Fractal Method for Statistical Analysis Geological Data

This paper establishes the phase space in the light of spacial series data , discusses the fractal structure of geological data in terms of correlated functions and studies the chaos of these data . In addition , it introduces the R/S analysis for time series analysis into spacial series to calculate the structural fractal dimensions of ranges and standard deviation for spacial series data -and to establish the fractal dimension matrix and the procedures in plotting the fractal dimension anomaly diagram with vector distances of fractal dimension . At last , it has examples of its application .

The efficiency and accuracy of probability diagram, spatial statistic and fractal methods in the identification of shear zone gold mineralization: a case study of the Saqqez gold ore district,NW Iran

In this study,geochemical anomaly separation was carried out with methods based on the distribution model,which includes probability diagram(MPD),fractal(concentration-area technique),and U-statistic methods.The main objective is to evaluate the efficiency and accuracy of the methods in separation of anomalies on the shear zone gold mineralization.For this purpose,samples were taken from the secondary lithogeochemical environment(stream sediment samples)on the gold mineralization in Saqqez,NW of Iran.Interpretation of the histograms and diagrams showed that the MPD is capable of identifying two phases of mineralization.The fractal method could separate only one phase of change based on the fractal dimension with high concentration areas of the Au element.The spatial analysis showed two mixed subpopulations after U=0 and another subpopulation with very high U values.The MPD analysis followed spatial analysis,which shows the detail of the variations.Six mineralized zones detected from local geochemical exploration results were used for validating the methods mentioned above.The MPD method was able to identify the anomalous areas higher than 90%,whereas the two other methods identified 60%(maximum)of the anomalous areas.The raw data without any estimation for the concentration was used by the MPD method using aminimum of calculations to determine the threshold values.Therefore,the MPD method is more robust than the other methods.The spatial analysis identified the detail soft hegeological and mineralization events that were affected in the study area.MPD is recommended as the best,and the spatial U-analysis is the next reliable method to be used.The fractal method could show more detail of the events and variations in the area with asymmetrical grid net and a higher density of sampling or at the detailed exploration stage.

Analysis of secondary electron emission using the fractal method

Based on the rough surface topography with fractal parameters and the Monte–Carlo simulation method for secondary electron emission properties, we analyze the secondary electron yield(SEY) of a metal with rough surface topography. The results show that when the characteristic length scale of the surface, G, is larger than 1 × 10^(-7), the surface roughness increases with the increasing fractal dimension D. When the surface roughness becomes larger, it is difficult for entered electrons to escape surface. As a result, more electrons are collected and then SEY decreases. When G is less than 1 × 10^(-7),the effect of the surface topography can be ignored, and the SEY almost has no change as the dimension D increases. Then,the multipactor thresholds of a C-band rectangular impedance transfer and an ultrahigh-frequency-band coaxial impedance transfer are predicted by the relationship between the SEY and the fractal parameters. It is verified that for practical microwave devices, the larger the parameter G is, the higher the multipactor threshold is. Also, the larger the value of D,the higher the multipactor threshold.

Running-in Test and Fractal Methodology for Worn Surface Topography Characterization

Studying and understanding of the surface topography variation are the basis for analyzing tribological problems,and characterization of worn surface is necessary.Fractal geometry offers a more accurate description for surface roughness that topographic surfaces are statistically self-similar and can be quantitatively evaluated by fractal parameters.The change regularity of worn surface topography is one of the most important aspects of running-in study.However,the existing research normally adopts only one friction matching pair to explore the surface topography change,which interrupts the running-in wear process and makes the experimental result lack authenticity and objectivity.In this paper,to investigate the change regularity of surface topography during the real running-in process,a series of running-in tests by changing friction pairs under the same operating conditions are conducted on UMT-II Universal Multifunction Tester.The surface profile data are acquired by MiaoXAM2.5X-50X Ultrahigh Precision Surface 3D Profiler and analyzed using fractal dimension D,scale coefficient C and characteristic roughness Ra ＊based on root mean square（RMS） method.The characterization effects of the three parameters are discussed and compared.The results obtained show that there exists remarkable fractal feature of surface topography during running-in process,both D and Ra ＊increase gradually,while C decreases slowly as the wear-in process goes on,and all parameters tend to be stable when the wear process steps into the normal wear process.Ra ＊illustrates higher sensitivity for rough surface characterization compared with the other two parameters.In addition,the running-in test carried with a set of identical surface properties is more scientific and reasonable than the traditional one.The proposed research further indicates that the fractal method can quantitatively measure the rough surface,which also provides an evidence for running-in process identification and tribology design.

