Delineation of Geochemical Anomalies Based on Cu by the Boxplot as an Exploratory Data Analysis (EDA) Method and Concentration-Volume (C-V) Fractal Modeling in Mesgaran Mining Area, Eastern Iran

The target in this investigation is separation and delineation of geochemical anomalies for the single element Cu in Mesgaran mining area, eastern Iran. Mesgaran mining area is located in south part of Sarbishe county with about 29 Km distance to the county center. This region is part of an Ophiolite sequence and the copper anomalies seem to be related to a volcanic massive sulfide (VMS) deposit whose main part (massive sulfide Lens) has been eroded. In order to delineate Cu anomalies, the boxplot as an Exploratory Data Analysis (EDA) method and concentration-volume (C-V) Fractal modeling are employed. Both of the methods reveal low-deep anomalies which are highly correlated with geological and geophysical studies. As the main result of this study we show that Fractal modeling in spite of the Boxplot, is not recommended for complex geological settings. The proved shallow anomalies recorded by geophysical studies and defined by the used methods are in accordance to the stringer zone of a volcanic massive sulfide (VMS) deposit in Mesgaran mining area which means this region is the bottom of a VMS deposit and geochemical anomalies are related to the remained parts of the deposit.

Fractal analysis of major faults and fractal dimension of lineaments in the Indo-Gangetic Plain on a regional scale

The Indo-Gangetic Plain(IGP)is one of the most seismically vulnerable areas due to its proximity to the Himalayas.Geographic information system(GIS)-based seismic characterization of the IGP was performed based on the degree of deformation and fractal dimension.The zone between the Main Boundary Thrust(MBT)and the Main Central Thrust(MCT)in the Himalayan Mountain Range(HMR)experienced large variations in earthquake magnitude,which were identified by Number-Size(NS)fractal modeling.The central IGP zone experienced only moderate to low mainshock levels.Fractal analysis of earthquake epicenters reveals a large scattering of earthquake epicenters in the HMR and central IGP zones.Similarly,the fault fractal analysis identifies the HMR,central IGP,and south-western IGP zones as having more faults.Overall,the seismicity of the study region is strong in the central IGP,south-western IGP,and HMR zones,moderate in the western and southern IGP,and low in the northern,eastern,and south-eastern IGP zones.

A Fractal Orifice-Throat Model for Seepage Characteristics of Multiscale Porous Media

The seepage characteristics of multiscale porous media is of considerable significance in many scientific and engineering fields.The Darcy permeability is one of the key macroscopic physical properties to characterize the seepage capacity of porous media.Therefore,based on the statistically fractal scaling law of porous media,fractal geometry is applied to model the multiscale pore structures.And a two-dimensional fractal orifice-throat model with multiscale and tortuous characteristics is proposed for the seepage flow through porous media.The analytical expression for Darcy permeability of porous media is derived,which is validated by comparing with available experimental data.The results show that the Darcy permeability is significantly influenced by porosity,orifice-throat fractal dimension,minimum to maximum diameter ratio,orifice-throat ratio and tortuosity fractal dimension.The present results are helpful for understanding the seepage mechanism of multiscale porous media,and may provide theoretical basis for unconventional oil and gas exploration and development,porous phase transition energy storage composites,CO2 geological sequestration,environmental protection and nuclear waste treatment,etc.

Fractal Modeling of Sphalerite Banding in Jinding Pb-Zn Deposit, Yunnan, Southwestern China

Sphalerite banding is a common texture in Jinding （金顶） Pb-Zn deposit, Yunnan （云南）, southwestern China. The frequency distribution and irregularity of sphalerite grains observed in the bandings are characterized quantitatively by fractal models. Fractal dimensions calculated by several fractal models including box-counting model, perimeter-area （P-A） model, and number-area （N-A） model show the gradual change from outer banding to inner banding, indicating a decrease in area percentage, in irregularity, in shape and in grain size, and an increase in the numbers of grains. These results may imply an inward growth of sphalerite during mineralization, and self-organization properties are involved in the nonlinear process of mineralization.

