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1.
分形不变分布及其在山东地区金矿床中的应用 总被引：5，自引：0，他引：5
自相似性(标度不变性)是地学中的一个普遍现象。研究表明,地球化学元素含量、矿床储量规模及其空间分布具有分形结构。分形不变分布的特点要求大于某一尺度物体的数目与物体大小之间存在幂指数关系。论证了幂函数分布、帕累托分布、对数正态分布和齐波夫定律在一定条件下具有分形不变性质,它们是分形模型的数学基础。基于分形模型,用求和方法确定中国山东省金地球化学元素异常值范围。等值线大于或等于金地球化学元素临界值(200×10-9)围成的异常面积包含了已知的大型、超大型金矿床。 相似文献
2.
Fractal Principle of Mineral Deposit Size Forecasting and Its Implication for Gold Resource Potential Evaluation in China 总被引：1，自引：0，他引：1
LI Changjiang MA Tuhu ZHU Xingsheng WANG Guowu Zhejiang Institute of Geology Mineral Resources Hangzhou Zhejiang Earth Science Department Zhejiang University Hangzhou Zhejiang Zhejiang Bureau of Geology Mineral Exploration Development Hangzhou Zhejiang 《《地质学报》英文版》2002,76(3):378-386
Mineralization distributions are very heterogeneous in nature. As large or superlarge mineral deposits are quite rare whether in time or in space, it is difficult to detect all the largest mineral deposits in a region in a limited period of time owing to the restriction of technology and exploration degrees-this is called "not all discovered". However, all discovered large, especially superlarge, mineral deposits generally have a complete census in the geological literatures. On the other hand, not all discovered small mineral deposits are recorded in the geological literatures because for economic reasons people have not much interest in them-this is called "not all recorded". This practice often results in the observation truncations, that is, the data points near the two ends in an observable population, which is obtained by fitting a power law size-frequency distribution to discovered mineral deposits in a given region, show concave-down departure from the correlation line fitted. The authors sugges 相似文献
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4.
WANG Nan LIU Yongshun PENG Nian WU Cailai LIU Ningqiang NIE Baofeng YANG Xiaoyu 《《地质学报》英文版》2015,89(1):121-132
Quantitative analyses of the spatial distribution of fault structures can provide a theoretical basis for forecasting prospective ore deposits. Characteristics and complexity of fault structure distribution in the Qitianling area, Southern Hunan Province, China, were quantitatively calculated and appraised by fractal and multifractal methods to evaluate the relation between fault structures and ore-prospecting potential. The results show that the lengths of faults can be modeled as multifractals. Multifractal spectra evidently reflect the characteristics of the scaling of fault structures. The boxcounting dimension value(D) of fault structures is equal to 1.656, as indicates complexity of the spatial distribution of faults and favorable structural conditions for the formation of ore deposits. Moreover, the D values of sub-regions were calculated and isopleths of their fractal dimension values were plotted accordingly. Overlay analyses of isopleths of fractal dimension values and distributions of known ore deposits show that areas with the larger fractal dimension values of fault structures have more ore deposits. This spatial coupling relationship between D values and ore deposits can be used to forecast and explore other ore deposits. On the basis of complexity theory for ore-forming systems, three exploration targets with high D values were delineated as prospective ore deposits. 相似文献
5.
Renguang Zuo Qiuming Cheng Frederik P. Agterberg Qinglin Xia 《Ore Geology Reviews》2009,35(3-4):415-422
This study is concerned with the problem of how many undiscovered mineral deposits can be expected to occur in the vicinity of any known deposit, especially if the deposit is nearly mined out. Skarn tin deposits in southern China were chosen to demonstrate that fractal modeling can be a useful tool to characterize the spatial–temporal distribution of mineral deposits, and to quantify their grades and tonnages. The results show that the spatial–temporal distribution of skarn tin deposits as well as their grades and tonnages satisfy fractal statistic, and suggest that 14 skarn tin deposits could be found around a known skarn tin deposit within a radius of 80 km. Monte Carlo simulation was used to combine the number of deposits and the frequency distributions of grade and tonnage and to capture the uncertainty in estimation of metal resources. At the 90%, 50% and 10% confidence levels, tin metal resources amount to 6 ton, 200 ton, and 1.0 × 104 ton around a known tin deposit within a radius of 80, respectively. 相似文献
6.
