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1.
Discrete multifractals 总被引：12，自引：0，他引：12
Qiuming Cheng 《Mathematical Geology》1997,29(2):245-266
The concept of multifractal modeling has been used intensively in various fields of science for characterizing measures with
self- similarity. It has been shown that multifractal modeling provides powerful tools for characterizing patterns in the
spatial distribution of geological quantities and objects. Existing multifractal models were proposed for the purpose of handling
spatially intertwined fractals with continuous fractal spectrum f(α) (or continuous codimension function C(γ)). In this paper, these conventional multifractals are termed “continuous multifractals” whereas multifractals with discrete
fractal dimensions are termed “discrete multifractals.” The properties of discrete multifractals are investigated. It is shown
by various artificial examples and a case study of stratigraphy of Ocean Drilling Program (ODP) site 645 that spatially intertwined
fractals/multifractals indeed can have discrete fractal dimensions. Histogram-and moment-based techniques are proposed for
discrete multifractal modeling and illustrated using the artificial examples. The new concept of discrete multifractals and
associated multifractal modeling yields not only techniques for characterizing multifractals with discrete fractal dimensions
but it also provides insight into the relationships between fractals, bifractals, and multifractals. 相似文献
2.
Markov Processes and Discrete Multifractals 总被引：7，自引：0，他引：7
Qiuming Cheng 《Mathematical Geology》1999,31(4):455-469
Fractals and multifractals are a natural consequence of self-similarity resulting from scale-independent processes. Multifractals are spatially intertwined fractals which can be further grouped into two classes according to the characteristics of their fractal dimension spectra: continuous and discrete multifractals. The concept of multifractals emphasizes spatial associations between fractals and fractal spectra. Distinguishing discrete multifractals from continuous multifractals makes it possible to describe discrete physical processes from a multifractal point of view. It is shown that multiplicative cascade processes can generate continuous multifractals and that Markov processes result in discrete multifractals. The latter result provides not only theoretical evidence for existence of discrete multifractals but also a fundamental model illustrating the general properties of discrete multifractals. Classical prefractal examples are used to show how asymmetrical Markov process can be applied to generate prefractal sets and discrete multifractals. The discrete multifractal model based on Markov processes was applied to a dataset of gold deposits in the Great Basin, Nevada, USA. The gold deposits were regarded as discrete multifractals consisting of three spatially interrelated point sets (small, medium, and large deposits) yielding fractal dimensions of 0.541 for the small deposits (<25 tons Au), 0.296 for the medium deposits (25--500 tons Au), and 0.09 for the large deposits (>500 tons Au), respectively. 相似文献
3.
分形概念应用在地球科学中来刻画地质量和物体的自相似特征。研究表明分形模型常常提供有力工具来刻画地质量和物体的基本空间分布结构。本文提出了n维自仿射分形的检验与定量评定方法。通过实例，说明n维自仿射分形的方法在实际问题中的方法和步骤，并解释了分维数的实际意义。分维数足反映区域化变量在某方向变化程度的定量指标。该方法不仅适用于地球化学金元素和银元素数据，而且还适用于其他元素和地质数据，具有普遍的意义。 相似文献
4.
裂隙网络多标度分形计算机模拟 总被引：1，自引：0，他引：1
岩体裂隙网络是不均匀，非对称的复杂分形，用简单分数维不能刻画其特征，必须采用多标度分形来研究，才能全面客观地描述其本质。文中介质了隙网络多标度分形计算机模拟原理与方法。 相似文献
5.
Multifractal Modeling and Lacunarity Analysis 总被引：2，自引：0，他引：2
Qiuming Cheng 《Mathematical Geology》1997,29(7):919-932
The so-called gliding box method of lacunarity analysis has been investigated for implementing multifractal modeling in comparison with the ordinary box-counting method. Newly derived results show that the lacunarity index is associated with the dimension (codimension) of fractal, multifractal and some types of nonfractals in power-law relations involving box size; the exponent of the lacunarity function corresponds to the fractal codimension (E – D) for fractals and nonfractals, and to the correlation codimension (E – lpar;2)) for multifractals. These results are illustrated with two case studies: De Wijs's zinc concentration values from the Pulacayo sphalerite-quartz vein in Bolivia and Cochran's tree seedlings example. Both yield low lacunarities and slightly depart from translational invariance. 相似文献
6.
