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...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.展开更多
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 characterize...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.展开更多
The damped Helmholtz-Duffing oscillator is a topic of great interest in many different fields of study due to its complex dynamics.By transitioning from conventional continuous differential equations to their fractal ...The damped Helmholtz-Duffing oscillator is a topic of great interest in many different fields of study due to its complex dynamics.By transitioning from conventional continuous differential equations to their fractal counterparts,one gains insights into the system's response under new mathematical frameworks.This paper presents a novel method for converting standard continuous differential equations into their fractal equivalents.This conversion occurs after the nonlinear system is transformed into its linear equivalent.Numerical analyses show that there are several resonance sites in the fractal system,which differ from the one resonance point found in the continuous system.One important finding is that the fractal system loses some of its stabilizing power when decaying behavior is transformed into a diffuse pattern.Interestingly,a decrease in the fractal order in resonance settings shows a stabilizing impact,highlighting the dynamics'complexity inside fractal systems.This endeavor to convert to fractals is a revolutionary technique that is being employed for the first time.展开更多
In this investigation,the Gradient Boosting(GB),Linear Regression(LR),Decision Tree(DT),and Voting algo-rithms were applied to predict the distribution pattern of Au geochemical data.Trace and indicator elements,inclu...In this investigation,the Gradient Boosting(GB),Linear Regression(LR),Decision Tree(DT),and Voting algo-rithms were applied to predict the distribution pattern of Au geochemical data.Trace and indicator elements,including Mo,Cu,Pb,Zn,Ag,Ni,Co,Mn,Fe,and As,were used with these machine learning algorithms(MLAs)to predict Au concentration values in the Doostbigloo porphyry Cu-Au-Mo mineralization area.The performance of the models was evaluated using the Mean Absolute Percentage Error(MAPE)and Root Mean Square Error(RMSE)metrics.The proposed ensemble Voting algorithm outperformed the other models,yielding more ac-curate predictions according to both metrics.The predicted data from the GB,LR,DT,and Voting MLAs were modeled using the Concentration-Area fractal method,and Au geochemical anomalies were mapped.To compare and validate the results,factors such as the location of the mineral deposits,their surface extent,and mineralization trend were considered.The results indicate that integrating hybrid MLAs with fractal modeling signifi-cantly improves geochemical prospectivity mapping.Among the four models,three(DT,GB,Voting)accurately identified both mineral deposits.The LR model,however,only identified Deposit I(central),and its mineralization trend diverged from the field data.The GB and Voting models produced similar results,with their final maps derived from fractal modeling showing the same anomalous areas.The anomaly boundaries identified by these two models are consistent with the two known reserves in the region.The results and plots related to prediction indicators and error rates for these two models also show high similarity,with lower error rates than the other models.Notably,the Voting model demonstrated superior performance in accurately delineating mineral deposit locations and identifying realistic mineralization trends while minimizing false anomalies.展开更多
Understanding the mesoscopic tensile fracture damage of rock is the basis of evaluating the deterioration process of mechanical properties of heat-damaged rock. For this, tensile tests of rocks under high-temperature ...Understanding the mesoscopic tensile fracture damage of rock is the basis of evaluating the deterioration process of mechanical properties of heat-damaged rock. For this, tensile tests of rocks under high-temperature treatment were conducted with a ϕ75 mm split Hopkinson tension bar (SHTB) to investigate the mesoscopic fracture and damage properties of rock. An improved scanning electron microscopy (SEM) experimental method was used to analyze the tensile fracture surfaces of rock samples. Qualitative and quantitative analyses were performed to assess evolution of mesoscopic damage of heat-damaged rock under tensile loading. A constitutive model describing the mesoscopic fractal damage under thermo-mechanical coupling was established. The results showed that the high temperatures significantly reduced the tensile strength and fracture surface roughness of the red sandstone. The three-dimensional (3D) reconstruction of the fracture surface of the samples that experienced tensile failure at 900 °C showed a flat surface. The standard deviation of elevation and slope angle of specimen fracture surface first increased and then decreased with increasing temperature. The threshold for brittle fracture of the heat-damaged red sandstone specimens was 600 °C. Beyond this threshold temperature, local ductile fracture occurred, resulting in plastic deformation of the fracture surface during tensile fracturing. With increase of temperature, the internal meso-structure of samples was strengthened slightly at first and then deteriorated gradually, which was consistent with the change of macroscopic mechanical properties of red sandstone. The mesoscopic characteristics, such as the number, mean side length, maximum area, porosity, and fractal dimension of crack, exhibited an initial decline, followed by a gradual increase. The development of microcracks in samples had significant influence on mesoscopic fractal dimension. The mesoscopic fractal characteristics were used to establish a mesoscopic fractal damage constitutive model for red sandstone, and the agreement between the theoretical and experimental results validated the proposed model.展开更多
