Coding random self-similar river networks and calculating geometric distances: 1. General methodology / Codage de réseaux hydrographiques auto-similaires aléatoires et calcul de distances géométriques: 1. Méthodologie générale

Abstract

This study proposes a preliminary method for coding random self-similar river networks as a series of numbers, and investigates the corresponding algorithm that calculates the geometric distances from the code series. The coding method, generating random self-similar patterns with various probabilities of particular pattern links, and transferring the pattern into numerical code series, is proposed, based on the wide range of stochastic characteristics of natural patterns. The heredity of self-similarity and the connecting relationships inside the generated pattern are discussed. Finally, the algorithm to calculate the geometric distances of the generated pattern are developed.     

Scaling properties and spatial organization of snow depth fields in sub‐alpine forest and alpine tundra

This paper reports on a study analysing the spatial distribution functions, the correlation structures, and the power spectral densities of high‐resolution LIDAR snow depths (～1 m) in two adjacent 500 m × 500 m areas in the Colorado Rocky Mountains, one a sub‐alpine forest the other an alpine tundra. It is shown how and why differences in the controlling physical processes induced by variations in vegetation cover and wind patterns lead to the observed differences in spatial organization between the snow depth fields of these environments. In the sub‐alpine forest area, the mean of snow depth increases with elevation, while its standard deviation remains uniform. In the tundra subarea, the mean of snow depth decreases with elevation, while its standard deviation varies over a wide range. The two‐dimensional correlations of snow depth in the forested area indicate little spatial memory and isotropic conditions, while in the tundra they indicate a marked directional bias that is consistent with the predominant wind directions and the location of topographic ridges and depressions. The power spectral densities exhibit a power law behaviour in two frequency intervals separated by a break located at a scale of around 12 m in the forested subarea, and 65 m in the tundra subarea. The spectral exponents obtained indicate that the snow depth fields are highly variable over scales larger than the scale break, while highly correlated below. Based on the observations and on synthetic snow depth fields generated with one‐ and two‐dimensional spectral techniques, it is shown that the scale at which the break occurs increases with the separation distance between snow depth maxima. In addition, the breaks in the forested area coincide with those of the corresponding vegetation height field, while in the tundra subarea they are displaced towards larger scales than those observed in the corresponding vegetation height field. Copyright © 2009 John Wiley & Sons, Ltd.     

塔中Ⅰ号断裂带北段构造裂缝面密度与分形统计

断裂如何控制其附近构造裂缝的发育程度是碳酸盐岩地区构造裂缝定量研究的重要方面,对碳酸盐岩裂缝性油气藏的储层预测具有重要的意义.文中以塔中Ⅰ号断裂带为例,重点研究逆冲断裂控制构造裂缝的分布规律,对其控制的构造裂缝面密度和分形进行了研究.研究结果表明,塔中工号断裂控制的构造裂缝的裂缝面密度与距断裂的距离呈指数关系,其控制的...     

Stochastic computational modelling of highly heterogeneous poroelastic media with long‐range correlations

The compaction of highly heterogeneous poroelastic reservoirs with the geology characterized by long‐range correlations displaying fractal character is investigated within the framework of the stochastic computational modelling. The influence of reservoir heterogeneity upon the magnitude of the stresses induced in the porous matrix during fluid withdrawal and rock consolidation is analysed by performing ensemble averages over realizations of a log‐normally distributed stationary random hydraulic conductivity field. Considering the statistical distribution of this parameter characterized by a coefficient of variation governing the magnitude of heterogeneity and a correlation function which decays with a power‐law scaling behaviour we show that the combination of these two effects result in an increase in the magnitude of effective stresses of the rock during reservoir depletion. Further, within the framework of a perturbation analysis we show that the randomness in the hydraulic conductivity gives rise to non‐linear corrections in the upscaled poroelastic equations. These corrections are illustrated by a self‐consistent recursive hierarchy of solutions of the stochastic poroelastic equations parametrized by a scale parameter representing the fluctuating log‐conductivity standard deviation. A classical example of land subsidence caused by fluid extraction of a weak reservoir is numerically simulated by performing Monte Carlo simulations in conjunction with finite elements discretizations of the poroelastic equations associated with an ensemble of geologies. Numerical results illustrate the effects of the spatial variability and fractal character of the permeability distribution upon the evolution of the Mohr–Coulomb function of the rock. Copyright © 2004 John Wiley & Sons, Ltd.     

