共查询到20条相似文献，搜索用时 31 毫秒
1.
Cheng Qiuming Department of Earth Atmospheric Science Department of Geography York University Toronto Ontario Canada MJ P 《中国地质大学学报(英文版)》2001,12(1)
1Multifractalities have been observed and estimated formany quantities in physics, chemistry, as well as earth andspace sciences (see a review in Agterberg, 20011 Cheng,1999al Agterberg et al., 1993 1 Schertzer and Love joy, 1991).The multifractal theory has provided a superior distributiontype for describing the complex measures in comparison withthe ordinary statistical distributions. The former usually involves the multiple moments and parameters (Cheng, 1999alAgterberg et al., 1993 1 Sc… 相似文献
2.
Mário A. Gonçalves 《Mathematical Geology》2001,33(1):41-61
The use of multifractals in the applied sciences has proven useful in the characterization and modeling of complex phenomena. Multifractal theory has also been recently applied to the study and characterization of geochemical distributions, and its relation to spatial statistics clearly stated. The present paper proposes a two-dimensional multifractal model based on a trinomial multiplicative cascade as a proxy to some geochemical distribution. The equations for the generalized dimensions, mass exponent, coarse Lipschitz–Hölder exponent, and multifractal spectrum are derived. This model was tested with an example data set used for geochemical exploration of gold deposits in Northwest Portugal. The element used was arsenic because a large number of sample assays were below detection limit for gold. Arsenic, however, has a positive correlation with gold, and the two generations of arsenopyrite identified in the gold quartz veins are consistent with different mineralizing events, which gave rise to different gold grades. Performing the multifractal analysis has shown problems arising in the subdivision of the area with boxes of constant side length and in the uncertainty the edge effects produce in the experimental estimation of the mass exponent. However, it was possible to closely fit a multifractal spectrum to the data with enrichment factors in the range 2.4–2.6 and constant K1 = 1.3. Such parameters may give some information on the magnitude of the concentration efficiency and heterogeneity of the distribution of arsenic in the mineralized structures. In a simple test with estimated points using ordinary lognormal kriging, the fitted multifractal model showed the magnitude of smoothing in estimated data. Therefore, it is concluded that multifractal models may be useful in the stochastic simulation of geochemical distributions. 相似文献
3.
Continuous-in-scale multifractal cascades has long been an attractive choice for mathematically modeling turbulent and turbulent-like geophysical fields. These fields are usually anisotropic as they are subject to both stratification and rotation, thereby questioning the isotropy assumption often made to model them. The self-affine and generalized scale invariance approaches to scaling are used here to introduce anisotropy in such models. These anisotropic simulations have (1) unresolved large-scale features and (2) statistics that deviate from the desired power-law scaling mainly in the small scales. The former issue is solved via nesting, whereas the latter is attempted to be overcome using singularity correction methods. While earlier studies have proposed isotropic correction methods, here they have been generalized to correct anisotropic simulations. These singularity corrections seem to improve the small-scale statistical properties of mildly anisotropic simulations; nesting, on the other hand, appears to enhance statistics over almost all scales even for strongly anisotropic simulations. Both the correction and nesting techniques lead to a reduction in computational time and memory usage suggesting that nested singularity-corrected cascades offer a better framework for quantitatively modeling the atmosphere, ocean, solid earth, and associated fields. 相似文献
4.
Multifractal Simulation of GeochemicalMap Patterns 总被引：3，自引：0，他引：3
Agterberg Frederik P Geological Survey of Canada Booth Street Ottawa KA E Canada 《中国地质大学学报(英文版)》2001,12(1)
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… 相似文献
5.
选用标准化降水指数作为气象干旱指标,通过引入多标度分形理论,运用乘法级联模型,以吉林西部6个气象站点1957年1月-2010年10月的月降水量数据为基础,对吉林西部气象干旱的多标度性质进行分析。研究结果表明,吉林西部气象干旱的发生在时间尺度上均具有多标度分形特征,但在不同站点多标度分形的强度不同,表现出一定的空间差异性。其强弱次序为：长岭<通榆<白城<前郭<扶余<乾安。 相似文献
6.