WITHDRAWAL:Zhang,J.J.,Guo,Y.Q.,Qin,Z.Y.,Wei,C.T.,Hu,Q.H.,Vandeginste,V.,Miao,H.Y.,Yao,P.,and Zhang,P.F.,“Predicting Irreducible Water Saturation of Unconventional Reservoirs by Using NMR T2 Spectra:Methods of Morphol...WITHDRAWAL:Zhang,J.J.,Guo,Y.Q.,Qin,Z.Y.,Wei,C.T.,Hu,Q.H.,Vandeginste,V.,Miao,H.Y.,Yao,P.,and Zhang,P.F.,“Predicting Irreducible Water Saturation of Unconventional Reservoirs by Using NMR T2 Spectra:Methods of Morphological Division and Fractal Models”,Acta Geologica Sinica-English Edition(Accepted Article):https://doi.org/10.1111/1755-6724.15094.展开更多
To comprehensively utilize the valuable geological map,exploration profile,borehole,and geochemical logging data and the knowledge on the formation of the Jinshan Ag-Au deposit for forecasting the exploration targets ...To comprehensively utilize the valuable geological map,exploration profile,borehole,and geochemical logging data and the knowledge on the formation of the Jinshan Ag-Au deposit for forecasting the exploration targets of concealed ore bodies,three-dimensional Mineral Prospectivity Modeling(MPM)of the deposit has been conducted using the weights-of-evidence(WofE)method.Conditional independence between evidence layers was tested,and the outline results using the prediction-volume(P-V)and Student's t-statistic methods for delineating favorable mineralization areas from continuous posterior probability map were critically compared.Four exploration targets delineated ultimately by the Student's t-statistic method for the discovery of minable ore bodies in each of the target areas were discussed in detail.The main conclusions include:(1)three-dimensional modeling of a deposit using multi-source reconnaissance data is useful for MPM in interpreting their relationships with known ore bodies;(2)WofE modeling can be used as a straightforward tool for integrating deposit model and reconnaissance data in MPM;(3)the Student's t-statistic method is more applicable in binarizing the continuous prospectivity map for exploration targeting than the PV approach;and(4)two target areas within high potential to find undiscovered ore bodies were diagnosed to guide future near-mine exploration activities of the Jinshan deposit.展开更多
Nowadays,wireless communication devices turn out to be transportable owing to the execution of the current technologies.The antenna is the most important component deployed for communication purposes.The antenna plays...Nowadays,wireless communication devices turn out to be transportable owing to the execution of the current technologies.The antenna is the most important component deployed for communication purposes.The antenna plays an imperative role in receiving and transmitting the signals for any sensor network.Among varied antennas,micro strip fractal antenna(MFA)significantly contributes to increasing antenna gain.This study employs a hybrid optimization method known as the elephant clan updated grey wolf algorithm to introduce an optimized MFA design.This method optimizes antenna characteristics,including directivity and gain.Here,the factors,including length,width,ground plane length,height,and feed offset-X and feed offset-Y,are taken into account to achieve the best performance of gain and directivity.Ultimately,the superiority of the suggested technique over state-of-the-art strategies is calculated for various metrics such as cost and gain.The adopted model converges to a minimal value of 0.2872.Further,the spider monkey optimization(SMO)model accomplishes the worst performance over all other existing models like elephant herding optimization(EHO),grey wolf optimization(GWO),lion algorithm(LA),support vector regressor(SVR),bacterial foraging-particle swarm optimization(BF-PSO)and shark smell optimization(SSO).Effective MFA design is obtained using the suggested strategy regarding various parameters.展开更多
Distinguishing geochemical anomalies from background is a basic task in exploratory geochemistry. The derivation of geochemical anomalies from stream sediment geochemical data and the decomposition of these anomalies ...Distinguishing geochemical anomalies from background is a basic task in exploratory geochemistry. The derivation of geochemical anomalies from stream sediment geochemical data and the decomposition of these anomalies into their component patterns were described. A set of stream sediment geochemical data was obtained for 1 880 km 2 of the Pangxidong area, which is in the southern part of the recently recognized Qinzhou-Hangzhou joint tectonic belt. This belt crosses southern China and tends to the northwest (NE) direction. The total number of collected samples was 7 236, and the concentrations of Ag, Au, Cu, As, Pb and Zn were measured for each sample. The spatial combination distribution law of geochemical elements and principal component analysis (PCA) were used to construct combination models for the identification of combinations of geochemical anomalies. Spectrum-area (S-A) fractal modeling was used to strengthen weak anomalies and separate them from the background. Composite anomaly modeling was combined with fractal filtering techniques to process and analyze the geochemical data. The raster maps of Au, Ag, Cu, As, Pb and Zn were obtained by the multifractal inverse distance weighted (MIDW) method. PCA was used to combine the Au, Ag, Cu, As, Pb, and Zn concentration values. The S-A fractal method was used to decompose the first component pattern achieved by the PCA. The results show that combination anomalies from a combination of variables coincide with the known mineralization of the study area. Although the combination anomalies cannot reflect local anomalies closely enough, high-anomaly areas indicate good sites for further exploration for unknown deposits. On this basis, anomaly and background separation from combination anomalies using fractal filtering techniques can provide guidance for later work.展开更多
The self-similar is a common phenomena arising in the field of geology. It has been shown that geochemical element data, mineral deposits, and spacial distribution conform to a fractal structure. A fractal distributio...The self-similar is a common phenomena arising in the field of geology. It has been shown that geochemical element data, mineral deposits, and spacial distribution conform to a fractal structure. A fractal distribution requires that the number of objects larger than a specified size have a power-law dependence on size. This paper shows that a number of distributions, including power-function, Pareto, lognormal, 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. The summation method is developed on the basis of fractal models to determine thresholds for Au data in Shandong Province, China. The anomalous area is enclosed by contours which have contour values greater than or equal to threshold （200 × 10^- 9） and contains known large-sized and super large-sized gold mineral deposits.展开更多