Non-Linear Theory and Power-Law Models for Information Integration and Mineral Resources Quantitative Assessments 总被引：7，自引：0，他引：7
Qiuming Cheng 《Mathematical Geosciences》2008,40(5):503-532
Singular physical or chemical processes may result in anomalous amounts of energy release or mass accumulation that, generally,
are confined to narrow intervals in space or time. Singularity is a property of different types of non-linear natural processes
including cloud formation, rainfall, hurricanes, flooding, landslides, earthquakes, wildfires, and mineralization. The end
products of these non-linear processes can be modeled as fractals or multifractals. Hydrothermal processes in the Earth’s
crust can result in ore deposits characterized by high concentrations of metals with fractal or multifractal properties. Here
we show that the non-linear properties of the end products of singular mineralization processes can be applied for prediction
of undiscovered mineral deposits and for quantitative mineral resource assessment, whether for mineral exploration or for
regional, national and global planning for mineral resource utilization. In addition to the general theory and framework for
the non-linear mineral resources assessment, this paper focuses on several power-law models proposed for characterizing non-linear
properties of mineralization and for geoinformation extraction and integration. The theories, methods, and computer system
discussed in this paper were validated using a case study dealing with hydrothermal Au mineral potential in southern Nova
Scotia, Canada. 相似文献
7.
8.
新疆东准噶尔地区断裂的多重分形研究 总被引：5，自引：1，他引：4
结合东准噶尔地区强应变构造带的空间展布情况和断裂的空间分布特征 ,用多重分形模型测算了各带的多重分维值。研究结果表明 :强应变构造带在不同尺度上具有自相似性 ;断裂的空间分布为多重分形结构 ,断裂的演化有从复杂几何结构的次级断裂组合向单一连续的大断裂过渡而分维值逐渐减小的趋势 ;不同的大地构造单元有不同的分维值 ,而且有靠近板块缝合带 (或海沟 )分维值减小、远离板块缝合带 (或海沟 )分维值增大的趋势 相似文献
9.
滑坡位移多重分形特征与滑坡演化预测 总被引：3，自引：1，他引：2
在系统分析滑坡位移监测资料和位移演化特征的基础上,根据多重分形理论基本原理,对滑坡位移演化所具有的复杂性、突变性和非线性特征进行了分析和研究。单一分形维数对滑坡位移的演化趋势预测存在不足,文中分别以新滩滑坡、丹巴滑坡和黄蜡石滑坡为例,计算了滑坡位移时序演化的多重分维数演化特征。分析和评价位移演化规律与多重分维数演化特征的关系发现,多重分维数D1 > D2 > … > D∞时,滑坡趋于稳定;D1 < D2 < … < D∞时,滑坡向失稳破坏演化。当滑坡位移时序多重分维数演化特征出现拐点时,即分维数由D1 > D2 > … > D∞,经D1 > … > Dn < Dn+1 < … < D∞到 D1 < D2 < … < D∞的演化过程时,滑坡向不稳定的状态演化;当分维数由D1 < D2 < … < D∞,经D1 > … > Dn D2 > … > D∞的演化过程时,滑坡向趋于稳定的状态演化。研究表明,可以运用多重分维数演化特征对滑坡位移演化趋势与规律进行评价与预测。 相似文献
10.
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
11.
四川地区断层空间分布的多重分形特征 总被引：8，自引：0，他引：8
断层系统多重分形避免了容量维Ｄ０的不足，考虑了每一条断层对整体分维的贡献，反映了断层的空间分布特征。根据四川地区断层分布图，运用多重分形理论检验了断层空间分布的自相似性，分区计算了四川地区各带的多重分维值。结果表明，断层破裂系统为分形结构，具有很好的自相似性，相关系数均达０．９９。不同带分维值的较大差异，反映不同构造区域的断层分布特点。最后，对分维的含义进行了深入探讨，对油气勘探的有利区域进行了分析。 相似文献
12.