The Relationship between Fe Mineralization and Magnetic Basement Faults using Multifractal Modeling in the Esfordi and Behabad Areas(BMD), Central Iran

Multifractal modeling is a mathematical method for the separation of a high potential mineralized background from a non-mineralized background. The Concentration-Distance to Fault structures(C-DF) fractal model and the distribution of the known iron(Fe) deposits/mines seen in the Esfordi and Behabad 1:100,000 sheets from the Bafq region of central Iran are used to distinguish Fe mineralization based on their distance to magnetic basement structures and surface faults, separately, using airborne geophysical data and field surveys. Application of the C-DF fractal model for the classification of Fe mineralizations in the Esfordi and Behabad areas reveals that the main ones show a correlation with their distance from magnetic basement structures. Accordingly, the distances of Fe mineralizations with grades of Fe higher than 55%(43% < Fe ≤ 60%) are located at a distance of less than 1 km, whereas for surfacial faults with grades of 43% ≤ Fe ≤ 60%, the distances are 3162< DF ≤ 4365 m from the faults. Thus, there is a positive relationship between Fe mineralization and magnetic basement structures. Also, the proximity evidence of Precambrian high-grade Fe mineralization related to magnetic basement structures indicates syn-rifting tectonic events. Finally, this C-DF fractal model can be used for exploration of magmatic and hydrothermal ore deposits.

Fractal Prediction Model of Thermal Contact Conductance of Rough Surfaces

The thermal contact conductance problem is an important issue in studying the heat transfer of engineering surfaces, which has been widely studied since last few decades, and for predicting which many theoretical models have been established. However, the models which have been existed are lack of objectivity due to that they are mostly studied based on the statistical methodology characterization for rough surfaces and simple partition for the deformation formats of contact asperity. In this paper, a fractal prediction model is developed for the thermal contact conductance between two rough surfaces based on the rough surface being described by three-dimensional Weierstrass and Mandelbrot fractal function and assuming that there are three kinds of asperity deformation modes： elastic, elastoplastic and fully plastic. Influences of contact load and contact area as well as fractal parameters and material properties on the thermal contact conductance are investigated by using the presented model. The investigation results show that the thermal contact conductance increases with the increasing of the contact load and contact area. The larger the fractal dimension, or the smaller the fractal roughness, the larger the thermal contact conductance is. The thermal contact conductance increases with decreasing the ratio of Young＇s elastic modulus to the microhardness. The results obtained indicate that the proposed model can effectively predict the thermal contact conductance at the interface, which provide certain reference to the further study on the issue of heat transfer between contact surfaces.

Elastoplastic Contact Mechanics Model of Rough Surface Based on Fractal Theory

Because the result of the MB fractal model contradicts with the classical contact mechanics, a revised elastoplastic contact model of a single asperity is developed based on fractal theory. The critical areas of a single asperity are scale dependent, with an increase in the contact load and contact area, a transition from elastic, elastoplastic to full plastic deformation takes place in this order. In considering the size distribution function, analytic expression between the total contact load and the real contact area on the contact surface is obtained. The elastic, elastoplastic and full plastic contact load are obtained by the critical elastic contact area of the biggest asperity and maximun contact area of a single asperity. The results show that a rough surface is firstly in elastic deformation. As the load increases, elastoplastic or full plastic deformation takes place. For constant characteristic length scale G, the slope of load-area relation is proportional to fractal dimension D. For constant fractal dimension D, the slope of load-area relation is inversely proportional to G. For constant D and G, the slope of load-area relation is inversely proportional to property of the material ~b, namely with the same load, the material of rough surface is softer, and the total contact area is larger. The contact mechanics model provides a foundation for study of the friction, wear and seal performance of rough surfaces.