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...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.展开更多
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 frompartic...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.展开更多
Many popular models have been proposed to study the fractal properties of the pores of porous materials based on mercury intrusion porosimetry(MIP).However,most of these models do not directly apply to the small-micro...Many popular models have been proposed to study the fractal properties of the pores of porous materials based on mercury intrusion porosimetry(MIP).However,most of these models do not directly apply to the small-micro pores of loess,which have a significant impact on the throat pores and tunnels for fluid flow.Therefore,in this study we used a combination of techniques,including routine physical examination,MIP analysis,and scanning electron microscope(SEM)image analysis,to study these small-micro pores and their saturated water permeability properties.The techniques were used to determine whether the fractal dimensions of six MIP fractal models could be used to evaluate the microstructure types and permeability properties of loess.The results showed that the Neimark model is suitable for analysis of small-micro pores.When applied to saturated water permeability,the results from this model satisfied the correlation significance test and were consistent with those from SEM analysis.A high clay content and density cause an increase in the number of small-micro pores,leading to more roughness and heterogeneity of the pore structure,and an increase in the fractal dimensions.This process further leads to a decrease in the content of macro-meso pores and saturated water permeability.Furthermore,we propose new parameters:the*Ellipse and its area ratios(*EAR).These parameters,coupled with 2D-SEM and 3D-MIP fractal dimensions,can effectively and quantitatively be used to evaluate the types of loess microstructures(from typeⅠto typeⅢ)and the saturated water permeability(magnitude from 1×10^(-4)cm/s to 1×10^(-5)cm/s).展开更多
Mapping mineral prospectivity in vegetated areas is a challenge. For this reason, we aimed to map spatial distribution characteristics of linear structures detected in remote sensing images using fractal and multifrac...Mapping mineral prospectivity in vegetated areas is a challenge. For this reason, we aimed to map spatial distribution characteristics of linear structures detected in remote sensing images using fractal and multifractal models. The selected study area was the Pinghe District of the Fujian Province（China）, located in the Shanghang-Yunxiao polymetallic and alunite ore belt（within the Wuyishan polymetallic belt）, where mineral resources such as copper, molybdenum, gold, silver, iron, lead, zinc, alunite and pyrophyllite have been discovered. The results of our study showed that：（1） the values of fractal dimension for all lineaments, NW-trending lineaments, and NE-trending lineaments, are 1.36, 1.32, and 1.23, respectively, indicating that these lineaments are statistically self-similar;（2） the fractal dimensions of the spatial distribution of the linear structures in the four selected hydrothermal-type ore deposits of the Pinghe District, named Zhongteng, Panchi, Xiaofanshan and Fanshan, are 1.43, 1.52, 1.37 and 1.37, respectively, which are higher than the mean value in South China;（3） the spatial distribution of the linear structures extracted from the remote sensing image and displayed by the contour map of fractal dimensions, correlates well with the known hydrothermal ore deposits; and（4） the results of the anomaly map decomposed by the spectrum-area（S-A） multifractal model is much better than the original fractal dimension contour map, which showed most of the known hydrothermal-type deposits occur in the high anomalous area. It is suggested that a high step tendency possibly matches with the boundary of the volcanic edifice and the deep fault controlling the development of the rock mass and the volcanic edifice. The complexity of the spatial distribution of mapped lineations（faults） in the Pinghe District, characterized by high values in the anomaly map, may be associated with the hydrothermal polymetallic ore mineralization in the study area.展开更多
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 co...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.展开更多
The surface morphology of Ti-Mg supported catalyst and the polyethyleneparticles are studied using scanning electron microscope(SEM) technology. The results show thateithen the catalyst's surface or polymer partic...The surface morphology of Ti-Mg supported catalyst and the polyethyleneparticles are studied using scanning electron microscope(SEM) technology. The results show thateithen the catalyst's surface or polymer particle's surface is irregular and has fractalcharacteristics, which can be described by fractal parameter. The more interesting discovery is thatthe surface fractal dimension values of the polymer particles vary periodically with thepolymerization 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 growingmodel (PFGM), and successfully describe and/or predict the whole evolving process of thepolyethylene particle morphology under the different slurry polymerization (includingpre-polymerization) conditions without H_2.展开更多
observations from the field and the taboratory show that en echelon fractures withinfracture zones have a foede1 within Ricdel structure’ The tensile fallure mecbanism of en echelonfractures can be described by the p...observations from the field and the taboratory show that en echelon fractures withinfracture zones have a foede1 within Ricdel structure’ The tensile fallure mecbanism of en echelonfractures can be described by the pile-ups of sbear crack-dislocations. A fractal model can be used tosimulate the Riedel within Xiedel geometry, allowing the direct rneasarement of tbe ftactal dimen sions of en echelon fractare systems. The energy dissipation of tbe en ccbe1on fracture system canbe deduced using a fracil damage evo1ution model which exptalns tbe evo1ution process of en eche lon fracture svstems. The fractal nature of the fractures can be used to dcrive an accurate estimateof total energy dissipation.展开更多