非线性成矿预测理论:多重分形奇异性-广义自相似性-分形谱系模型与方法 总被引：24，自引：0，他引：24
介绍了“奇异性-广义自相似性-分形谱系”(“3S”: Singularity-generalized self-Similarity-fractal Spectrum)为核心的多重分形现代成矿预测理论与模型(Multifractal Mineralization Prediction Theory and Models)的基本内容和前沿研究方向.讨论了作为非线性、复杂性理论的重要领域之一, 多重分形理论所提供的“奇异性-广义自相似性-分形谱系”等概念和相关的模型.这些新概念和模型不仅能够合理地描述成矿系统、成矿过程、成矿富集规律、矿产资源时空分布, 还提供了定量模拟和识别成矿异常(地质、地球物理、地球化学、遥感异常)的有效模型和实用方法.将多重分形原理与成矿过程、矿产资源分布规律、矿产资源信息获取研究相结合, 可形成具有良好应用前景的现代成矿预测理论与模型.采用该多重分形矿产资源预测理论和在此基础上所开发的专用地学非线性空间信息GeoDASGIS技术, 对国内外多个金属成矿区带进行了矿产资源勘查与评价, 均取得了较理想的预测效果, 表明对开展矿产资源勘查和评价是有效和可行的. 相似文献
13.
甘肃玛曲大水金矿成矿过程中资源量生长的数量规律 总被引：1，自引：0，他引：1
大水金矿床是著名的超大型矿床.在借鉴前人矿床地质研究成果的基础上, 通过对矿体规模数据的多重分形特征及吨-品位关系研究, 揭示了成矿过程中资源量生长的数量规律.矿体长度服从简单分形分布, 矿床资源量的吨-品位关系能用指数函数或直线方程更好地拟合, 矿床与矿体资源量双对数图、吨-品位的双对数图的多重分形特征表明: 在分形构造成矿空间中, 特定成矿阶段的矿床资源量的生长方式是自组织非线性增殖过程, 与自组织有关的随机性使吨-品位关系趋于指数关系; 在整个成矿过程中, 矿床资源量的生长方式是各阶段矿体资源量的线性叠加.进一步根据熵最大化原理及效用理论导出了与统计结果吻合的矿床吨-品位方程, 并得到柴家庄金矿矿体地质数据的验证. 相似文献
14.
Multifractal modeling and spatial statistics 总被引：9，自引：0，他引：9
In general, the multifractal model provides more information about measurements on spatial objects than a fractal model. It also results in mathematical equations for the covariance function and semivariogram in spatial statistics which are determined primarily by the second-order mass exponent. However, these equations can be approximated by power-law relations which are comparable directly to equations based on fractal modeling. The multifractal approach is used to describe the underlying spatial structure of De Wijs 's example of zinc values from a sphalerite-bearing quartz vein near Pulacayo, Bolivia. It is shown that these data are multifractal instead of fractal, and that the second-order mass exponent (=0.979±0.011 for the example) can be used in spatial statistical analysis. 相似文献
15.
Fractal models for predicting soil hydraulic properties: a review 总被引：33，自引：0，他引：33
Modern hydrological models require information on hydraulic conductivity and soil-water retention characteristics. The high cost and large spatial variability of measurements makes the prediction of these properties a viable alternative. Fractal models describe hierarchical systems and are suitable to model soil structure and soil hydraulic properties. Deterministic fractals are often used to model porous media in which scaling of mass, pore space, pore surface and the size-distribution of fragments are all characterized by a single fractal dimension. Experimental evidence shows fractal scaling of these properties between upper and lower limits of scale, but typically there is no coincidence in the values of the fractal dimensions characterizing different properties. This poses a problem in the evaluation of the contrasting approaches used to model soil-water retention and hydraulic conductivity. Fractal models of the soil-water retention curve that use a single fractal dimension often deviate from measurements at saturation and at dryness. More accurate models should consider scaling domains each characterized by a fractal dimension with different morphological interpretations. Models of unsaturated hydraulic conductivity incorporate fractal dimensions characterizing scaling of different properties including parameters representing connectivity. Further research is needed to clarify the morphological properties influencing the different scaling domains in the soil-water retention curve and unsaturated hydraulic conductivity. Methods to functionally characterize a porous medium using fractal approaches are likely to improve the predictability of soil hydraulic properties. 相似文献
16.