Numerical Modelling of Ore-forming Dynamics of Fractal Dispersive Fluid Systems

Based on an analysis of the fractal structures and mass transport mechanism of typical shear-fluid-ore formation system, the fractal dispersion theory of the fluid system was used in the dynamic study of the ore formation system. The model of point-source diffusive illuviation of the shear-fluid-ore formation system was constructed, and the numerical simulation of dynamics of the ore formation system was finished. The result shows that: (1) The metallogenic system have nested fractal structure. Different fractal dimension values in different systems show unbalance and inhomogeneity of ore-forming processes in the geohistory. It is an important parameter to symbolize the process of remobilization and accumulation of ore-forming materials. Also it can indicate the dynamics of the metallogenic system quantitatively to some extent. (2) In essence, the fractal dispersive ore-forming dynamics is a combination of multi-processes dominated by fluid dynamics and supplemented by molecule dispersion in fluids and fluid-rock interaction. It changes components and physico-chemical properties of primary rocks and fluids, favouring deposition and mineralization of ore-forming materials. (3) Gold ore-forming processes in different types of shear zones are quite different. (1) In a metallogenic system with inhomogeneous volumetric change and inhomogeneous shear, mineralization occurs in structural barriers in the centre of a shear zone and in geochemical barriers in the shear zone near its boundaries. But there is little possibility of mineralization out of the shear zone. (2) As to a metallogenic system with inhomogeneous volumetric change and simple shear, mineralization may occur only in structural barriers near the centre of the shear zone. (3) In a metallogenic system with homogeneous volumetric change and inhomogeneous shear, mineralization may occur in geochemical barriers both within and out of the shear zone.

Performance-based fractal fracture model for complex fracture network simulation

The paper presents a novel hydraulic fracturing model for the characterization and simulation of the complex fracture network in shale gas reservoirs. We go beyond the existing method that uses planar or orthogonal conjugate fractures for representing the ＇＇complexity＇＇ of the network. Bifurcation of fractures is performed utilizing the Lindenmayer system based on fractal geometry to describe the fracture propagation pattern, density and network connectivity. Four controlling parameters are proposed to describe the details of complex fractures and stimulated reservoir volume（SRV）. The results show that due to the multilevel feature of fractal fractures, the model could provide a simple method for contributing reservoir volume calibration. The primary-and second-stage fracture networks across the overall SRV are the main contributions to the production, while the induced fracture network just contributes another 20% in the late producing period. We also conduct simulation with respect to different refracturing cases and find that increasing the complexity of the fracture network provides better performance than only enhancing the fracture conductivity.

Contact Model of Revolute Joint with Clearance Based on Fractal Theory

The contact sti ness of a mechanical bonding surface is an important parameter in determining the normal and radial contact force. To improve the calculation accuracy of the contact force model, the surface roughness of the bonding surface and the energy loss that necessarily occurs during the impact process should be considered com?prehensively. To study the normal contact force of a revolute joint with clearance more accurately in the case of dry friction, a nonlinear sti ness coe cient model considering the surface roughness was established based on fractal theory, which considers the elastic, elastic?plastic, and plastic deformations of the asperities of the contact surface during the contact process. On this basis, a modified nonlinear spring damping model was established based on the Lankarani–Nikravesh contact force model. The laws influencing the surface roughness, recovery coe cient, initial velocity, and clearance size on the impact force were revealed, and were compared with the Lankarani–Nikravesh model and a hybrid model using MATLAB. The maximum impact force was obtained using a modified contact force model under di erent initial velocities, di erent clearances, and di erent degrees of surface roughness, and the calculated results were then compared with the experiment results. This study indicates that the modified model can be used more widely than other models, and is suitable for both large and small clearances. In particular, the modified model is more accurate when calculating the contact force of a revolute joint with a small clearance.

Dynamic development model for long gap discharge streamer-leader system based on fractal theory

Establishing a long air gap discharge model considering the streamer-leader transition and randomness of the discharge path is of great signiflcance to improve the accuracy of discharge characteristic prediction and optimize external insulation design.Based on fractal theory and thermal ionization theory of streamer-leader transition,this work establishes a dynamic development model for the long air gap discharge streamer-leader system,which includes streamer inception,streamer development,leader inception,development of streamer-leader system and flnal jump.The positive discharge process of a 3 m rod plate is simulated to obtain the fractal distribution of the discharge path and the law of leader development for comparison with the discharge test results.The results show that the simulation model is similar to test results in the development characteristics of leader path distribution,each stage time and leader velocity.Finally,a simulation calculation of a 50%breakdown voltage of the rod-plate gap and ball-plate gap is carried out,with results fairly consistent with test data,proving the effectiveness and practicality of the model.