Spontaneous imbibition(SI)is an important mechanism for enhancing oil recovery in low-permeability reservoirs.Due to the strong heterogeneity,and the non-Darcy flow,the construction of SI model for lowpermeability res...Spontaneous imbibition(SI)is an important mechanism for enhancing oil recovery in low-permeability reservoirs.Due to the strong heterogeneity,and the non-Darcy flow,the construction of SI model for lowpermeability reservoirs is extremely challenging.Commonly,traditional SI models based on single or averaged capillary tortuosity ignore the influence of heterogeneity of pore seepage channels and the threshold pressure(TP)on imbibition.Therefore,in this work,based on capillary model and fractal theory,a mathematical model of characterizing SI considering heterogeneity of pore seepage channels is established.On this basis,the threshold pressure was introduced to determine the pore radius at which the wetted phase can displace oil.The proposed new SI model was verified by imbibition experimental data.The study shows that for weakly heterogeneous cores with permeability of 0-1 m D,the traditional SI model can characterize the imbibition process relatively accurately,and the new imbibition model can increase the coefficient of determination by 1.05 times.However,traditional model has serious deviations in predicting the imbibition recovery for cores with permeability of 10-50 m D.The new SI model coupling with heterogeneity of pore seepage channels and threshold pressure effectively solves this problem,and the determination coefficient is increased from 0.344 to 0.922,which is increased by2.68 times.For low-permeability reservoirs,the production of the oil in transitional pores(0.01-0.1μm)and mesopores(0.1-1μm)significantly affects the imbibition recovery,as the research shows that when the heterogeneity of pore seepage channels is ignored,the oil recovery in transitional pores and mesopores decreases by 7.54%and 4.26%,respectively.Sensitivity analysis shows that increasing interfacial tension,decreasing contact angle,oil-water viscosity ratio and threshold pressure will increase imbibition recovery.In addition,there are critical values for the influence of these factors on the imbibition recovery,which provides theoretical support for surfactant optimization.展开更多
Mineralization distributions are very heterogeneous in nature. As large orsuperlarge mineral deposits are quite rare whether in time or in space, it is difficult to detectall the largest mineral deposits in a region i...Mineralization distributions are very heterogeneous in nature. As large orsuperlarge mineral deposits are quite rare whether in time or in space, it is difficult to detectall the largest mineral deposits in a region in a limited period of time owing to the restriction oftechnology and exploration degrees-this is called 'not all discovered'. However, all discoveredlarge, especially superlarge, mineral deposits generally have a complete census in the geologicalliteratures. On the other hand, not all discovered small mineral deposits are recorded in thegeological literatures because for economic reasons people have not much interest in them-this iscalled 'not all recorded'. This practice often results in the observation truncations, that is, thedata points near the two ends in an observable population, which is obtained by fitting a power lawsize-frequency distribution to discovered mineral deposits in a given region, show concave-downdeparture from the correlation line fitted. The authors suggest that the size and number ofundiscovered deposits may be forecast by fitting a fractal size distribution to discovered mineraldeposit sizes between the upper and lower truncation observations and then extrapolating thescale-independent area to deposit sizes larger than the upper truncation limit. Based on thestatistical results obtained by the fractal size-frequency distributions of 394 discovered golddeposits with sizes greater than 2 t Au in China and 83 known gold deposits with sizes over 0.3 t Auin the Jiaodong area of China, the authors forecast according to the present commercial standardsfor gold ores that the total resources of undiscovered gold deposits ranging in tonnage from 50 to2000 t Au are more than 4500 tin China, and that in the Jiaodong area of China the total resourcesof potential gold deposits with sizes in the range of 30 to 650 t Au are about 700 t.展开更多
Without considering the influence of heat,existing fractal contact models are not applicable to analyze the contacts when the temperature changes.For this problem,the normal load model and the normal stiffness model o...Without considering the influence of heat,existing fractal contact models are not applicable to analyze the contacts when the temperature changes.For this problem,the normal load model and the normal stiffness model of thermal elasto-plastic contact of rough surfaces are developed respectively in this paper.The proposed model is based on the normal contact mechanics model of fractal theory of anisotropic and thermal elasto-plastic contact theory which can be used to characterize the rough surface thermodynamic properties.Then the validity of the model is verified.Finally,the influence of main parameters on the total normal load and the whole normal stiffness of thermal elasto-plastic contact at the interface is analyzed by contact simulation.The results show that the total normal load of thermal elasto-plastic contact increases with the increases of temperature.The whole normal stiffness of thermal elasto-plastic contact increases with increasing coefficient of linear expansion,scale factor,temperature difference or fractal dimension,but decreases with increasing fractal roughness.This model expands basic theory and applications of traditional models,and can be used to calculate and analyze the contacts when the temperature changes.展开更多
文摘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.
