.
Mark E. Kuchta 《Mathematical Geology》2002,34(6):631-645
For a fractal curve, the measured perimeter length increases as the ruler length decreases. When the perimeter of a fractal curve is traced with a given ruler size, there are areas between the straight-line segments and the true curve. If the underlying geometric rule for creating the fractal curve is known, then the size of the areas can be calculated. An equation has been developed for calculating the absolute value of the area between a straight-line approximation and the true curve for the random function ordinary one-dimensional Brownian motion. One potential application of the equation developed is in estimating the amount of ore loss and waste rock dilution that would occur in a mining operation as a result of the errors in the geologic model of the boundaries of an orebody. 相似文献
6.
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
7.
The fractal dimension of pores in sedimentary rocks and its influence on permeability 总被引：2，自引：0，他引：2
E. M. Schlueter R. W. Zimmerman P. A. Witherspoon N. G. W. Cook 《Engineering Geology》1997,48(3-4):199-215
Perimeter-area power-law relationship of pores in five sedimentary rocks are estimated from scanning electron micrographs of thin sections. These relationships for the pores of four sandstones were found to lie between 1.43 and 1.49, while that of an Indiana limestone was found to be 1.67. We show how the perimeter-area power-law relationship of pores, along with a pore-size distribution, can be used to estimate the hydraulic permeability. A discussion is given of how the fractal dimension of the pore perimeter derived by Mandelbrot for islands whose boundaries are fractal: P = εDAD/2, where ε is some constant that depends on the length of the measuring grid size and D is the fractal dimension of the pore perimeter, influences permeability. 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
10.
Thomas H. Wilson 《Mathematical Geology》2001,33(5):591-613
Detailed box counting analysis was conducted of (1) fractures observed in exposures of the Devonian Shale in the central Appalachians Valley and Ridge Province of West Virginia, (2) several fracture patterns presented in the literature, and (3) active faults mapped throughout the main island (Honshu) of Japan. Box curves reveal, with few exceptions, that most naturally occurring fracture patterns are characterized by nonfractal behavior. In many cases, two linear regions separated by an abrupt transition are observed in the logN/logr box curves. The small-scale (larger r) features generally have higher fractal dimension than do the larger scale features in the pattern. Transitions from one region to another are usually abrupt. These transitions are not associated with sampling problems or other data limitations. In some cases three or more linear regions may appear. Box counting analysis of model fracture patterns indicate that transitions are related to the dominant spacing of individual sets or to the dominant fragment size in the network. This study provides detailed documentation of scale invariant features in natural fracture and active fault patterns. Although the relationship of the geometrical properties of a pattern to the location of transitions is understood in terms of the models, to understand the physical mechanisms responsible for these transitions deserves further study. 相似文献
11.
遥感线性构造分形统计和蚀变信息提取在桂东地区金铅锌锡多金属成矿预测中的应用 总被引：2，自引：1，他引：1
在桂东地区ETM+遥感影像742波段融合的基础上,进行了线性构造和环形构造解译,运用分形几何学的原理和方法对研究区的遥感线性构造进行定量分析,利用计盒维数法求得研究区的线性构造分维值,得出该区线性构造具有良好的统计自相似性和分形特征,利用Surfer软件求得线性构造分维等值线图,采用主成分分析和比值法组合提取遥感蚀变异... 相似文献
12.
分形噪声、（多维）分形滤波及地球物理测井典型处理应用 总被引：6，自引：0，他引：6
白噪声、布郎运动以及其它满足在双对数坐标中呈一直线的信号具分形结构、自相似性或尺度无关性。地球物理信号通常表现为多个这类信号的叠加，为多维分形特征。研究、模拟在双对数坐标中成一直线的信号以及如何将多维分形中多个这种信号剖分出来，对于理解相应的地质、地球物理成因机制具有重要意义。通过对两口井的地球物理测井曲线处理，可以初步看出，在选定的地球物理测井曲线中，其具多维分形特征，不同的沉积过程相互叠加在原始测井曲线中。用滤波方法分析分解信号，可以了解不同沉积作用特征并进一步分析可能的环境变化控制机制。开发的图形界面程序使得这一过程极为容易实现。 相似文献
13.