Multifractal and entropic properties of landslides in Japan 总被引：4，自引：0，他引：4
C. Goltz 《International Journal of Earth Sciences》1996,85(1):71-84
Landslide distributions in two major areas of northern Japan, Tohoku and Hokkaido, are analysed for multifractal properties. For the latter data set, also the multifractal spectrum for the spatial landslide size distribution is determined and compared to the probability distribution. It is concluded that the fields possess definite multifractal character. This finding is supported by the known multifractality of the main triggering processes, rain and earthquakes. Further support comes from a configuration entropy analysis which is found to be a useful complimentary tool to multifractal analysis. Models leading to multifractality are briefly reviewed. Careful attention is paid to the algorithms used and to the verification of the numerical results. Some general suggestions concerning numerical methods are made. 相似文献
7.
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
8.
Fractal and Multifractal Properties of Geochemical Fields 总被引：12，自引：0，他引：12
A fractal model, introduced by De Wijs to study the distribution, redistribution, or enrichment/depletion of element concentrations in a region, has become widely accepted. This paper uses it to simulate various geochemical fields for element concentration values. The frequency distribution and spatial pattern of the simulated values or concentrations are analyzed by the method of moments and the concentration–area (C–A) model. The spatial pattern of the original De Wijs model is shown to be intrinsically characterized by -shaped and symmetrical multifractal spectrum curves, whose center and width change systematically with the enrichment factors set in the simulation. The corresponding frequency distribution pattern on the log–log plot of frequency versus concentrations is called simple continuous multifractal (SCM) by the authors. In other experiments, when a De Wijs model is locally superimposed by another De Wijs model of different enrichment factors, the symmetry of the multifractal spectrum graph is broken and a different pattern of frequency distribution is found. It is referred to as highly accumulated continuous multifractals (HACM). Concentrations of 12 elements in 1448 rock samples from Shaoguan district, North Guangdong Province, South China, and 12 oil/gas indexes in surface soils from Sangtamu region, Tarim Basin, Northwest China, have been applied. The real geochemical fields, both metallic and oil/gas, are found to be remarkably compatible to those simulated patterns of De Wijs models with backgrounds of various enrichment and different degrees of superimposition, indicating that the frequency and spatial distribution patterns revealed by the authors are most possibly universal features of geochemical fields. It is particularly interesting to note that the major geochemical indicators of oil/gas geochemical fields are closer to the results of De Wijs models with a small enrichment factor, either with or without local superimposition, whereas those of the metallic geochemical field correspond more closely to De Wijs models with a background field of larger enrichment factors. The results obtained herein potentially have important implications in mineral and oil/gas resource assessment. 相似文献
9.
矿物微观结构的多重分形 总被引：4，自引：1，他引：3
分形与多重分形已广泛地应用于不同领域, 不同尺度下的各种分布特征研究更是受到广泛关注.以云南个旧松树脚矿田中2件含矿矽卡岩样品中黄铁矿颗粒为研究对象, 通过分形与多重分形方法研究了黄铁矿颗粒在二维空间上的分布特征.结果显示, 黄铁矿在微观尺度空间上的分布不均一, 具有明显的分形与多重分形分布特征.所选研究区外接触带黑绿色含硫化物矿石矽卡岩和接触带矽卡岩型块状硫化物矿石显微照片分析结果显示, 前者黄铁矿颗粒分布的盒子维数D0、信息维数D1、关联维数D2及广义多重分形维数Dq的变化范围均较小, 而后者较大; 前者外接触带黑绿色含硫化物矿石矽卡岩含矿性相对较弱, 而后者矿石矿物相对富集.从这个意义上说, 分形与多重分形维数与样品含矿性有一定的对应关系, 因此, 分形与多重分形分析有望进一步为岩石含矿性的定量化评价提供微观尺度上的证据. 相似文献
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11.
