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   

Invariance and scaling properties in the distributions of contributing area and energy in drainage basins     

P. La Barbera  G. Roth 《水文研究》1994,8(2):125-135

The cumulative probability distributions for stream order, stream length, contributing area, and energy dissipation per unit length of channel are derived, for an ordered drainage system, from Horton's laws of network composition. It is shown how these distributions can be related to the fractal nature of single rivers and river networks. Finally, it is shown that the structure proposed here for these probability distributions is able to fit the observed frequency distributions, and their deviations from straight lines in a log-log plot.  相似文献   

区域交通网络分形的DBM特征--交通网络Laplacian分形性质的实证研究   总被引：25，自引：3，他引：22  

陈彦光  刘继生 《地理科学》1999,19(2):114-118

城镇体系在理论状态下的三角点阵格局暗示着现实中的交通网络在一定时空条件下具有ＤＢＭ模型的某些特征。从形态分析和维数对比两个方面论证了区域交通网络扔Ｌａｐｌａｃｉａｎ分形性质,认为可用ＤＢＭ模型模拟城镇体系－交通网络的形成和演化过程,从而揭示其动力学机制。  相似文献   

Changing grading of soil: effect on critical states   总被引：6，自引：3，他引：3  

David Muir Wood  Kenichi Maeda 《Acta Geotechnica》2008,3(1):3-14

Examples of situations are presented where the grading of a soil changes during its lifetime either by crushing of particles leading to an increase of fine material or by slow transport of fine particles with seepage leading to a decrease of fine material. Such grading changes influence the basic constitutive properties of the soil, in particular properties such as critical states which are dependent on the available range of densities of packing. Discrete element modelling is used to show the dependence of critical state conditions on grading and the way in which the particle assembly seeks out new critical state conditions as the grading changes.  相似文献   

Fractal analysis of mingled/mixed magmas: an example from the Upper Pollara eruption (Salina Island, southern Tyrrhenian Sea, Italy)     

Rosanna De Rosa  Paola Donato  Guido Ventura   《Lithos》2002,65(3-4):299-311

Upper Pollara eruption products (13 ka, Salina Island, Italy) include both homogeneous and heterogeneous pumices resulting from mixing/mingling processes between an HK andesite and a high-SiO₂ rhyolite. Representative samples of heterogeneous pumices are collected and analyzed in order to check the correspondence between glass composition and morphological features of the mingling/mixing structures. Image analysis techniques are applied and eight grey color ranges (classes) are extracted from high-resolution scans of pumice. Class 1 (lighter colors) and class 8 (darker colors) show end-member glass compositions, i.e. HK andesite and high-SiO₂ rhyolite, respectively. These two classes show spot- to cluster-like morphological structures. Intermediate classes show an HK dacitic to rhyolitic composition and a banding- to fold-like morphology. Fractal analysis by box-counting of the boundary pattern of eight grey classified images is performed over a length scale of 0.028–1.8 cm. Fractal dimension D is between 1.01 and 1.84. Coupled fractal analysis and geochemical data reveal that D increases as the degree of magma interaction (homogenization) increases. This feature well fits the results from numerical models on the convective mixing of fluids driven by thermal convection. We conclude that the increase of D observed in the Upper Pollara samples reflects the transition from fractal mixing to homogenization. End-member magmas (HK andesite and high-SiO₂ rhyolite) represent isolated mixing regions, while homogenized magmas represent active mixing regions. In the analyzed pumices, isolated and active mixing regions coexist at scales between 10⁻⁴ and 10⁻² m. Morphological and compositional features of the Upper Pollara pumices result from turbulence.  相似文献   

Analysis and simulation of magma mixing processes in 3D   总被引：2，自引：0，他引：2  

D. Perugini  G. Poli  G. D. Gatta 《Lithos》2002,65(3-4):313-330

Magma mixing structures from the lava flow of Lesbos (Greece) are analyzed in three dimensions using a technique that, starting from the serial sections of rock cubes, allows the reconstruction of the spatial distribution of magmas inside rocks. Two main kinds of coexisting structures are observed: (i) “active regions” (AR) in which magmas mix intimately generating wide contact surfaces and (ii) “coherent regions” (CR) of more mafic magma that have a globular shape and do not show large deformations. The intensity of mingling is quantified by calculating both the interfacial area (IA) between interacting magmas and the fractal dimension of the reconstructed structures. Results show that the fractal dimension is linearly correlated with the logarithm of interfacial area allowing discrimination among different intensities of mingling.

