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.

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。

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.

成渝双城经济圈高质量发展质量及协调性研究

选取2006—2020年成渝双城经济圈16个市作为研究对象,探究人口与经济之间的时空协调性、构建空间面板模型探究各驱动因素对经济发展的影响机制、剖析社会发展质量、城市群结构发展空间分布格局等特征。实证结果表明:(1)人口发展协调指数整体呈现震荡式分布态势,2020年,城市耦合协调度基本高于0.8;(2)仅有人均GDP、对外开放水平对其经济指数具有明显促进作用;(3)社会发展格局呈现“核心高,中部、东北部低”的空间差异;(4)城市规模质量由2006年极度集中(D=2.05)降至2020年的相对均衡(D=1.08),整体规模表现为以成都和重庆为联系中心的放射状非均衡结构。

基于三维体视分析技术对金属断口的分形研究

金属断口包含金属材料的性质、性能及服役过程的重要信息,是金属断裂定性分析、定量表征的关键证据。研究证明分形维数与材料断裂参数密切相关,但传统二维图像分析难以全面揭示断口特征。为了更深入了解断裂机制和材料性能,三维形貌技术逐渐成为研究热点。在分析仪器中三维体视显微镜可以提供更便捷、更准确的断口信息,进而通过计算分形维数推测材料断裂性质。其中计盒维数分析方法具有易于实现和理解、应用范围广、稳定性好、可解释性强等优势。利用三维体视显微镜和MATLAB程序获取断口三维形貌并计算分形维数。实验表明,拉伸断口抗拉强度和屈服强度与分形维数呈负相关,冲击断口的冲击值与分形维数呈正相关。

森林公园景观绿化演变视觉模拟方法

由于森林公园景观人为干预较少,其绿化演变过程的随机性较强,视觉模拟过程中缺少对森林景观中细节细分的过程,导致森林层次区域的模拟失真。为解决这种问题,提高森林公园景观绿化演变视觉模拟效果,提出一种基于智能算法的模拟方法,即运用中点位移法与连续随机增加法对森林景观图像去褶皱,利用多细节层次法生成原始森林景观三角形网格,利用分形技术递归细分该森林景观的三角形网格,视觉过渡不同细节层次区域,经视觉渲染后最终获得景观绿化演变视觉模拟结果。测试实验表明,该方法模拟的森林公园景观绿化演变图像较为清晰、逼真。

Adaptability of n-γdiscrimination and filtering methods based on plastic scintillation

Neutrons have been extensively used in many fields,such as nuclear physics,biology,geology,medical science,and national defense,owing to their unique penetration characteristics.Gamma rays are usually accompanied by the detection of neutrons.The capability to discriminate neutrons from gamma rays is important for evaluating plastic scintillator neutron detectors because similar pulse shapes are generated from both forms of radiation in the detection system.The pulse signals measured by plastic scintillators contain noise,which decreases the accuracy of n-y discrimination.To improve the performance of n-y discrimination,the noise of the pulse signals should be filtered before the n-y discrimination process.In this study,the influences of the Fourier transform,wavelet transform,moving-average filter,and Kalman algorithm on the charge comparison method,fractal spectrum method,and back-propagation neural network methods were studied.It was found that the Fourier transform filtering algorithm exhibits better adaptability to the charge comparison method than others,with an increasing accuracy of 6.87%compared to that without the filtering process.Meanwhile,the Kalman filter offers an improvement of 3.04%over the fractal spectrum method,and the adaptability of the moving-average filter in backpropagation neural network discrimination is better than that in other methods,with an increase in 8.48%.The Kalman filtering algorithm has a significant impact on the peak value of the pulse,reaching 4.49%,and it has an insignificant impact on the energy resolution of the spectrum measurement after discrimination.

Relevance between abutment pressure and fractal dimension of crack network induced by mining

Based on the geological conditions of coal mining face No.15-14120 at No.8 mine of Pingdingshan coal mining group,the real-time evolution of coal-roof crack network with working face advancing was collected with the help of intrinsically safe borehole video instrument.And according to the geology of this working face,a discrete element model was calculated by UDEC.Combining in situ experimental data with numerical results,the relationship between the fractal dimension of boreholes'wall and the distribution of advanced abutment pressure was studied under the condition of mining advance.The results show that the variation tendency of fractal dimension and the abutment pressure has the same characteristic value.The distance between working face and the peak value of the abutment pressure has a slight increasing trend with the advancing of mining-face.When the working face is set as the original point,the trend of fractal dimension from the far place to the origin can be divided into three phases:constant,steady increasing and constant.And the turning points of these phases are the max-influencing distance(50 m)and peak value(15 m)of abutment pressure.

一种基于分形理论的破碎岩体稳定性分级的改进方法

在对破碎岩体稳定性分级过程中,传统RMR岩体分级方法中RQD和节理间距指标容易受到测量方位和测量角度的影响。针对这一不足,引入岩体分形理论,以岩体分形维数代替RMR分级方法中的RQD和节理间距两项指标,改进性的提出了一种适用于破碎岩体稳定性分级的FT分级方法。以岩体分形理论为基础,现场获取结构面信息并导入三维重构模型,借助CAD内置VAB程序,计算破碎岩体分形维数。根据各指标评分细则,制定FT分级方法评价标准。以某金矿6个试验区岩体结构面调查数据及岩体力学参数为基础,运用改进的FT法分别对试验区破碎岩体稳定性进行评价。结果表明:FT法提高了分级准确性,减少了现场工作量,提高了分级效率,同时在对岩体稳定性描述方面更加合理,将为地下矿山破碎岩体稳定性分级带来极大便利。

Metallogenic mechanism of Pingguo bauxite deposit,western Guangxi,China:Constraints from REE geochemistry and multi-fractal characteristics of major elements in bauxite ore

Major and REE geochemistry and multi-fractal analysis of two types of bauxite(primary bauxite and accumulated bauxite) ores were studied in Pingguo bauxite orefield in western Guangxi,China.The results of geochemical data show that the accumulated bauxite has a feature of high Al_2O_3 whereas relative low Fe_2O_3 and SiO_2 contents compared to the primary bauxite.The similar chondrite-normalized rare earth element(REE) patterns illustrate that they have a cognate relationship.However,the negative Ce anomalies of primary bauxite and positive Ce anomalies of accumulated bauxite indicate that the ore-forming system changed from reducing environment to oxidation environment.The results of multi-fractal spectrum and parameters of Al_2O_3,Fe_2O_3 and SiO_2 between primary bauxite and accumulated bauxite show that the distinct multi-fractal spectrum parameters reflect the different grade distribution between accumulated and primary bauxite ores.Metallogenic process from primary bauxite to accumulated bauxite is accompanied by the loss of diffluent elements(e.g.,Si and S) and enrichment of stable elements(e.g.,Al and Fe) in the surface environment.Among the rest,the migration mechanism of iron during the evolutionary process from primary ore to accumulated ore can be described as combined leaching and chemical weathering action with participation of sulfur.