共查询到20条相似文献，搜索用时 15 毫秒
1.
Fractal geostatistics are being applied to subsurface geological data as a way of predicting the spatial distribution of hydrocarbon reservoir properties. The fractal dimension is the controlling parameter in stochastic methods to produce random fields of porosity and permeability. Rescaled range (R/S)analysis has become a popular way of estimating the fractal dimension, via determination of the Hurst exponent (H). A systematic investigation has been undertaken of the bias to be expected due to a range of factors commonly inherent in borehole data, particularly downhole wireline logs. The results are integrated with a review of previous work in this area. Small datasets. overlapping samples, drift and nonstationariry of means can produce a very large bias, and convergence of estimates of H around 0.85–0.90 regardless of original fractal dimension. Nonstationarity can also account for H>1, which has been reported in the literature but which is theoretically impossible for fractal time series. These results call into question the validity of fractal stochastic models built using fractal dimensions estimated with the R/Smethod. 相似文献
2.
Is the ocean floor a fractal? 总被引：1，自引：0，他引：1
The topographic structure of the ocean bottom is investigated at different scales of resolution to answer the question: Can the seafloor be described as a fractal process? Methods from geostatistics, the theory of regionalized variables, are used to analyze the spatial structure of the ocean floor at different scales of resolution. The key to the analysis is the variogram criterion: Self-similarity of a stochastic process implies self-similarity of its variogram. The criterion is derived and proved here: it also is valid for special cases of self-affinity (in a sense adequate for topography). It has been proposed that seafloor topography can be simulated as a fractal (an object of Hausdorff dimension strictly larger than its topological dimension), having scaling properties (self-similarity or self-affinity). The objective of this study is to compare the implications of these concepts with observations of the seafloor. The analyses are based on SEABEAM bathymetric data from the East Pacific Rise at 13°N/104°W and at 9°N/104°W and use tracks that run both across the ridge crest and along the ridge flank. In the geostatistical evaluation, the data are considered as a stochastic process. The spatial continuity of this process is described by variograms that are calculated for different scales and directions. Applications of the variogram criterion to scale-dependent variogram models yields the following results: Although the seafloor may be a fractal in the sense of the definition involving the Hausdorff dimension, it is not self-similar, nor self-affine (in the given sense). Mathematical models of scale-dependent spatial structures are presented, and their relationship to geologic processes such as ridge evolution, crust formation, and sedimentation is discussed. 相似文献
3.
4.
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
5.
The reliability of using fractal dimension (D) as a quantitative parameter to describe geological variables is dependent mainly
on the accuracy of estimated D values from observed data. Two widely used methods for the estimation of fractal dimensions
are based on fitting a fractal model to experimental variograms or power-spectra on a log-log plot. The purpose of this paper
is to study the uncertainty in the fractal dimension estimated by these two methods. The results indicate that both spectrum
and variogram methods result in biased estimates of the D value. Fractal dimension calculated by these two methods for the
same data will be different unless the bias is properly corrected. The spectral method results in overestimated D values.
The variogram method has a critical fractal dimension, below which overestimation occurs and above which underestimation occurs.
On the bases of 36,000 simulated realizations we propose empirical formulae to correct for biases in the spectral and variogram
estimated fractal dimension. Pitfalls in estimating fractal dimension from data contaminated by white noise or data having
several fractal components have been identified and illustrated by simulated examples. 相似文献
6.
N. E. Odling 《Rock Mechanics and Rock Engineering》1994,27(3):135-153
Summary Thirteen natural rock profiles (Barton and Choubey, 1977) are analyzed for their fractal properties. Most of the profiles were found to approximate fractal curves but some also showed features of specific wavelengths and amplitudes superimposed on fractal characteristics. The profiles showed fractal dimensions from 1.1 to 1.5 covering a range of selfsimilar and self-affine curves. The analysis results suggest a negative correlation between fractal dimension,D, and amplitude,A. Joint roughness coefficients (JRC) show a positive correlation with amplitude,A, and a negative correlation with fractal dimension,D. A numerical model of fracture closure is used to investigate the effects of different profile characteristics (D, A and sample size) on the nature of dilation and contact area, using the natural profiles and synthetic fractional Brownian motion profiles. Smooth profiles (low JRC, highD, lowA) display many small contact regions whereas rough fractures (high JRC, lowD, highA) display few large contact areas. The agreement with published experimental data supports the suggested correlations between JRC and the fractal parameters,A andD. It is suggested that observed scale effects in JRC and joint dilation can be explained by small differential strain discontinuities across fractures, which originate at the time of fracture formation. 相似文献
7.