Multifractal modeling and spatial point processes 总被引：8，自引：0，他引：8
The multifractal model can be applied to spatial point processes. It provides new, approximately power-law type, expressions for their second-order intensity and K (r) functions. The box-counting and cluster dimensions are different but mutually interrelated according to multifractal theory. This approach is used to describe the underlying spatial structure of gold mineral occurrences in the Iskut River area, northwestern British Columbia. The box-counting and cluster dimensions for the example are estimated to be 1.335±0.077 and 1.219±0.037, respectively. The relatively strong clustering of the gold deposits is reflected by the fact that both values are considerably less than the corresponding Euclidean dimension (=2). 相似文献
12.
以研究区成矿地质背景为基础，将其划分为4个地球化学区，从多重分形理论出发，应用“元素含量—面积”模型方法，对各区主要成矿元素的地球化学(异常)场进行分析研究。结果表明，由于地质构造背景和化探元素富集的成因机理不同，各区元素地球化学(异常)场具有两种不同的多重分形特征模式：只有两个无标度区的简单多重分形模式和有两个以上无标度区的高丛集多重分形模式，具有相同成因的元素组合具有相似的多重分形特征。在此基础上．探讨了各区元素的成矿富集规律和空间分布特征，进而划分了地球化学背景和异常，经检验对比，证明了该方法的有效性和实用性。 相似文献
13.
新疆塔里木盆地艾协克—桑塔木南地区油气地球化学指标的多重分形性分析 总被引：1，自引：0，他引：1
用分形与多重分形的方法研究地球化学场中地球化学指标的分布规律具有重要的意义。本文运用多重分形矩方法研究了新疆塔里木盆地艾协克一桑塔木南地区2000km^2内采集的2085个土壤样中20项油气化探指标的多重分形谱函数形态特征。结果表明，主要成油气指示指标的多重分形谱基本上呈单一“钩状”，显示较弱的多重分形或单一分形；而其他指标多显示较强的多重分形特征。这些性质在研究区广泛存在，将对区域含油性研究有重要的指示意义。 相似文献
14.
Fractal and Multifractal Modeling of Hydrothermal Mineral Deposit Spectrum： Application to Gold Deposits in Abitibi Area, Ontario, Canada 总被引：2，自引：0，他引：2
ChengQiuming 《中国地质大学学报(英文版)》2003,14(3):199-206
A number of fractal/multifractal methods are introduced for quantifying the mineral de-lmsit spectrum which include a number-size, grade-tonnage model, power spectrmn model,multi-fractal model and an eigeavalue spectrmn model The first two models characterize mineral deposits spec-tra based on relationships among the measures of mineral deposits.These include the number of deposits,size of deposits,concentration and volume of mineral deposits.The last three methods that deal with the spatial-temporal spectra of mineral deposit studies are all expected to be popularized in near future.A case study of hydrothermal gold deposits from the Abitibi area,a world-class mineral district is used to demonstrate the principle as well as the applications of methods proposed in this paper,It has been shown that fractal and multifractal models are generally applicable to modeling of mineral deposits and occurrences.Clusters of mineral deposits were identified by several methods including the power spectral eral deposits in the Timmins and Kirkland Lake camps. 相似文献
15.
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
16.
探讨了土壤水非均匀流动特性和描述方法,通过染色示踪剂调查了三种试验尺度条件下非均匀流动模式,并采用随机层叠模型对不同实验尺度条件下非均匀流动模式进行了模拟。随机层叠模型中具有对数正态分布性质的随机层叠发生器被用来描述水流入渗过程,不同的方法被用于模型参数求解。试验观测和模拟计算结果均表明,尺度特性是非均匀流动的重要影响因素之一,准确的描述不同研究尺度下的非均匀流动特征,须同时考虑流动在水平和垂直方向的变异性。随着研究尺度的增加,流动的非均匀性变异程度更加明显。 相似文献
17.