基金the Open Fund of the State Key Laboratory of Geological Processes and Mineral Resources of Chinaan NSERC Discovery Research Grant (ERC-OGP0183993) NSFC (No. 40373003).
文摘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.
文摘The damped Helmholtz-Duffing oscillator is a topic of great interest in many different fields of study due to its complex dynamics.By transitioning from conventional continuous differential equations to their fractal counterparts,one gains insights into the system's response under new mathematical frameworks.This paper presents a novel method for converting standard continuous differential equations into their fractal equivalents.This conversion occurs after the nonlinear system is transformed into its linear equivalent.Numerical analyses show that there are several resonance sites in the fractal system,which differ from the one resonance point found in the continuous system.One important finding is that the fractal system loses some of its stabilizing power when decaying behavior is transformed into a diffuse pattern.Interestingly,a decrease in the fractal order in resonance settings shows a stabilizing impact,highlighting the dynamics'complexity inside fractal systems.This endeavor to convert to fractals is a revolutionary technique that is being employed for the first time.
文摘In this investigation,the Gradient Boosting(GB),Linear Regression(LR),Decision Tree(DT),and Voting algo-rithms were applied to predict the distribution pattern of Au geochemical data.Trace and indicator elements,including Mo,Cu,Pb,Zn,Ag,Ni,Co,Mn,Fe,and As,were used with these machine learning algorithms(MLAs)to predict Au concentration values in the Doostbigloo porphyry Cu-Au-Mo mineralization area.The performance of the models was evaluated using the Mean Absolute Percentage Error(MAPE)and Root Mean Square Error(RMSE)metrics.The proposed ensemble Voting algorithm outperformed the other models,yielding more ac-curate predictions according to both metrics.The predicted data from the GB,LR,DT,and Voting MLAs were modeled using the Concentration-Area fractal method,and Au geochemical anomalies were mapped.To compare and validate the results,factors such as the location of the mineral deposits,their surface extent,and mineralization trend were considered.The results indicate that integrating hybrid MLAs with fractal modeling signifi-cantly improves geochemical prospectivity mapping.Among the four models,three(DT,GB,Voting)accurately identified both mineral deposits.The LR model,however,only identified Deposit I(central),and its mineralization trend diverged from the field data.The GB and Voting models produced similar results,with their final maps derived from fractal modeling showing the same anomalous areas.The anomaly boundaries identified by these two models are consistent with the two known reserves in the region.The results and plots related to prediction indicators and error rates for these two models also show high similarity,with lower error rates than the other models.Notably,the Voting model demonstrated superior performance in accurately delineating mineral deposit locations and identifying realistic mineralization trends while minimizing false anomalies.
基金supported by The National Natural Science Foundation of China(Grant Nos.12272411 and 42007259).