滇东南丘北区峰丛—洼地地貌形态特征分析 总被引：1，自引：0，他引：1
云贵高原东南部丘北区为峰丛—洼地岩溶组合地貌。利用统计分析方法考察了该区48个岩溶洼地及峰体的形态参数特征;利用分形理论方法计算了不同高程的等高线和地表水系的分维数。结果表明:（1）洼地的平均边数为5.6,平均周长3.4km,平均面积0.8km2;（2）洼地的加深和扩大近于同步,原始地面对后期溶蚀面的发育起控制作用;（3）峰丛—洼地的形态分形特征对岩溶演化具有很好的响应关系,可溶岩区等高线分维数平均为1.30,非可溶岩区为1.16,地表水文网分维数为1.07,反映岩溶区地形变化复杂,地下水文网较发育,岩溶发育程度较高;（4）研究区岩溶发育仍处于幼年至壮年期,将继续缓慢发育。 相似文献
14.
The low-grade Palaeoproterozoic stratabound banded iron ores of the Krivoy Rog basin (Ukraine) underwent strong tectonometamorphic deformation into superimposed folds of several orders, with amplitudes from centimetres to hundreds of metres. The across-strike sections of bed surfaces defining the low-grade ore bodies resemble self-similar fractal curves; hence, a fractal geometrical model was developed in order to quantify the complexity and sinuosity of bed contours. Two different methods of measurement (polygonal approximation and two-dimensional grid cell counting) were used for 5–8 different scales. Factual similarity dimension D and other model parameters have been estimated by means of linear regression and compared for both measurement methods. From the fractal model a sinuosity coefficient of contours of the folded bed surfaces K
s
and a coefficient of degree of exploration of iron ore bodies K
e
were constructed. It is pointed out that parameters of the model can be used for determination of the optimal exploration length scales. 相似文献
15.
分形几何理论的产生和发展为刻画非欧几里得几何系统(即分维系统)的性质提供了有效手段，使用这一工具对油气渗流规律进行重新认识，对传统描述油气运动的数学模型加以改进，并应用于试井分析中．根据传统模型图版制作原理，作出分形麦金利图版，可以看出：与传统模型拟和很差的实际数据，与分形麦金利图版的匹配效果却很好．说明油气藏更接近分维系统，所求得的各种参数更接近地下真实复杂情况，这对于油气田开发工作有重要的指导意义． 相似文献
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随着鄂尔多斯盆地子洲-清涧地区上古生界碎屑岩气藏研究的深入,其物源问题引起了人们的关注。为查明物源问题,本文应用分形理论对山西组山2~3段的沉积物源进行了研究,系统地分析了铀、钍、钾测井曲线的分形特征、分形特征在沉积物源分析中的应用过程以及分形特征对沉积物源的响应机理。结果表明,铀、钍、钾测井曲线具有分形特征,其分形特征对沉积物源具有一定程度的响应,研究区内西北部物源控制区与东北部物源控制区具有不同的沉积物源分形响应特征,通过分形响应得到的沉积物源分析结果与已有的地质认识较为吻合。分形特征研究为沉积物源的分析提供了一种途径,具有一定的应用价值。 相似文献
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河南祁雨沟金矿及外围高植被区遥感找矿预测 总被引：1，自引：0，他引：1
应用ENVI4.8软件,对河南嵩县祁雨沟金矿及外围ETM+遥感数据通过主成分分析、彩色合成、直方图拉伸、监督分类等方法,成功地提取了高植被覆盖区遥感影像上金的植物地球化学异常信息。利用卷积滤波和形态学分析方法进行线性构造解译,利用计盒维数法求得研究区的线性构造分维值,得出本区线性构造具有良好的统计自相似性和分形特征。比较线性构造分维等值线图和植物地球化学异常图可知,线性构造集中区与植被异常区基本吻合,区内已知85%以上的矿点分布于植被异常和线性构造集中区。综合分析地层岩性、岩浆岩、矿点、线性构造分维等值线特征和遥感植被异常特征等信息,圈出了三级9个找矿靶区。 相似文献
20.
Brenda B. Jensen 《Geochimica et cosmochimica acta》1973,37(10):2227-2242
When a phenocryst and its lava matrix have been analysed for both major and trace elements, plots of partition coefficient (mineral/matrix) against ionic radius give a family of sub-parallel curves, one univalent, one divalent, etc. Onuma et al. (1968) demonstrated this with two analyses and concluded, from the shape of these curves, that trace element partition between phenocryst and groundmass is determined primarily by crystal structure of the phenocryst. In this study, over 50 such analyses, taken from the literature, have been plotted on modified Onuma diagrams, in order to analyse the constant and variable factors in the curves. It is demonstrated that these curves can provide important additional information in trace element studies by revealing, for example, the site or sites in a mineral which a given element is occupying, the valency state of the element and even, in some cases, the proportion of different valency states present. 相似文献