Geostatistics Studies and Geochemical Modeling Based on Core Data,Sheytoor Iron Deposit,Iran

In general,the purpose of the mineralization modeling is the advancement of a mineral exploration project and ultimately,the extractive design of a deposit,which is one of the most important stages in mining engineering.Mineralization modeling is divided into two general categories,superficial and deep modeling.In surface modeling,the aim is finding abnormal locations in terms of mineralization at the study area,which is commonly used in the early stages of exploration as one of the means for locating exploratory boreholes.After drilling in the study area with the aim of identifying mineralization and reserve estimation it is necessary to obtain deep mineralization position and its geometric features,using statistical and modeling methods.Using mathematical,statistical and modeling methods,we can predict the position of iron mineralization in places where drilling is not done and eventually reach a three-dimensional model of the mineral materials underground.As a case study,the deep information about the boreholes of the sheytoor mining area in Yazd province of Iran was investigated.Iron mineralization was modeled as 2D cumulative model and 3D block model,and the results were presented.Finally the geochemical threshold and the anomalous limit of iron element are calculated by concentration-volume(C-V)fractal method in this deposit.Geochemical threshold and the anomalous limit for Fe in this deposit are 24.7%and 34.3%respectively.

A Research on Fractal Dimension and Nonlinear Dynamic Model of Xintan Landslide，China

The dynamic research of landslide is one of the key Points in landslidology. In the paper,from the view point of nonlinear dynamic theory. some features of Xintan landslide, such as the distribution regularities of spatial and temporal fractal dimensions and their corresponding relationships to landslide occurring are researched. The accumulative principles of fractal dimension reduction is exploratively pointed out. The nonlinear dynamic equation of the landslide is built by analyzing the relationship between the correlation dimension and the phase space. Finally, the forecasted results and error analysis are listed. The research results are satisfactory.

Prospectivity modeling of porphyry copper deposits: recognition of efficient mono-and multi-element geochemical signatures in the Varzaghan district, NW Iran

The Varzaghan district at the northwestern margin of the Urumieh–Dokhtar magmatic arc, is considered a promising area for the exploration of porphyry Cu deposits in Iran. In this study we identified mono-and multi-element geochemical anomalies associated with Cu–Au–Mo–Bi mineralization in the central parts of the Varzaghan district by applying the concentration–area fractal method. After mono-element geochemical investigations, principal component analysis was applied to ten selected elements in order to acquire a multi-element geochemical signature based on the mineralization-related component. Quantitative comparisons of the obtained fractal-based populations were carried out in accordance with known Cu occurrences using Student's t-values. Then,significant mono-and multi-element geochemical layers were separately combined with related geologic and structural layers to generate prospectivity models, using the fuzzy GAMMA approach. For quantitative evaluation of the effectiveness of different geochemical signatures in final prospectivity models, a prediction-area plot was adapted. The results show that the multi-element geochemical signature of principal component one(PC1) is more effective than mono-element layers in delimiting exploration targets related to porphyry Cu deposits.

Applicability of Fractal Models in Estimating Soil Water Retention Characteristics from Particle-Size Distribution Data

Soil water retention characteristics are the key information required in hydrological modeling. Frac-tal models provide a practical alternative for indirectly estimating soil water retention characteristics fromparticle-size distribution data. Predictive capabilities of three fractal models, i.e, Tyler-Wheatcraft model,Rieu-Sposito model, and Brooks-Corey model, were fully evaluated in this work using experimental datafrom an international database and literature. Particle-size distribution data were firstly interpolated into20 classes using a van Genuchten-type equation. Fractal dimensions of the tortuous pore wall and the poresurface were then calculated from the detailed particle-size distribution and incorporated as a parameter infractal water retention models. Comparisons between measured and model-estimated water retention cha-racteristics indicated that these three models were applicable to relatively different soil textures and pressurehead ranges. Tyler-Wheatcraft and Brooks-Corey models led to reasonable agreements for both coarse- andmedium-textured soils, while the latter showed applicability to a broader texture range. In contrast, Rieu-Sposito model was more suitable for fine-textured soils. Fractal models produced a better estimation of watercontents at low pressure heads than at high pressure heads.