The topographic structure of the ocean bottom is investigated at different scales of resolution to answer the question: Can the seafloor be described as a fractal process? Methods from geostatistics, the theory of regionalized variables, are used to analyze the spatial structure of the ocean floor at different scales of resolution. The key to the analysis is the variogram criterion: Self-similarity of a stochastic process implies self-similarity of its variogram. The criterion is derived and proved here: it also is valid for special cases of self-affinity (in a sense adequate for topography). It has been proposed that seafloor topography can be simulated as a fractal (an object of Hausdorff dimension strictly larger than its topological dimension), having scaling properties (self-similarity or self-affinity). The objective of this study is to compare the implications of these concepts with observations of the seafloor. The analyses are based on SEABEAM bathymetric data from the East Pacific Rise at 13°N/104°W and at 9°N/104°W and use tracks that run both across the ridge crest and along the ridge flank. In the geostatistical evaluation, the data are considered as a stochastic process. The spatial continuity of this process is described by variograms that are calculated for different scales and directions. Applications of the variogram criterion to scale-dependent variogram models yields the following results: Although the seafloor may be a fractal in the sense of the definition involving the Hausdorff dimension, it is not self-similar, nor self-affine (in the given sense). Mathematical models of scale-dependent spatial structures are presented, and their relationship to geologic processes such as ridge evolution, crust formation, and sedimentation is discussed. 相似文献
8.
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
9.
Fractal Analysis of the Complexity of United States Coastlines 总被引：10，自引：0，他引：10
Coastlines have long been used as a principal example of a natural feature that exhibits fractal structure. With the advent of large digitized databases, it has become possible to examine in detail large regions of coast and to examine differences in complexity, as measured by the fractal dimension, among regions. In this study, we have determined the fractal dimension of the Atlantic and Pacific coastlines of the conterminous United States. The traditional divider method was used in obtaining the fractal dimension of each coastline arc from the NOAA Medium-Resolution Shoreline Data Set. On average, the Atlantic coast has much higher fractal dimension than the Pacific coast. The results also indicate that the complexity of the Atlantic coast increases toward low latitudes. These results have implications for the interpretation of species distributions and diversity patterns along the coast and for the understanding of the dynamics of biotic recovery from mass extinctions. 相似文献
10.
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
11.
12.
The variations of rock magnetism reflect the geological inhomogeneities of the earth's crust, i.e. its petrological-mineralogical and structural organization. The present state of the crust bears meaningful information of its past dynamic processes and evolution. We analysed magnetic susceptibility data series from the boreholes of the German Continental Deep Drilling Project (KTB). By means of spectral and rescaled-range (R/S) analyses we could detect a scaling behaviour of magnetic data series and quantify it in fractal terms. In particular, the R/S method yields more precise results than the Fourier analysis and leads to Hurst coefficients H > 0.5, which means that the magnetic variations exhibit some persistence with depth. Because of the relation between rock magnetism and crustal features, we suggest that the magnetic vertical inhomogeneities in the KTB area can be described by a self-affine model with H 0.8, corresponding to a fractal dimension D 1.2. 相似文献
13.
Fractal trees as a model for drainage systems are described in its generalized non-homogeneous form from the viewpoint of fractal geometry. Box covering techniques are used to show the numerical equivalence between the Hausdorff-Besicovitch dimension and the similarity dimension of the fractally-dominant dust formed by the sources. In this way, the similarity relationD=log (N)/log (1/r) is reinterpreted in terms of bifurcation and length ratio (r
B
andr
L
) asD=log (r
B
)/log (r
L
). We test this relation for non-homogeneous exact fractal trees and two natural drainage systems. The fact thatr
B
andr
L
are common parameters in quantitative geomorphology allows a trivial stimation of the fractal dimension of well-known drainage basins. 相似文献
14.
The aim of this short note is to test whether the morphological skeletal network (MSN) of water bodies that resembles a river network follows Horton's laws. A fractal relationship of MSN of a water body is also shown. This investigation shows that the MSN of the Nizamsagar reservoir follows Horton's laws. Furthermore, this reservoir has a fractal dimension (D
m) of 1.92 which was computed by using two morphometric quantities and the fractal dimension of the main skeletal length (d). This value tallies exactly with the fractal dimension (D
f) of the whole MSN computed through box-counting method. 相似文献
15.
Quantification of Aperture and Relations Between Aperture,Normal Stress and Fluid Flow for Natural Single Rock Fractures 总被引：1，自引：0，他引：1
Pinnaduwa H. S. W. Kulatilake Jinyong Park Pirahas Balasingam Robert Morgan 《Geotechnical and Geological Engineering》2008,26(3):269-281
Accurate quantification of rock fracture aperture is important in investigating hydro-mechanical properties of rock fractures.