湘中锑矿床空间分布的分形特征 总被引：4，自引：0，他引：4
本文运用分形理论对湘中锑矿床（点）的空间分布特征进行了研究,结果表明,锑矿床的空间分布可以认为具有统计自相似性,分形几何学可以描述矿田分布规律。应用计盒维数法计算了锑矿床空间分布的分维值,对不同区块的分维特征进行了比较,探讨了分维值的地质意义。实际资料计算结果显示,盒子数目与尺度有很好的相关性,其相关系数均达０．９９以上 相似文献
7.
Fred J. Molz Tomasz J. Kozubowski Krzysztof Podgórski James W. Castle 《Hydrogeology Journal》2007,15(4):809-816
In order to generalize the fractal/facies concept, a new stochastic fractal model for ln(K) increment probability density functions (PDFs) is presented that produces non-Gaussian behavior at smaller lags and converges to Gaussian at larger lags. The model is based on the classical Laplace PDF. The new stochastic fractal family is called fractional Laplace motion (fLam) having stationary increments called fractional Laplace noise (fLan). This fractal is different from other fractals because the character of the underlying increment PDFs changes dramatically with lag size, which leads to lack of self-similarity. Data also appear to display this characteristic. In the larger lag size ranges, approximate self-affinity does hold. The basic field procedure for further testing of the fractional Laplace theory is to measure ln(K) increment distributions along transects, calculate frequency distributions from the data, and compare results to appropriate fLan family members. The variances of the frequency distributions should also change with lag size (scale) in a prescribed manner. There are mathematical reasons such as the geometric central limit theorem, for surmising that fLam/fLan may be more fundamental than other approaches that have been proposed for modeling ln(K) frequency distributions. 相似文献
8.
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
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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
10.
Weight percentages of different size incremental particles in a mineral slurry is integrated into the ultrasonic attenuation model to derive a relation between ultrasonic attenuation and particle sizes. However, in the inertial and scattering regimes of frequency–radius space, irregularity and aggregation of particles can results in values of ultrasonic attenuation that are significantly different from those predicted by the derived model, which is based on the assumption of separated smooth spherical particles in mineral slurries. Experimental attenuation data obtained previously from mineral slurries of iron ores particles are compared with predicted values. It is shown that there is a negligible difference between predictions and experimental data. A new modification of theoretical model for ultrasonic attenuation is derived. The theory uses ωτv or κR as a fractal scale. It requires an empirical determination of the difference between the fractal dimension of the measured mineral slurry and that of a hypothetical slurry of spheres with the same particle size distribution. The new fractal modification of ultrasonic attenuation model is found to enable better agreement with measured attenuation as a function concentration for irregular particles than the theoretical model. Moreover, the fractal approach is found to discriminate between the effects of particle irregularity and aggregation. 相似文献
11.
分形概念应用在地球科学中来刻画地质变量与地质体自相似特征。研究表明分形模型常常提供有力工具来刻画地质变量和地质体的基本空间分布结构。许多地质现象的频度和大小之间的分布具有尺度不变性, 如岩石碎片、断层、地震、火山喷发、矿藏和油井等。中国白垩纪的矿床大量地分布在东北、阴山-燕山、华北地台、秦岭-大别山、扬子地台和东南沿海等6个矿集区, 它们是中国白垩纪矿床分布的重要地区, 而西北和西南地区已知的白垩纪矿床尚少; 中国白垩纪矿床分布具有在时间上集中于早白垩世, 在空间上集中于东北和华南的分形特性。以中国白垩纪金矿床为例, 对金矿床空间分布进行了分形建模与预测, 该方法不仅适用于金矿床, 而且还适用于其它矿床, 具有普遍的意义。 相似文献
12.