Randomness: a property of the mathematical and physical systems

ABSTRACT

This article is a concept paper, which discusses the definition of randomness, and the sources of randomness in the mathematical system as well as in the physical system (the Universe). We document that randomness is an inherited property of mathematics and of the physical world, shaping all observed forms and structures, and we discuss its role.

Editor D. Koutsoyiannis; Guest editor E. Volpi     

基于Hurst指数的矿化强度识别－以山东大尹格庄金矿为例

探索成矿元素分布的分形特征是揭示矿化富集程度的重要途径之一。运用重标极差分析（R/S）方法,研究了山东大尹格庄金矿-210 m中段多勘探线Au品位序列随采样尺度变化的趋势,探讨元素序列的Hurst指数与矿化强度的关系。结果显示:具有不同矿化强度的勘探线Au的Hurst指数存在明显差异,且均大于0.5;矿化连续分布或间断出现的勘探线元素品位序列的Hurst指数大于0.65,表明元素序列具有标度不变性和长相关性,序列的持续强度与矿化程度基本一致,可为区域矿化强度定量识别提供一种新的有效方法。     

Correlation analysis of large-scale structure using data from the SDSS DR5 LRG catalog

Correlation properties of the large-scale structure of the distribution of luminous red galaxies are evaluated using data from Data Release 5 of the Sloan Digital Sky Survey. The correlations on small scales are characterized by the distribution of distances to the nearest neighboring galaxy ω(r). The conditional number density Γ(r) indicates a power law correlation with an exponent γ = 1.0±0.1 over scales of [1, 30] Mpc/h in redshift space. For larger scales of [30, 200] Mpc/h, a transition from a power law to a flat segment is observed. However, the presence of a flat segment in the estimated conditional density is only a necessary, but not sufficient, condition for homogeneity of a given sample. In particular, the flat segment may be caused by the presence of superlarge structures (such as have been discovered in the most recent ultra-deep COSMOS survey) which lead to a systematic shift in the estimated conditional number density. The behavior of the reduced two-point correlation function) ξ(r) is also discussed for scales of [1, 200] Mpc/h. Over small scales, where ξ(r) >> 1, the slopes of the reduced correlation function and the conditional number density are the same. __________ Translated from Astrofizika, Vol. 51, No. 3, pp. 393–408 (August 2008).     

On a geometric method for determining the masses of the Galilean satellites of Jupiter

A geometric method for calculating the relative masses of the Galilean satellites of Jupiter is proposed. Local characteristics coincident with the Hausdorff—Bezikovich dimension have been calculated for each planet—satellite pair. The relative masses calculated by the geometric method differ from those obtained by analyzing the motion of spacecraft by no more than 0.1%.     

Multiscale sources of spatial variation in soil. III. Improved methods for fitting the nested model to one-dimensional semivariograms

The previous paper in this series presented a one-dimensional stochastic nested model to account for superimposed sources of soil variation at various scales. This paper shows how the nested model can be fitted to experimental data using weighted or generalized least-squares methods that account for correlations between consecutive terms that had previously been neglected. This paper also presents a method of estimating effective degrees of freedom for each sampling interval and thus for estimating 90% confidence limits for the semivariogram of the nested model.     

Multifractal Simulation of GeochemicalMap Patterns

INTRODUCTIONThe mathematical modeling of geochemical data continuesto present an important challenge to earth scientists. Basically,the available data are 2-dimensional realizations of 3dimensional patterns, which are the results of one or more genetic processes that usually are poorly understood. It may bedifficult to project from the observations into the rock mass. Inthis paper, multifractal modeling is advocated as a methodologyto characterize geochemical patterns. If a geochemical pa…