Liquefied wood’s metal was used successfully to determine the spatial distribution of aperture with normal stress for natural
single rock fractures. A modified 3D box counting method is developed and applied to quantify the spatial variation of rock
fracture aperture with normal stress. New functional relations are developed for the following list: (a) Aperture fractal
dimension versus effective normal stress; (b) Aperture fractal dimension versus mean aperture; (c) Fluid flow rate per unit
hydraulic gradient per unit width versus mean aperture; (d) Fluid flow rate per unit hydraulic gradient per unit width versus
aperture fractal dimension. The aperture fractal dimension was found to be a better parameter than mean aperture to correlate
to fluid flow rate of natural single rock fractures. A highly refined variogram technique is used to investigate possible
existence of aperture anisotropy. It was observed that the scale dependent fractal parameter, K
v, plays a more prominent role than the fractal dimension, D
a1d, on determining the anisotropy pattern of aperture data. A combined factor that represents both D
a1d and K
v, D
a1d × K
v, is suggested to capture the aperture anisotropy. 相似文献
16.
This paper establishes the phase space in the light of spacial series data,discussesthe fractal structure of geological data in terms of correlated functions and studies thechaos of these data.In addition,it introduces the R/S analysis for time series analysisinto spacial series to calculate the structural fractal dimensions of ranges and standard de-viation for spacial series data,and to establish the fractal dimension matrix and the proce-dures in plotting the fractal dimension anomaly diagram with vector distances of fractal di-mension.At last,it has examples of its application. 相似文献
17.
Knowledge of mineral aggregate morphologies is of importance to analyze characteristic differences in rock-forming features. For quantifying these differences, the fractal geometry of quartz aggregate cuts digitized from polish sections of different types of granites has been studied. As an approach to measure fractal dimension (D), a power-law dependence of square of aggregate cuts on their linear size has been used. The D values thus calculated mainly increase from 1.48–1.62 for amazonite granites to 1.63–1.70 for alaskite granites and 1.75–1.81 for standard granites. To account for the data of morphometry, the model of nucleation and growth as applied to silicate melt freezing has been considered. For comparison between the nature and model textures, the fractal properties of cluster cuts in the system of overlapping spheres randomly distributed with random radii have been investigated through computer simulation. It has been demonstrated that the distributions of quartz aggregates in granites may be simulated by homogeneous or heterogeneous Poisson models, and both order of crystallization and metamorphic recrystallization should be taken for explaining textural variability. The results of the simulation have enabled the granitic texture to be discussed with respect to the random configuration of the spatial percolation cluster. 相似文献
18.
断裂构造是控制川西北地区金矿形成与分布的主导因素。运用分形方法定量计算了该区金矿化异常和控矿断裂体系的计盒维数和信息维数。研究结果表明 ,利用地球化学数据二维空间序列的R/S分形方法可以较为精确有效地厘定金矿化的空间结构特征 ,分数维D值的大小能表征控矿断裂体系的复杂性。金矿化带整体上受NW向断裂控制 ,但金矿体则产出于NW向断裂与NE向断裂的复合部位。根据对三个矿化区断裂体系分维特征与金矿发育特征关系的分析 ,发现断裂体系的分维高值区与金矿分布密集区对应。阿坝地块西南缘的找矿前景不如东北缘 相似文献
19.
This work presents the application of a Monte Carlo simulation method to perform an statistical analysis of transient variably saturated flow in an hypothetical random porous media. For each realization of the stochastic soil parameters entering as coefficients in Richards' flow equation, the pressure head and the flow field are computed using a mixed finite element procedure for the spatial discretization combined with a backward Euler and a modified Picard iteration in time. The hybridization of the mixed method provides a novel way for evaluating hydraulic conductivity on interelement boundaries. The proposed methodology can handle both large variability and fractal structure in the hydraulic parameters. The saturated conductivity K
s and the shape parameter vg in the van Genuchten model are treated as stochastic fractal functions known as fractional Brownian motion (fBm) or fractional Gaussian noise (fGn). The statistical moments of the pressure head, water content, and flow components are obtained by averaging realizations of the fractal parameters in Monte Carlo fashion. A numerical example showing the application of the proposed methodology to characterize groundwater flow in highly heterogeneous soils is presented. 相似文献
20.
断裂尺度的分形分布与其损伤演化的关系 总被引：3，自引：1，他引：2
借助于分形几何学和损伤力学的方法,重新考察和分析计算了有关的岩石断裂实验所提供的实验数据。分析计算结果表明:岩石断裂的损伤演化过程具有良好的统计自相似性,断裂尺度分布的分形维数能够很好地刻画岩石的损伤程度,并且在岩石断裂的损伤演化过程中,断裂尺度分布的分形维数(DL)随外载荷(σ)呈线性增大。对断裂尺度分布的分形维数而言,损伤演化过程是一个增维过程。根据计算结果给出了分形维数(DL)与损伤变量(ω)之间的经验关系。 相似文献