选取渝西地区五峰组-龙一1亚段富有机质页岩开展场发射扫描电镜、核磁共振和X射线衍射等实验,在图像处理和多重分形理论的基础上,分析了页岩储层孔隙结构特征及非均质性.结果表明:（1）扫描电镜分析认为,研究区有机孔平均孔径偏小, < 50 nm的有机孔数量占比82%,>100 nm的有机孔面孔率占比52%;（2）依据核磁T2谱峰形态划分为Ⅰ~Ⅲ类,分别为单峰、双峰和三峰3种类型,Ⅲ类页岩储层孔径、孔隙度较大,具备更优越的储集条件和渗流能力;（3）基于多重分形理论表征储层非均质性,石英含量越高,黏土含量越低非均质性越弱,进而控制着孔隙度和渗透率的大小.多重分形参数与矿物组分、物性参数的联系有效表征了储层孔隙结构,并为其非均质性的评估提供了新的视角. 相似文献
18.
由不同尺度过程或作用叠加而形成的混合场在地学领域很常见,研究如何量化这些场的尺度不变性以及如何刻画其各项异性特征具有重要意义.介绍了近期研发的图像各向异性尺度不变性模拟和分解方法,并将其应用于遥感图像处理中.该方法是将各向异性尺度不变性模拟(SIG)和分形滤波(S-A)方法融合的,对于任意二维场,先用S-A模型判断其是否为混合场.如果是混合场,用S-A模型对其进行模式分解,然后再运用SIG模型量化分解后的各组分的各向异性尺度不变性,并描述其具体变换特征.基于一幅混合遥感影像的应用实例表明,该方法能够有效地量化二维混合场的各向异性尺度不变性.此外,混合场只有在正确分解成不同尺度的组分之后才能得到合理的利用. 相似文献
19.
矿井槽波地震勘探数据中,含有多种类型地震波,包括线性极化的纵波、横波、勒夫型槽波和椭圆极化的瑞利型槽波。由于槽波频散现象严重,不同类型槽波互相重叠,在地震记录上难以区分,合理地进行波场分离是槽波数据处理的重要环节。根据不同类型槽波振动极化特征,提出基于S变换的时频域自适应协方差矩阵极化滤波方法;在时频域中,针对槽波水平双分量信号建立自适应协方差矩阵;利用矩阵对应特征值和特征向量,计算椭圆率和方位角参数来描述槽波极化振动特征;依据极化参数建立极化滤波函数,对槽波地震信号进行波场分离。经过理论合成信号和实际数据测试表明,该方法可以有效地从槽波地震记录中提取出勒夫型槽波,避免其它类型地震波在槽波数据处理过程中产生的干扰,为槽波地震勘探数据处理提供新的技术手段。 相似文献
20.
成矿过程奇异性与矿产预测定量化的新理论与新方法 总被引：5，自引：0，他引：5
在分析地震、滑坡、洪水、暴雨、森林火灾等一系列非线性地球系统过程共同特征的基础上,笔者提出了成矿过程作为奇异性过程的命题。探讨了成矿过程奇异性、广义自相似性、自组织临界性等基本非线性特征的内在联系。从多重分形理论出发给出了:(1)度量成矿域空间结构不均匀性的局部奇异性分析模型;(2)度量成矿多样性与自相似性关系的系列广义自相似性度量模型;(3)首次给出了奇异性指标作为度量控矿要素与矿床分布相关关系的非线性模型,提出了从奇异性出发计算成矿后验概率的新的对数概率模型;(4)介绍了成矿奇异性的动力学模拟过程。详细介绍了非线性矿产资源预测理论和方法的基本内容和模型。 相似文献