Fractal Geometry of Element Distribution on Mineral Surfaces 总被引：3，自引：0，他引：3
Fractal models have been established for the distributions of Au, As, S, Fe, and Si on mineral surface based on perimeter–area power-law association observed in mineral samples from fine-disseminated gold deposits at Jinya (JY), Larima (LRM), and Dongbeizhai (DBZ). The fractal index DAL, involved in the fractal perimeter–area relationship is a function of the formation conditions of the mineral. Minerals formed at higher temperatures have a larger value of DAL. For the same mineral, the values of DAL obtained for different elements are approximately the same. DAL may serve as a quantitative index characterizing the distribution configuration of elements on mineral surface. 相似文献
13.
Fractal modelling has been applied extensively as a means of characterizing the spatial distribution of geological phenomena
that display self-similarity at differing scales of measurement. A fractal distribution exists where the number of objects
exhibiting values larger than a specified magnitude displays a power-law dependence on that magnitude, and where this relationship
is scale-invariant. This paper shows that a number of distributions, including power-function, Pareto, log-normal and Zipf,
display fractal properties under certain conditions and that this may be used as the mathematical basis for developing fractal
models for data exhibiting such distributions. Population limits, derived from fractal modelling using a summation method,
are compared with those derived from more conventional probability plot modelling of stream sediment geochemical data from
north-eastern New South Wales. Despite some degree of subjectivity in determining the number of populations to use in the
models, both the fractal and probability plot modelling have assisted in isolating anomalous observations in the geochemical
data related to the occurrence of mineralisation or lithological differences between sub-catchments. Thresholds for the main
background populations determined by the fractal model are similar to those established using probability plot modelling,
however the summation method displays less capacity to separate out anomalous populations, especially where such populations
display extensive overlap. This suggests, in the geochemical data example provided, that subtle differences in the population
parameters may not significantly alter the fractal dimension. 相似文献
14.
A fractal theory of rock fragmentation is applied to block-and-ash flow deposits from the Fugendake dome, Unzen Volcano, Kyushu, Japan, in order to analyze the material strength and the energy required for size reduction of the source lava dome. Two fractal dimensions h and Ds, which are mutually interchangeable, represent the relative strength and energy for particles reduced to a given size. They can be theoretically estimated from the power relations of a reference grain size to the cumulative mass and number of fragments smaller than that size. The Unzen–Fugendake block-and-ash flow deposits have been further modified by size sorting and secondary fragmentation that occurred during flowage, so that the h value decreases (or Ds value increases) with increasing distance from the source. Coarse, reversely graded deposits are, however, found to retain the original size population relatively well. The Ds values estimated from deposits of this type are compatible with those previously reported from decompression–fragmentation experiments conducted on the same dome material. The employed fractal approach could thus give insights into the potential mode of dome collapse that generates block-and-ash flows. 相似文献
15.
Breakage models and particle analyses have been widely used as tools for describing and interpreting various deposits and
providing parameters for assessing the particle-size distribution of the deposits. Debris flows can be seen as a two-phase
rheological fluid with a clay-fluid composition, and debris-flow deposits comprise mud, silt, sand, and boulders, with grain
sizes ranging from less than one μm to more than several meters. As a consequence, according to fractal theory, the particles
in debris-flow deposits have self-similarity in geometrical shape and scale invariance in size. In this paper, the fractal
dimensions of particles in various debris-flow deposits are calculated and corresponding fractal features are determined based
on fractal-statistical theory. The aims of the study are: to provide a quantitative grain parameter that reflects both the
grain composition and grain-size distribution in debris-flow deposits; to compare the fractal dimensions of grains in different
types of debris-flow deposits and the degree of self-organization of debris flows; as well as to discuss the geological implications
of fractal dimensions and fractal features of particles in debris-flow deposits. 相似文献
16.