文摘Understanding the mesoscopic tensile fracture damage of rock is the basis of evaluating the deterioration process of mechanical properties of heat-damaged rock. For this, tensile tests of rocks under high-temperature treatment were conducted with a ϕ75 mm split Hopkinson tension bar (SHTB) to investigate the mesoscopic fracture and damage properties of rock. An improved scanning electron microscopy (SEM) experimental method was used to analyze the tensile fracture surfaces of rock samples. Qualitative and quantitative analyses were performed to assess evolution of mesoscopic damage of heat-damaged rock under tensile loading. A constitutive model describing the mesoscopic fractal damage under thermo-mechanical coupling was established. The results showed that the high temperatures significantly reduced the tensile strength and fracture surface roughness of the red sandstone. The three-dimensional (3D) reconstruction of the fracture surface of the samples that experienced tensile failure at 900 °C showed a flat surface. The standard deviation of elevation and slope angle of specimen fracture surface first increased and then decreased with increasing temperature. The threshold for brittle fracture of the heat-damaged red sandstone specimens was 600 °C. Beyond this threshold temperature, local ductile fracture occurred, resulting in plastic deformation of the fracture surface during tensile fracturing. With increase of temperature, the internal meso-structure of samples was strengthened slightly at first and then deteriorated gradually, which was consistent with the change of macroscopic mechanical properties of red sandstone. The mesoscopic characteristics, such as the number, mean side length, maximum area, porosity, and fractal dimension of crack, exhibited an initial decline, followed by a gradual increase. The development of microcracks in samples had significant influence on mesoscopic fractal dimension. The mesoscopic fractal characteristics were used to establish a mesoscopic fractal damage constitutive model for red sandstone, and the agreement between the theoretical and experimental results validated the proposed model.
文摘WITHDRAWAL:Zhang,J.J.,Guo,Y.Q.,Qin,Z.Y.,Wei,C.T.,Hu,Q.H.,Vandeginste,V.,Miao,H.Y.,Yao,P.,and Zhang,P.F.,“Predicting Irreducible Water Saturation of Unconventional Reservoirs by Using NMR T2 Spectra:Methods of Morphological Division and Fractal Models”,Acta Geologica Sinica-English Edition(Accepted Article):https://doi.org/10.1111/1755-6724.15094.
基金financially supported by the Ministry of Science and Technology of China(Nos.2022YFF0801201,2021YFC2900300)the National Natural Science Foundation of China(Nos.41872245,U1911202)the Guangdong Basic and Applied Basic Research Foundation(No.2020A1515010666)。
文摘To comprehensively utilize the valuable geological map,exploration profile,borehole,and geochemical logging data and the knowledge on the formation of the Jinshan Ag-Au deposit for forecasting the exploration targets of concealed ore bodies,three-dimensional Mineral Prospectivity Modeling(MPM)of the deposit has been conducted using the weights-of-evidence(WofE)method.Conditional independence between evidence layers was tested,and the outline results using the prediction-volume(P-V)and Student's t-statistic methods for delineating favorable mineralization areas from continuous posterior probability map were critically compared.Four exploration targets delineated ultimately by the Student's t-statistic method for the discovery of minable ore bodies in each of the target areas were discussed in detail.The main conclusions include:(1)three-dimensional modeling of a deposit using multi-source reconnaissance data is useful for MPM in interpreting their relationships with known ore bodies;(2)WofE modeling can be used as a straightforward tool for integrating deposit model and reconnaissance data in MPM;(3)the Student's t-statistic method is more applicable in binarizing the continuous prospectivity map for exploration targeting than the PV approach;and(4)two target areas within high potential to find undiscovered ore bodies were diagnosed to guide future near-mine exploration activities of the Jinshan deposit.
文摘Nowadays,wireless communication devices turn out to be transportable owing to the execution of the current technologies.The antenna is the most important component deployed for communication purposes.The antenna plays an imperative role in receiving and transmitting the signals for any sensor network.Among varied antennas,micro strip fractal antenna(MFA)significantly contributes to increasing antenna gain.This study employs a hybrid optimization method known as the elephant clan updated grey wolf algorithm to introduce an optimized MFA design.This method optimizes antenna characteristics,including directivity and gain.Here,the factors,including length,width,ground plane length,height,and feed offset-X and feed offset-Y,are taken into account to achieve the best performance of gain and directivity.Ultimately,the superiority of the suggested technique over state-of-the-art strategies is calculated for various metrics such as cost and gain.The adopted model converges to a minimal value of 0.2872.Further,the spider monkey optimization(SMO)model accomplishes the worst performance over all other existing models like elephant herding optimization(EHO),grey wolf optimization(GWO),lion algorithm(LA),support vector regressor(SVR),bacterial foraging-particle swarm optimization(BF-PSO)and shark smell optimization(SSO).Effective MFA design is obtained using the suggested strategy regarding various parameters.
