A novel box-counting method for quantitative fractal analysis of threedimensional pore characteristics in sandstone

Fractal theory offers a powerful tool for the precise description and quantification of the complex pore structures in reservoir rocks,crucial for understanding the storage and migration characteristics of media within these rocks.Faced with the challenge of calculating the three-dimensional fractal dimensions of rock porosity,this study proposes an innovative computational process that directly calculates the three-dimensional fractal dimensions from a geometric perspective.By employing a composite denoising approach that integrates Fourier transform(FT)and wavelet transform(WT),coupled with multimodal pore extraction techniques such as threshold segmentation,top-hat transformation,and membrane enhancement,we successfully crafted accurate digital rock models.The improved box-counting method was then applied to analyze the voxel data of these digital rocks,accurately calculating the fractal dimensions of the rock pore distribution.Further numerical simulations of permeability experiments were conducted to explore the physical correlations between the rock pore fractal dimensions,porosity,and absolute permeability.The results reveal that rocks with higher fractal dimensions exhibit more complex pore connectivity pathways and a wider,more uneven pore distribution,suggesting that the ideal rock samples should possess lower fractal dimensions and higher effective porosity rates to achieve optimal fluid transmission properties.The methodology and conclusions of this study provide new tools and insights for the quantitative analysis of complex pores in rocks and contribute to the exploration of the fractal transport properties of media within rocks.

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.

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 .

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.

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.

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.

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.

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.

Two Phase Flow Simulation of Fractal Oil Reservoir Based on Meshless Method

The reservoir is the networked rock skeleton of an oil and gas trap,as well as the generic term for the fluid contained within pore fractures and karst caves.Heterogeneity and a complex internal pore structure characterize the reservoir rock.By introducing the fractal permeability formula,this paper establishes a fractal mathematical model of oil-water two-phase flow in an oil reservoir with heterogeneity characteristics and numerically solves the mathematical model using the weighted least squares meshless method.Additionally,the method’s correctness is verified by comparison to the exact solution.The numerical results demonstrate that the fractal oil-water two-phase flow mathematical model developed using the meshless method is capable of more accurately and efficiently describing the flow characteristics of the oil-water two-phase migration process.In comparison to the conventional numerical model,this method achieves a greater degree of convergence and stability.This paper examines the effect of varying the initial viscosity of the oil,the initial formation pressure,and the production and injection ratios on daily oil production per well,water cut in the block,and accumulated oil in the block.For 10 and 60 cp initial crude oil viscosities,the water cut can be 0.62 and 0.80,with 3100 and 1900 m^(3)cumulative oil production.Initial pressures have little effect on production.In this case,the daily oil production of well PRO1 is 1.7 m^(3)at 7 and 10 MPa initial pressure.Block cumulative oil production is 3465.4 and 2149.9m^(3)when the production injection ratio is 1.4 and 0.8.The two-phase meshless method described in this paper is essential for a rational and effective study of production dynamics patterns in complex reservoirs and the development of reservoir simulations of oil-water flow in heterogeneous reservoirs.

A Statistical Method for Determining the Fractal Dimension of Time Series

In this paper,we present a new method for determining the fractal dimension of time series and the algorithm of H index(Hurst index).

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.

Research and experimental analysis of precision degradation method based on the ball screw mechanism

As a key transmission component in computer numerical control(CNC) machine tools,the ball screw mechanism(BSM) is usually investigated under working load conditions. Its accuracy degradation process is relatively long,which is not conducive to the design and development of new products. In this paper,the normal wear depth of the BSM nut raceway is calculated under the variable speed operation condition using the fractal wear analysis method and the BSM’s accelerated degradation proportional wear model. Parameters of the acceleration degradation model of the double-nut preloaded ball screw pair are calculated based on the physical simulation results. The accelerated degradation test platform of the BSM is designed and manufactured to calculate the raceway wear model when the lubrication condition is broken under the variable-speed inertial load and the boundary lubrication condition under the uniform speed state. Three load forces and two samples are selected for the accelerated degradation test of the BSM. The measured friction torque of the BSM is employed as the evaluation index of the accuracy degradation test. In addition,the life cycle of the accuracy retention is accurately calculated by employing the parameters of the physical simulation model of the BSM. The calculations mentioned above can be used to estimate BSM’s accuracy performance degradation law under normal operating conditions. The application of the proposed model provides a new research method for researching the precision retention of the BSM.

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。

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。

冲刷作用下砂岩宏观力学特性及微观结构

水流环境下库岸边坡岩石劣化会严重危害坡体稳定性,如何精细化揭示动水冲刷作用下岩石宏观力学特性及微观结构对库区灾害防治具有重要意义。为模拟库岸边坡所处的水流环境,设计了一套岩石抗冲刷试验装置。以砂岩为研究对象,考虑自然、静水浸泡和动水冲刷3种工况。结合室内试验、数字图像相关方法、扫描电镜和分形理论,从宏观力学参数、应变场分布特征、微观结构等角度系统探讨了不同水环境对岩石力学特性的影响。研究结果表明:(1)动水冲刷后的岩石抗压强度和弹性模量软化系数比饱水试件分别降低了0.07和0.06;(2)应变场分异速率-轴向应变曲线在峰值应力前出现拐点P,与断裂过程区的集聚相关,可作为岩石破裂的前兆信号;相较于饱水作用,冲刷作用使得破裂前兆点出现变早,这是因为冲刷作用加剧了岩石内部缺陷的发育,更易形成裂纹;(3)相较于饱水试件,动水冲刷后砂岩内部矿物颗粒和胶结物流失程度加大,微观结构劣化更为显著,这种变化在扫描电镜图像的分形维数计算结果中得到了印证,冲刷试件的分形维数最大。

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。

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。