The Study of Area-Concentration Fractal Method in Litho-Geochemical Data in Tanurjeh Area, Khorasan Province

Given the scientific progresses as well as the invention of new methods in exploration, it is necessary to conduct some re-investigations in several exploration zones. So, in the present research, geochemical data on Tanurjeh exploration zone, (located in Northern Neishaboor, Khorasane Razavi province) is studied by using some modern statistical methods. Fractal methods are appropriated to study and separate the grades societies in deposits. In this article, litho-geochemical analysis results (ICP) are processed by concentration area fractal method (CA). The distribution diagrams related to the statistical populations are drawn, and anomaly populations of Copper, Gold and Molybdenum are determined besides previous studies (petrography and alteration), the results of statistic methods (CA) and aid presence of the porphyry system in depth.

Application of fractal content-gradient method for delineating geochemical anomalies associated with copper occurrences in the Yangla ore field,China

Fractal and multi-fractal content area method finds application in a wide variety of geological,geochemical and geophysical fields.In this study,the fractal content-gradient method was used on1：10,000 scale to delineate geochemical anomalies associated with copper mineralization.Analysis of geochemical data from the Yangla super large Cu-Pb-Zn polymetallic ore district using the fractal content-gradient method,combined with other geological data from this area,indicates that oreprospecting in the ore district should focus on Cu as the main metal and Pb-Zn and Au as the auxiliary metals.The types of deposits include（in chronological order） re-formed sedimentary exhalative（SEDEX）,skarns,porphyries,and hydrothermal vein-type deposits.Three ore-prospecting targets are divided on a S-N basis：（1） the Qulong exploration area,in which the targets are porphyry-type Cu deposits;（2） the Zongya exploration area,where the targets are porphyry-type Cu and hydrothermal vein-type Cu-Pb polymetallic deposits;and（3） the Zarelongma exploration area,characterized mainly skarn-type ＂Yangla-style＂ massive sulfide Cu-Pb deposits.Our study demonstrates that the fractal content-gradient method is convenient,simple,rapid,and direct for delineating geochemical anomalies and for outlining potential exploration targets.

A Successive Shift Box-Counting Method for Calculating Fractal Dimensions and Its Application in Identification of Faults

Fractal dimensions of a terrain quantitatively describe the self-organizedstructure of the terrain geometry. However, the local topographic variation cannot be illustrated bythe conventional box-counting method. This paper proposes a successive shift box-counting method,in which the studied object is divided into small sub-objects that are composed of a series of gridsaccording to its characteristic scaling. The terrain fractal dimensions in the grids are calculatedwith the successive shift box-counting method and the scattered points with values of fractaldimensions are obtained. The present research shows that the planar variation of fractal dimensionsis well consistent with fault traces and geological boundaries.

Сomputational Experience Optimization of Colors in Complex Fractal Images in Carpet Design Using the Simplex Method

This article proposes a new approach based on linear programming optimization to solve the problem of determining the color of a complex fractal carpet pattern.The principle is aimed at finding suitable dyes for mixing and their exact concentrations,which,when applied correctly,gives the desired color.The objective function and all constraints of the model are expressed linearly according to the solution variables.Carpet design has become an emerging technological field known for its creativity,science and technology.Many carpet design concepts have been analyzed in terms of color,contrast,brightness,as well as other mathematical concepts such as geometric changes and formulas.These concepts represent a common process in the carpet industry.This article discusses the use of complex fractal images in carpet design and simplex optimization in color selection.