Computer‑aided CT image processing and modeling method for tibia microstructure

We present a method for computed tomography(CT)image processing and modeling for tibia microstructure,achieved by using computer graphics and fractal theory.Given the large-scale image data of tibia species with DICOM standard for clinical applications,we take advantage of algorithms such as image binarization,hot pixel removing and close operation to obtain visually clear image for tibia microstructure.All of these images are based on 20 CT scanning images with 30μm slice thickness and 30μm interval and continuous changes in pores.For each pore,we determine its profile by using an improved algorithm for edge detection.Then,to calculate its three-dimensional fractal dimension,we measure the circumference perimeter and area of the pores of bone microstructure using a line fitting method based on the least squares.Subsequently,we put forward an algorithm for the pore profiles through ellipse fitting.The results show that the pores have significant fractal characteristics because of the good linear correlation between the perimeter and the area parameters in log–log scale coordinates system,and the ratio of the elliptical short axis to the long axis through ellipse fitting tends to 0.6501.Based on support vector machine and structural risk minimization principle,we put forward a mapping database theory of structure parameters among the pores of CT images and fractal dimension,Poisson’s ratios,porosity and equivalent aperture.On this basis,we put forward a new concept for 3D modeling called precision-measuring digital expressing to reconstruct tibia microstructure for human hard tissue.

Fractal Evolving Theory and Growing Model of Olefin Polymerization Process

The surface morphology of Ti-Mg supported catalyst and the polyethylene particles are studied using scanning electron microscope(SEM) technology.The results show that either the catalyst's surface or polymer particle's surface is irregular and has fractal characteristics,which can be described by fractal parameter.The more interesting discovery is that the surface fractal dimension values of the polymer particles vary periodically with the polymerization time.We call this phenomenon fractal evolution,which can be divided into the 'revolution' stage and the 'evolution' stage,And then we present polymerization fractal growing model(PFGM),and successfully describe and /or predict the whole evolving process of the polyethylene particle morphology under the different slurry polymerization(including pre-polymerization) conditions without H2.

FRACTAL PORE DIFFUSION MODEL OF FLUIDS IN POROUS MEDIA

A fractal pore diffusion model of fluids in porous media which is in good agreement with the experimental data of the coke-CO2 reaction, has been derived by using the Mandelbrot's fractal length-area relation. Based on the model, a new formula and its interpretation about the tortuosity of pore structures of a porous medium have been suggested, from which the fractal pore diffusion resistance has been defined. The resistance ascends obviously with the fractal pore dimension and the conversion ratio increasing, especially in the middle-latter period of fluid-solid reactions.

A two scale nonlinear fractal sea surface model in a one dimensional deep sea

Using the theory of nonlinear interactions between long and short waves, a nonlinear fractal sea surface model is presented for a one dimensional deep sea. Numerical simulation results show that spectra intensity changes at different locations （in both the wave number domain and temporal-frequency domain）, and the system obeys the energy conservation principle. Finally, a method to limit the fractal parameters is also presented to ensure that the model system does not become ill-posed,

The Influence of the Model Fractal Parameters on the Electromagnetic Response in Environment with Cylindrical Layers

The induced polarization response of an environment presenting cylindrical layers was obtained. The fractal model for complex resistivity was employed as an intrinsic property of the polarizable layers. The influence of the model fractal parameters on the electromagnetic response was investigated. The results demonstrated that the fractal parameters dominate the apparent resistivity phase response;measurements of the induced polarization data allow for the determination of the fractal properties of the environment without noticeable electromagnetic coupling effects at frequencies below 104 Hz.