多龙矿集区控矿构造信息提取、识别与融合 总被引：1，自引：0，他引：1
西藏多龙矿集区近年来发现了大量的铜、金矿床,具有可观的资源潜力而倍受关注。通过对区内地质调查及矿产勘查数据的系统梳理与二次开发,利用基于分形理论的空间分析方法对该区成矿背景、构造格架等方面进行了深入细致的研究与探索。通过主成分分析方法,将水系沉积物地球化学数据中与斑岩铜金成矿相关元素和构造活动指示元素进行融合,并利用S-A(能谱-面积)模型对元素组合异常进行信息挖掘工作。结果表明,与区内构造格架相关的地球化学异常空间分布模式在指示矿化的同时,还对其与区域断裂构造之间的成生关系具有相当程度的指示意义。此外,区内开展的空间定量研究同时表明,S-A(能谱-面积)模型对描述由特定地质作用所造成的异常空间分布模式的自相似性有效,特别是针对地球化学背景模式的空间定量化描述,能更加深刻地刻画区内的构造格架并反映成矿背景。其结果推断了控制区内斑岩成矿系统的网格状断裂体系。此外,数据分析建模过程为在该区开展进一步的多元信息提取与融合提供了思路和借鉴经验,有利于找矿新靶区的发现与圈定。 相似文献
17.
地球物理学中的分形与分维研究进展 总被引：5，自引：0，他引：5
应用分形理论来研究地球物理现象,是近年来地球物理学研究中的新方法和新思路。本文介绍了分形与分维的基本概念,并综述了地球物理学中分形研究的最新进展。 相似文献
18.
为研究流域地貌形态特征的量化指标,提出基于高程分布概率的多重分形计算模型,结合大理河岔巴沟流域和大堡岔流域DEM数据进行多重分形计算,对流域地貌形态特征多重分形谱的表征意义进行了探讨。结果表明:流域地貌形态特征多重分形谱可以更加敏感、更加全面地对流域地貌形态的总体特征进行描述;多重分形谱的顶点对应简单分形的容量维,多重分形谱的宽度可以定量表征流域表面的起伏程度,多重分形谱的端点维数的差别可以间接地反映流域峰谷数目的比例;流域地貌形态特征多重分形谱能够分层次地刻画流域内部的精细结构,从而更加突出地表现异常局部地貌变化特征;流域地貌形态特征多重分形谱的无标度区间的合理范围,应该确定为DEM像元尺度到流域最大高程值的1.5倍左右最为合适。 相似文献
19.
高寒湖沼区水系沉积物中元素迁移富集的分形伸展机制 总被引：1，自引：1，他引：1
孙忠军 《物探化探计算技术》2005,27(3):246-249
水系沉积物中成矿元素迁移富集的动力学机制是复杂性科学的研究课题。利用分形理论研究空间结构复杂性特征,适宜于元素分散过程的动力学研究。从元素迁移过程的分形特征揭示出元素分散过程的分形伸展机制。并在进一步研究了元素粒级层分维特征后,得出了成矿元素物理空间结构的复杂性特征和相互联系。研究成矿元素相态层分维和其间非线性关联,揭示出成矿元素分散过程分形伸展的涌现原因。 相似文献
20.
空间模式的广义自相似性分析与矿产资源评价 总被引：20，自引：3，他引：17
尺度不变性(scale invariance)包括自相似性(各向同性)、自仿射性(成层结构)、广义自相似性(各向异性标度不变性),是由各种地质过程和地质事件所产生的地质特征和模式的本质属性．尺度不变性可用分形和多重分形模型来表征．这些尺度特征的定量化可为刻画地质空问模式和模式识别提供有力的工具．例如。热液矿床的群聚现象可以用局部分形特征(局部奇异性)来刻画．通过在特征空问中(如频率空问)识别空问模式的广义自相似性．可以将空间混合模式进行分解或异常的识别．介绍了几种相关的分形模型和方法。包括度量空问模式广义尺度独立性(GSI)的线性模型;基于广义尺度独立性的异常分解S—A方法;度量空问模式的局部奇异性方法;以及如何利用分形特征预测未发现矿床的2种方法．有些方法已应用于许多矿产资源评价实例中．给出了对加拿大Nova Scotia省西南部湖泊沉积物样品中的4种元素As、Pb、Zn和Cu的地球化学数据处理分析结果。证明了局部奇异性分析和S—A异常分解方法对地球化学异常的增强和分离的有效性．研究表明：由S—A方法分解的异常往往具有多重分形的特点,而且普遍具有局部奇异性．研究区内具有明显奇异性的地区(元素含量富集区)是金矿异常区域。它们与金矿成矿作用和已知矿床的赋存密切相关． 相似文献