云南永胜古滑坡堰塞湖沉积物粒度多重分形特征及其指标适用研究

本文以云南永胜县下院滑坡堰塞湖沉积物为研究对象,依据粒度测试结果采用传统粒度指标与分形理论相结合的方式对其沉积环境进行系统化研究,探讨各传统指标在堰塞湖沉积解析中的适用性,探索多重分形理论在沉积学中的应用价值。研究结果表明:①堰塞湖沉积物粒度统计参数明显不同于其他环境下的沉积物,具有河湖相沉积独特的分布曲线形式、分选状态和分形特征。优势粒级在分形计算中起主导地位,全局分形维数与分选系数有着良好的对应关系。不同的分形维数对应着不同的堰塞湖沉积条件,分形维数在堰塞湖粒度解析中有着很好的运用前景;②多重分形结果显示2种不同时期的堰塞湖沉积物均以高聚集度组分为主体,表明粒径分布集中,反映出堰塞湖沉积过程中水动力的稳定性,沉积来源的唯一性,进一步证明了该堰塞湖曾长期存在。细粒组沉积粒径分布范围较窄,分布相对集中,优势粒组多但单个含量低,尾端含量低,内部分异较大;粗粒组分布呈局部集中整体分散的趋势,高聚集度粒组数量少但含量高,低聚集度粒组数量多但单个含量低,呈现中间高,四周低的特点。③多重分形分析表明Δα、Δf在沉积物粒度分析中能够解析粒组内部分布特征,具有传统指标不可替代的作用,D_(0)和D_(1)两者结合可作为沉积环境解析的替代指标,与其他q阶多重分形联合可进一步作为堰塞湖解析指标,而D_(1)/D_(0)和D2则存在一定局限。

基于孔隙分形特征的水泥基毛细吸力预测模型

为深入理解水泥基毛细吸力与含水量的关系,采用分形几何学方法和毛细管理论提出了考虑孔隙分形特征的水泥基毛细吸力预测模型。该模型通过建立分形模型参数与试样配合比的拟合关系,实现了不同配合比水泥基毛细吸力的快速预测。基于相对湿度法开展了水泥基孔径分布测量验证试验,结果表明:不同配合比(水、灰、砂)水泥基试样孔隙均具有明显分形特性,可用Menger海绵体分形模型较好描述;毛细吸力模型预测结果与验证试验测试结果的偏差主要集中在±20%以内,模型可以较为准确地预测水泥基毛细吸力与含水量的关系。

Structural Control on the Salmas Geothermal Region, Northwest Iran, from Fractal Analysis and Paleostress Data

The Salmas geothermal field is located in NW Iran. Subduction of Neo-Tethys oceanic crust beneath the Iranian microcontinent caused to propagation of the magmatic-Arc. Fractures and faults in the convergent zone have created path-ways for the circulation of geothermal fluid. Fracture concentration in the Salmas geothermal field has been characterized using of the fractal method and creation of a fracture density map that shows the highest concentration in the central part of the study area. The permeability of fractures has been evaluated by analyzing their orientation in respect to the paleostress axes. Also, the fractal analyzing result indicates the maximum fractal dimension（1.96） is around the thermal spring outlet. Paleostress analyzing revealed that in the central part of the study area, σ1 axes orientation is S90°W/10° and the σ2 dip is near to the vertical in this stress field, where strike slip faults can be propagated. In the SE part near the recharge of the thermal springs, the σ3 plunge increases to 70？ and σ1 orientation is N15°E/20°, in this local tectonic regime thrust fault developed. Fractures have an important role in the circulation of fluid and the fractal dimension increases near the thermal springs in the Salmas geothermal field. Regarding the paleostress data fracture with N-S direction such as the F1 fault zone（parallel to the σ1 axes）, a suitable pathway for deep circulation of geothermal fluid flow has been created.