The process of mingling of magmas is simulated using a three-dimensional chaotic dynamical system consisting of stretching and folding processes. The intensity of mingling is measured by calculating the interfacial area between interacting magmas and the fractal dimension, as for natural magma mixing structures. Results suggest that, as in the natural case, the fractal dimension is linearly correlated with the logarithm of the interfacial area allowing to conclude that magma mixing can be regarded as a chaotic process.

Since chemical exchange and physical dispersion of one magma inside another by stretching and folding are closely related, we performed coupled numerical simulations of chaotic advection and chemical diffusion in three dimensions. Our analysis reveals the occurrence in the same system of “active mixing regions” and “coherent regions” analogous to those observed in nature. We will show that the dynamic processes are able to generate magmas with wide spatial heterogeneity related to the occurrence of magmatic enclaves inside host rocks in both plutonic and volcanic environments.  相似文献   

复杂等高线自动综合的分形处理方法研究     

王桥  吴纪桃 《测绘学院学报》1995,(2)

复杂等高线自动综合是计算机辅助制图领域中一项重要且难度较大的任务。本文根据分形理论的基本原理，提出了一种基于量化等高线形状结构特征的复杂等高线自动综合的新方法。研究和实验表明，该方法充分顾及了地貌形态特征，能够对等高线图形进行客观、有效地概括。  相似文献   

分形与混沌理论在地震学中的应用与探讨   总被引：1，自引：2，他引：1  

安镇文 《地球物理学进展》1994,9(2):84-90

分形与混沌理论的研究与发展，揭示了自然界中一大类无规几何形体物理过程的内在规律性及其动力演化过程的内在随机性。这给我们探索自然界中分形客体的几何形态及其与内部物理本质的关系提供了一条暂新的途径。特别是这一理论给我们探讨地震问题，例如：探讨地震活动时空分布的确定性图像、地震演化过程的动力学行为、临界特征以及未来大地震的发生等问题，带来了某些希望。本文较详细地综述了近年来分形与混沌理论在地震学中的应用研究。全文共分５部分。第１部分是孕震过程的一般概述。第２部分描述单分形与多分形在地震学中的某些应用．文中第３部分介绍了混沌动力学中的某些研究在测震学与模型中的应用。第４部分综述了自组织临界现象和闪变噪声的研究．最后，第５部分是分形理论与混沌动力学在地球科学中的应用前景与展望．  相似文献   

Generating fracture networks using iterated function systems     

U. Mohrlok  R. Liedl 《International Journal of Earth Sciences》1996,85(1):92-95

In order to model flow and transport in fractured rocks it is important to know the geometry of the fracture network. A stochastic approach is commonly used to generate a synthetic fracture network from the statistics measured at a natural fracture network. The approach presented herein is able to incorporate the structures found in a natural fracture network into the synthetic fracture network. These synthetic fracture networks are the images generated by Iterated Function Systems (IFS) as introduced by Barnsley (1988). The conditions these IFS have to fulfil to determine images resembling fracture networks and the effects of their parameters on the images are discussed. It is possible to define the parameters of the IFS in order to generate some properties of a fracture network. The image of an IFS consists of many single points and has to be suitably processed for further use.  相似文献   

The fractal geometry of flow paths in natural fractures in rock and the approach to percolation   总被引：2，自引：0，他引：2  

D. D. Nolte  L. J. Pyrak-Nolte  N. G. W. Cook 《Pure and Applied Geophysics》1989,131(1-2):111-138

The distributions of contact areas in single, natural fractures in quartz monzonite (Stripa granite) are found to have fractal dimensions which decrease fromD=2.00 to values nearD=1.96 as stress normal to the fractures is increased from 3 MPa up to 85 MPa. The effect of stress on fluid flow is studied in the same samples. Fluid transport through a fracture depends on two properties of the fracture void space geometry. the void aperture; and the tortuosity of the flow paths, determined through the distribution of contact area. Each of these quantities change under stress and contribute to changes observed in the flow rate. A general flow law is presented which separates these different effects. The effects of tortuosity on flow are largely governed by the proximity of the flow path distribution to a percolation threshold. A fractal model of correlated continuum percolation is presented which quantitatively reproduces the flow path geometries. The fractal dimension in this model is fit to the measured fractal dimensions of the flow systems to determine how far the flow systems are above the percolation threshold.  相似文献