基金Project(1212010071012) supported by Guangdong Pangxidong Mineral Prospect Investigation, ChinaProject(41004051) supported by the National Natural Science Foundation of ChinaProject ([2007]038-01-18) supported by Nationwide Mineral Resource Potential Evaluation Projects of Ministry of Land and Resources, China
文摘Distinguishing geochemical anomalies from background is a basic task in exploratory geochemistry. The derivation of geochemical anomalies from stream sediment geochemical data and the decomposition of these anomalies into their component patterns were described. A set of stream sediment geochemical data was obtained for 1 880 km 2 of the Pangxidong area, which is in the southern part of the recently recognized Qinzhou-Hangzhou joint tectonic belt. This belt crosses southern China and tends to the northwest (NE) direction. The total number of collected samples was 7 236, and the concentrations of Ag, Au, Cu, As, Pb and Zn were measured for each sample. The spatial combination distribution law of geochemical elements and principal component analysis (PCA) were used to construct combination models for the identification of combinations of geochemical anomalies. Spectrum-area (S-A) fractal modeling was used to strengthen weak anomalies and separate them from the background. Composite anomaly modeling was combined with fractal filtering techniques to process and analyze the geochemical data. The raster maps of Au, Ag, Cu, As, Pb and Zn were obtained by the multifractal inverse distance weighted (MIDW) method. PCA was used to combine the Au, Ag, Cu, As, Pb, and Zn concentration values. The S-A fractal method was used to decompose the first component pattern achieved by the PCA. The results show that combination anomalies from a combination of variables coincide with the known mineralization of the study area. Although the combination anomalies cannot reflect local anomalies closely enough, high-anomaly areas indicate good sites for further exploration for unknown deposits. On this basis, anomaly and background separation from combination anomalies using fractal filtering techniques can provide guidance for later work.
基金supported by the National Basic Research Program of China(Grant No.2006CB701406)the National Natural Science Foundation of China(Grant Nos.40672196, 40638041)the Program of Introducing Talents of Discipline to Universities of China(Grant No.B07011)
文摘The self-similar is a common phenomena arising in the field of geology. It has been shown that geochemical element data, mineral deposits, and spacial distribution conform to a fractal structure. A fractal distribution requires that the number of objects larger than a specified size have a power-law dependence on size. This paper shows that a number of distributions, including power-function, Pareto, lognormal, 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. The summation method is developed on the basis of fractal models to determine thresholds for Au data in Shandong Province, China. The anomalous area is enclosed by contours which have contour values greater than or equal to threshold （200 × 10^- 9） and contains known large-sized and super large-sized gold mineral deposits.
文摘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.
基金Project supported by the National Natural Science Foundation of China (No, 49971041), the National Key Basic Research Support Foundation (NKBRSF) of China (No. G1999011803) the Director Foundation of the Institute of Soil Science, CAS (No. ISSDF0004).
文摘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.
基金supported by the China Geological Survey Project(No.DD20190642)the Shaanxi Provincial Key Research Program of China(No.2019ZDLSF07-07-02)。
文摘Many popular models have been proposed to study the fractal properties of the pores of porous materials based on mercury intrusion porosimetry(MIP).However,most of these models do not directly apply to the small-micro pores of loess,which have a significant impact on the throat pores and tunnels for fluid flow.Therefore,in this study we used a combination of techniques,including routine physical examination,MIP analysis,and scanning electron microscope(SEM)image analysis,to study these small-micro pores and their saturated water permeability properties.The techniques were used to determine whether the fractal dimensions of six MIP fractal models could be used to evaluate the microstructure types and permeability properties of loess.The results showed that the Neimark model is suitable for analysis of small-micro pores.When applied to saturated water permeability,the results from this model satisfied the correlation significance test and were consistent with those from SEM analysis.A high clay content and density cause an increase in the number of small-micro pores,leading to more roughness and heterogeneity of the pore structure,and an increase in the fractal dimensions.This process further leads to a decrease in the content of macro-meso pores and saturated water permeability.Furthermore,we propose new parameters:the*Ellipse and its area ratios(*EAR).These parameters,coupled with 2D-SEM and 3D-MIP fractal dimensions,can effectively and quantitatively be used to evaluate the types of loess microstructures(from typeⅠto typeⅢ)and the saturated water permeability(magnitude from 1×10^(-4)cm/s to 1×10^(-5)cm/s).