基于分形特征和阈值分析的图像边缘检测

针对传统的边缘检测算法对噪声敏感且伪边缘较多,提出一种基于分形特征和阈值分析的图像边缘检测方法。该方法利用改进的毯覆盖算法计算出图像的分形特征,将图像的灰度分布映射到分形维数空间上,再根据提取的分形特征图进行阈值分析,获得高低两个阈值,将像素值分为非边缘、弱边缘和强边缘3类,再对弱边缘像素进一步加以判断。实验结果与其他算法相比较表明,该算法检测出来的图像边缘伪边缘和噪声最少。

基于多季相分形特征的Landsat 8 OLI影像耕地信息提取方法

利用遥感技术快速准确地提取耕地信息是耕地保护的关键环节。以山东省商河县为例,提出了一种基于多季相分形特征的Landsat 8 OLI影像耕地信息提取方法。首先采用毯子覆盖法计算多季相遥感影像每个像元的上分形信号和下分形信号,对比分析耕地和其他土地利用类型的分形特征,选取上分形信号的第3尺度作为特征尺度,提取商河县耕地空间分布特征;其次采用同时期的土地利用矢量数据、Esri land cover数据和统计数据进行耕地信息提取精度评价;最后分别设置多季相分形提取与单季相分形提取、现有土地利用数据产品的对比实验,并基于点位匹配度和面积匹配度进行评价。结果表明:多季相数据更能反映农作物生长的复杂性,有助于提高耕地信息的提取精度;不同土地利用类型在不同分形尺度的信号值各不相同,分形特征可以在不同尺度上清晰地刻画出不同土地利用类型的分异性;基于矢量数据和Esri land cover数据评价的多季相分形特征耕地提取点位匹配度为87.13%和89.83%,面积匹配度为99.73%和97.91%,均比单季相分形提取结果精度高;综合考虑点位匹配度、面积匹配度和空间分布特征,研发方法能有效区分耕地和其他土地利用类型,提取结果更优,且与统计数据有更高的一致性。该方法可准确提取耕地信息,为耕地的动态监测和损害评估提供技术支撑。

基于分形理论的城市轨道交通客流动态特征研究

随着城市轨道交通的发展,其站点与线路设施将逐渐完善,并引发客流的变化。为评价轨道交通客流的动态特征,针对轨道交通客流时空不确定的特点,采用半径-面积法,分析轨道交通客流进/出站维数与其分枝维数,探究轨道交通建设过程中客流分维的短时与长期变化特征。为研究轨道客流的自仿射特性,采用功率谱分析法,计算自仿射记录维数。以苏州市轨道交通为例,发现客流的全天变化趋势可用分形维数量化分析。采用功率谱分析方法逐一求解不同时间段下的自仿射记录维数,发现平峰期的客流空间衰减率更高,同质性更低。研究成果可为进一步解析与优化轨道交通的利用效率与服务能力提供理论指导。

钢渣细骨料泡沫混凝土制备及抗压强度计算

为实现钢渣资源化利用,以钢渣作为细骨料,采用不同钢渣粒径、钢渣取代量和水胶比制备了钢渣泡沫混凝土试块,通过7 d无侧限抗压强度确定出最优配合比为1.18 mm钢渣粒径、20%(与水泥质量比,下同)钢渣取代量、0.45水胶比。根据分形理论建立了最优配合比下钢渣泡沫混凝土抗压强度与孔隙率的关系式,试样的分形维数D可由盒计数法算出。此分形模型计算的抗压强度预测值与试验值吻合度较高。通过对比其他文献中泡沫混凝土抗压强度的实测值,证明了分形计算模型能够准确预测出泡沫混凝土的抗压强度,具有良好的应用前景。

