Self-affine gravity covariance model for the Bay of Bengal     

Abhey Ram Bansal  Vijay P. Dimri 《Geophysical Journal International》2005,161(1):21-30

  相似文献   

Fractures: Finite-size scaling and multifractals   总被引：1，自引：0，他引：1  

L. J. Pyrak-Nolte  L. R. Myer  D. D. Nolte 《Pure and Applied Geophysics》1992,138(4):679-706

The distributions of contact area and void space in single fractures in granite rock have been determined experimentally by making metal casts of the void spaces between the fracture surfaces under normal loads. The resulting metal casts on 52 cm diameter core samples show a complex geometry for the flow paths through the fracture. This geometry is analyzed using finite-size scaling. The spanning probabilities and percolation probabilities of the metal casts are calculted as functions of observation scale. Under the highest stresses of 33 MPa and 85 MPa there is a significant size-dependence of the geometric flow properties for observation scales smaller than 2 mm. Based on this data, the macroscopic percolation properties of the extended fracture can be well represented by relatively small core samples, even under normal stresses larger than 33 MPa. The metal casts also have rich multifractal structure that changes with changing stress.  相似文献   

长江中游城市群空间结构的多分形特征     

郑文升  杜南乔  杨瑶  王晓芳  熊志飞 《地理学报》2022,77(4):947-959

在城市群越来越演化为多尺度、多区域复杂系统背景下,有必要引入多分形理论与方法研究其空间结构。本文基于2018年NPP-VIIRS夜间灯光数据,计算长江中游城市群整体及其局部的多分维谱,根据谱线分析不同尺度下长江中游城市空间结构的多分形特征。结果显示：① 长江中游城市群夜间灯光容量维在整体和局部都出现双标度现象。② q < -5.5时,整体广义关联维谱线突破理论上限2,在q > 0时,武汉城市圈和环长株潭城市群的分维显著较高。③ 整体的局部分维谱和武汉城市圈、环长株潭城市群、环鄱阳湖城市群、宜荆荆城市群局部分维谱表现为单峰偏右。根据上述结果,得到和验证了以下结论：① 长江中游城市群区域一体化程度较低。② 长江中游城市群不同层级和区域的空间结构差异显著,呈现出多尺度复杂特征。③ 长江中游城市群在不同尺度中均倾向于中心集聚式发展。研究揭示多分形模型能够从尺度依赖视角有效揭示巨型城市群空间结构的复杂性及其背后的问题,具有很好的理论探索和实践分析前景。  相似文献   

Finite cube elements method for calculating gravity anomaly and structural index of solid and fractal bodies with defined boundaries     

Mostafa E. Mostafa 《Geophysical Journal International》2008,172(3):887-902

In this paper, we present the finite cube elements method (FCEM); a novel numerical tool for calculating the gravity anomaly g and structural index SI of solid models with defined boundaries and variable density distributions, tilted or in normal position (e.g. blocks, faulted blocks, cylinders, spheres, hemispheres, triaxial ellipsoids). Extending the calculation to fractal objects, such as Menger sponges of different orders and bodies defined by polyhedrons, demonstrates the robustness of FCEM. In addition, approximating the cube element by a sphere of equal volume makes the calculation of gravitation and related derivatives much simpler. In gravity modelling of a sphere, cubes with edges of 100 m and 200 m achieve a good compromise between running time and overall error.
Displaying the distribution of SI of the studied models on contour maps and profiles will have a strong impact on the forward and inverse modelling of potential field data, especially for Euler deconvolution.
For Menger sponges, plots of gravity elements g and its derivatives show similar patterns independent of fractal order. Moreover, both the pattern and magnitude of SI are independent of fractal order, allowing the use of SI as a new invariant measure for fractal objects. However, SI pattern and magnitude strongly depend on the depth to the buried bodies as do other elements
In this study, we also present a new type of plot; the structural index against distance variation diagrams from which we extract the three critical SI ( CSI ) values, one per axis. The inversion of gravity anomaly data at CSI values gives the optimal mean location of the buried body.  相似文献   

Montecarlo DLA-type simulations of wetting effects in fluid displacement in porous media     