《Chemie der Erde / Geochemistry》2016,76(4):491-499
Separation of geochemical anomalies from background are one of the important steps in mineral exploration. The Khooni mineral district (Central Iran) has complex geochemical surface expression due to a complex geological background. This region was chosen as a study area for recognition of the spatial distribution of geochemical elements and separating anomalies from background using stream sediment geochemical data. In the past decades, geochemical anomalies have been identified by means of various methods. Some of these separation methods include: statistical analysis methods, spatial statistical methods and fractal and multi-fractal methods. In this article, two efficient methods, i.e. U-statistics and the fractal concentration-area for separation and detection of anomalous areas of the background were used. The U spatial statistic method is a weighted mean, which considers sampling point positions and their spatial relation in the estimation of anomaly location. Also, fractal and multi-fractal models have also been applied to separate anomalies from background values. In this paper, the concentration–area model (C–A) was suggested to separate the anomaly of background. For this purpose, about 256 stream sediment samples were collected and analyzed. Then anomaly maps of elements were generated based on U spatial statistics and the C-A fractal methods for Au, As and Sb elements. According to obtained results, the U-statistics method performed better than C-A method. Because the comparisons of the known deposits and occurrences against the anomalous area created using thresholds from U-statistics and C-A method show that the spatial U-statistics method hits all of 3 known deposits and occurrences, the C-A fractal method hits 1 and fails 2. In addition, the results showed that these methods with regard to spatial distribution and variability within neighboring samples, in addition to concentration value frequency distributions and correlation coefficients, have more accurate results than the traditional approaches. 相似文献
17.
应用分形理论来研究石油地质现象，是近年来地质学研究中的新方法和新思路。本文扼要介绍了分形和分维的基本概念和最新进展；并以四川地区为例，通过对川东、川西南、川南、川西北以及川中等地２００个气藏的统计研究，结果表明气藏的体积分布很好地遵从幂律分布规律，一定区域内油气藏的体积分布是一种分形分布。本文对分形分布的意义进行了探讨，提出了初步预测油气藏数目及储量的方法。该项成果为油气藏的研究开拓了新的领域。 相似文献
18.
In this paper,we show that geo-anomalies can be delineated for mineral deposit prediction according to singularity theories developed to characterize nonlinear mineralization processes.Associating singularity and geo-anomalies makes it possible to quantitatively study geo-anomalies with modern nonlinear theories and methods.This paper introduces a newly developed singularity analysis of nonlinear mineralization processes and nonlinear methods for characterizing and mapping geo-anomalies for mineral depos... 相似文献
19.
泥石流堆积物作为泥石流发育最终的产物,含有大量与泥石流发生过程和发育特征相关的信息,能够反映泥石流灾害程度和活动强度。研究表明,泥石流堆积物颗粒具有明显的自相似性和无标度区间,运用分形理论,计算泥石流堆积物颗粒分布的分维数。分析分维数与主沟长度、泥砂补给段长度比、主沟平均比降、流域最大相对高差和松散物源量的关系,结果表明分维数与各因素之间存在较强的非线性响应关系。以乌东德库区泥石流实测数据为例,以上述的5个因素作为输入单元,建立了泥石流堆积物分维数支持向量机预测模型,并对分维数进行了预测,其预测结果的最大误差为1.25%,说明预测值与实测值吻合度较高。综合表明支持向量机预测模型能够较好地模拟和泛化数据,是一种行之有效的泥石流堆积物分形维数预测方法,可用于不具备筛析条件的泥石流堆积物粒度分布特征的预测与研究,进而可为研究泥石流的形成机理、类型、危险度和堆积物的形成演化特征及物理力学性质提供一个新思路。 相似文献
20.
We show the presence of fractal ordering of copper grade in bore core data at short range in the Cadia Ridgeway porphyry deposit and measure its persistence after mining by monitoring the output of the... 相似文献