中阶煤的孔隙特征研究

明确煤体的孔隙结构对煤层气的开采及瓦斯突出危险性评价有重要意义。为了解中阶煤孔隙特征,首先通过扫描电子显微镜测试煤层表面,后采用低温液氮吸附法和压汞法分析孔隙结构,并对测得实验数据进行绘图,研究其分形特征。结果表明:钱家营焦煤(QJY)、宁夏1/3焦煤(NX)、东欢坨气煤(DHT)三种煤样的吸附等温曲线均属于Ⅱ类吸附曲线,且呈倒"S"型。东欢坨煤的比表面积最大,宁夏煤次之,钱家营煤的比表面积较小,煤的变质程度与比表面积呈现明显的负相关性。孔径在≥50 nm的孔含量与平均孔径呈正相关;3个煤样中孔径≤10 nm的孔容占比均最大,煤孔隙主要是由微孔组成。孔隙发育情况:DHT>NX>QJY;钱家营煤与东欢坨煤的分形维数都呈现出吸附孔D _(2)>渗流孔D 1的特征,其微小孔的孔隙结构比较复杂,且无规则性。宁夏煤吸附孔的分形维数D_(2)=2.890,在2~3之间,微小孔具有分形特征。

基于分形特征的阿尔茨海默病脑网络结构分析

阿尔茨海默病患者的功能脑网络在小世界及聚类系数等拓扑属性上与认知正常者存在差异。为进一步揭示阿尔茨海默病患者脑网络的结构特征及其与认知正常者脑网络结构的差异,引入分形特征进行对比分析。实验结果表明,阿尔茨海默病患者与认知正常者的脑网络在相同盒覆盖半径下的最小盒子数与连接比例存在显著差异。脑网络阈值为0.4时,认知正常者脑网络的连接比例值分布在区间[0,1],而阿尔茨海默病患者脑网络的连接比例值分布在区间(0.5,1)。同时,不同阈值下,阿尔茨海默病患者脑网络的平均连接比例均高于认知正常者。上述网络结构差异可为阿尔茨海默病的诊断提供一种新参考。

甘肃三白墩地区化探数据处理异常下限确定方法的对比研究

迭代剔除法是目前化探工作者常采用的异常下限确定方法,该方法在圈定异常过程中,要求数据须服从对数正态分布或正态分布。但在实际工作中,原始数据常不符合对数正态分布或正态分布,需弱化高背景场、强化低背景场,最终实现凸显低缓异常,缩小高背景区。本文以玉门市三白墩地区1∶1万岩屑地球化学测量数据为例,采用经典数理统计方法研究元素间相互关系。在此基础上,分别运用迭代剔除法(均值标准差法)、剖面法、累频法和分形法确定背景上限即异常下限。应用上述4种方法确定异常值分别圈定单元素异常,相互对比显示,采用分形法圈定的Au元素异常与矿化体对应性好,对找矿具指导作用,其余3种方法确定的异常面积大,局部反映了地质体岩石地球化学特征,而非真正意义上的异常,给查证带来一定难度。应用迭代剔除法圈定的As元素异常与矿化体吻合程度较高,可较好指导找矿。分形法与85%累频法圈定的异常,弱异常局部丢失,导致矿化丢失。因此,建议采用多种异常下限确定方法进行对比研究,合理确定异常下限,圈定有利找矿异常区。

基于分形理论的蚀变异常遥感解译——以广东阳山县为例

围岩蚀变异常是热液型矿床的重要找矿标志,运用遥感技术解译提取围岩蚀变信息是辅助地质找矿的重要手段。本文采用主成分分析法提取广东阳山地区Landsat-5的TM遥感影像中铁染和泥化蚀变信息,对影像中所提取的异常主成分进行“像元-面积”划分并统计像元个数,再将异常阈值进行分形非线性划分,得到更为精准的分级方法。门限法是基于突变点选择阈值进行等级划分,在提取蚀变异常的结果中往往会包含大量的背景信息,利用分形理论确定临界值进行分级减少了这些信息的影响。本次研究通过门限法和分形方法两种划分方法对研究区的蚀变异常进行对比,最后根据研究区蚀变异常信息的分形特征,利用求和方法对研究区的铁染和泥化蚀变异常信息进行分级。结果表明,相对于门限法,在遥感蚀变信息提取中分形方法加强了阈值选取的准确度,并发现研究区泥化蚀变与铁染蚀变主要分布于北东部及北部区域,其它区域小面积离散分布,这可为矿产勘查工作提供更好的技术支撑。