Rafael Rangel  Sergio Rojas 《Computational Geosciences》2009,13(2):215-225

In this work, we report diffusion-limited aggregation (DLA)-type Montecarlo computations of a stochastic model of displacement of a viscous fluid by another that preferentially wets a porous medium, for the case when both fluids are immiscible in the absence of buoyancy forces. The model has the aim to simulate cooperative invasion processes found in experiments of immiscible wetting displacement. The model considers the nonlocal effects of the Laplacian pressure field and the capillary forces via hydrodynamic equations in the Darcy regime with a boundary condition for the pressure at the interface. The boundary condition contains two different types of disorder: the capillary term, which constitutes an additive random disorder, and a term containing an effective random surface tension, which couples to a curvature (it constitutes a multiplicative random term that carries nonlocal information of the whole pressure). We generate different displacement patterns for different setting of the parameters of the model. We analyze these patterns by studying the scaling properties of the interface that separate the two fluids and calculating the fractal dimension of the interface. The results show the existence of three distinct regimes of scaling. One regime at the smallest-length scales is due to the multiplicative random disorder together with the nonlocal coupling; it reveals itself in a roughness exponent α ≈ 0.80. Additionally, we find a DLA-type scaling regime with a roughness exponent α ≈ 0.60 at the largest scales and intermediate scaling regime with α ≈ 0.70 corresponding to invasion percolation with trapping. Each regime has definite scaling ranges that depend on the capillary number and the relative wetting tendency of the fluids. The behavior of the fractal dimensions of the interfaces of the aggregates constitutes a further confirmation of the existence of three scaling regimes and the multi-self-affinity of the perimeter of the interface boundaries.  相似文献   

城市地理研究中的单分形、多分形和自仿射分形   总被引：1，自引：0，他引：1  

陈彦光 《地理科学进展》2019,38(1):38-49

分形几何学在城市地理研究中具有广泛的应用,然而很多基本概念却让初学者感到迷惑。如何区分单分形、自仿射分形与多分形,是一个基本而重要的问题。简单分形容易理解,而真实的地理现象很少是单分形的。城市生长过程具有自仿射特征,而城市空间格局却具有多分形性质。作者发现,各种分形的共性在于三个方面：标度律、分数维和熵守恒。论文基于标度、分维和熵守恒公式,借助隐喻城市生长的规则分形来区分单分形、多分形和自仿射分形,讨论分形系统演化的机理、分形与空间自相关和空间异质性的联系,同时澄清一些在地理分形研究中的常见错误概念。最后以城市位序-规模分布为例,说明并对比单分形和多分形在城市地理研究中的建模与应用思路。  相似文献   

城市形态的分维估算与分形判定   总被引：3，自引：3，他引：0  

陈彦光 《地理科学进展》2017,36(5):529-539

城市形态的分形是城市发育到一定阶段涌现出的有序格局和复杂结构,其基本特征是空间分布的无尺度性质。当研究者基于某个显著性水平推断城市分维存在时,实际上就是基于相应的置信度判断分形特征。虽然分形城市研究已经多年,但大量有关维数测算的基础问题依然悬而未决。本文根据分形几何学的基本思想论证城市形态分维测算的若干问题。分维测量的准则是最佳覆盖——不多不少、恰到好处的覆盖。盒子覆盖是最容易理解的测量方法。采用盒子覆盖法测量城市形态分维时,应考虑三个标准：一是快速逼近,二是简便操作,三是稳定拟合。直观估计分维的办法是利用双对数坐标图。由于城市形态不是严格意义的分形,而是类似于文献中的“前分形”,测量尺度与相应测度的幂律关系通常仅在一定尺度范围内有效,从而形成所谓标度区。本文围绕城市形态的分维测量和分形判断开展一系列讨论,包括尺度选取、标度区识别和统计标准等问题,对今后城市分形研究具有理论启示和方法论的参考价值。  相似文献   

Multifractal comparison of the outputs of two optical disdrometers   总被引：1，自引：1，他引：0  

A. Gires  I. Tchiguirinskaia  D. Schertzer 《水文科学杂志》2016,61(9):1641-1651

ABSTRACT

In this paper a universal multifractals comparison of the outputs of two types of collocated optical disdrometers installed on the roof of the Ecole des Ponts ParisTech is performed. A Campbell Scientific PWS100 which analyses the light scattered by the hydrometeors and an OTT Parsivel² which analyses the portion of occluded light are deployed. Both devices provide a binned distribution of drops according to their size and velocity. Various fields are studied across a range of scales: rain rate (R), liquid water content (ρ), polarimetric weather radar quantities such the horizontal reflectivity (Z_h) and the specific differential phase (K_dp), and drop size distribution (DSD) parameters such as the total drop concentration (N_t) and the mass-weighted diameter (D_m). For both devices, good scaling is retrieved on the whole range of available scales (2?h–30?s), except for the DSD parameters for which the scaling only holds down to few minutes. For R, the universal multifractal parameters are found to equal 1.5 and 0.2 for α and C₁, respectively. Results are interpreted with the help of the classical Z_h–R and R–K_dp radar relations.