基金supported by the“Quantitative Models for Prediction of Strategic Mineral Resources in China”(No.201211022)by the Ministry of Land and Resources of China and“Integrated Prediction Theory for Mineral Resource in Desert and Grassland Covered Areas and Geoinformation Extraction of Buried Mineral Resource”(No.41430320)by the National Natural Science Foundation of China
文摘Mapping mineral prospectivity in vegetated areas is a challenge. For this reason, we aimed to map spatial distribution characteristics of linear structures detected in remote sensing images using fractal and multifractal models. The selected study area was the Pinghe District of the Fujian Province（China）, located in the Shanghang-Yunxiao polymetallic and alunite ore belt（within the Wuyishan polymetallic belt）, where mineral resources such as copper, molybdenum, gold, silver, iron, lead, zinc, alunite and pyrophyllite have been discovered. The results of our study showed that：（1） the values of fractal dimension for all lineaments, NW-trending lineaments, and NE-trending lineaments, are 1.36, 1.32, and 1.23, respectively, indicating that these lineaments are statistically self-similar;（2） the fractal dimensions of the spatial distribution of the linear structures in the four selected hydrothermal-type ore deposits of the Pinghe District, named Zhongteng, Panchi, Xiaofanshan and Fanshan, are 1.43, 1.52, 1.37 and 1.37, respectively, which are higher than the mean value in South China;（3） the spatial distribution of the linear structures extracted from the remote sensing image and displayed by the contour map of fractal dimensions, correlates well with the known hydrothermal ore deposits; and（4） the results of the anomaly map decomposed by the spectrum-area（S-A） multifractal model is much better than the original fractal dimension contour map, which showed most of the known hydrothermal-type deposits occur in the high anomalous area. It is suggested that a high step tendency possibly matches with the boundary of the volcanic edifice and the deep fault controlling the development of the rock mass and the volcanic edifice. The complexity of the spatial distribution of mapped lineations（faults） in the Pinghe District, characterized by high values in the anomaly map, may be associated with the hydrothermal polymetallic ore mineralization in the study area.
基金supported by National Natural Science Foundation of China(No.51674279)China Postdoctoral Science Foundation(No.2016M602227)a grant from National Science and Technology Major Project(No.2017ZX05049-006)
文摘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.
基金Supported by the National Natural Science Foundation of China (No. 29706010, No. 20203016).
文摘The surface morphology of Ti-Mg supported catalyst and the polyethyleneparticles are studied using scanning electron microscope(SEM) technology. The results show thateithen the catalyst's surface or polymer particle's surface is irregular and has fractalcharacteristics, which can be described by fractal parameter. The more interesting discovery is thatthe surface fractal dimension values of the polymer particles vary periodically with thepolymerization 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 growingmodel (PFGM), and successfully describe and/or predict the whole evolving process of thepolyethylene particle morphology under the different slurry polymerization (includingpre-polymerization) conditions without H_2.
文摘observations from the field and the taboratory show that en echelon fractures withinfracture zones have a foede1 within Ricdel structure’ The tensile fallure mecbanism of en echelonfractures can be described by the pile-ups of sbear crack-dislocations. A fractal model can be used tosimulate the Riedel within Xiedel geometry, allowing the direct rneasarement of tbe ftactal dimen sions of en echelon fractare systems. The energy dissipation of tbe en ccbe1on fracture system canbe deduced using a fracil damage evo1ution model which exptalns tbe evo1ution process of en eche lon fracture svstems. The fractal nature of the fractures can be used to dcrive an accurate estimateof total energy dissipation.
基金supported by China Natural Science Foundation(Grant No.52274053)Beijing Natural Science Foundation(Grant No.3232028)Open Fund of State Key Laboratory of Offshore Oil Exploitation(Grant No.CCL2021RCPS0515KQN)。
文摘Spontaneous imbibition(SI)is an important mechanism for enhancing oil recovery in low-permeability reservoirs.Due to the strong heterogeneity,and the non-Darcy flow,the construction of SI model for lowpermeability reservoirs is extremely challenging.Commonly,traditional SI models based on single or averaged capillary tortuosity ignore the influence of heterogeneity of pore seepage channels and the threshold pressure(TP)on imbibition.Therefore,in this work,based on capillary model and fractal theory,a mathematical model of characterizing SI considering heterogeneity of pore seepage channels is established.On this basis,the threshold pressure was introduced to determine the pore radius at which the wetted phase can displace oil.The proposed new SI model was verified by imbibition experimental data.The study shows that for weakly heterogeneous cores with permeability of 0-1 m D,the traditional SI model can characterize the imbibition process relatively accurately,and the new imbibition model can increase the coefficient of determination by 1.05 times.However,traditional model has serious deviations in predicting the imbibition recovery for cores with permeability of 10-50 m D.The new SI model coupling with heterogeneity of pore seepage channels and threshold pressure effectively solves this problem,and the determination coefficient is increased from 0.344 to 0.922,which is increased by2.68 times.For low-permeability reservoirs,the production of the oil in transitional pores(0.01-0.1μm)and mesopores(0.1-1μm)significantly affects the imbibition recovery,as the research shows that when the heterogeneity of pore seepage channels is ignored,the oil recovery in transitional pores and mesopores decreases by 7.54%and 4.26%,respectively.Sensitivity analysis shows that increasing interfacial tension,decreasing contact angle,oil-water viscosity ratio and threshold pressure will increase imbibition recovery.In addition,there are critical values for the influence of these factors on the imbibition recovery,which provides theoretical support for surfactant optimization.
文摘Mineralization distributions are very heterogeneous in nature. As large orsuperlarge mineral deposits are quite rare whether in time or in space, it is difficult to detectall the largest mineral deposits in a region in a limited period of time owing to the restriction oftechnology and exploration degrees-this is called 'not all discovered'. However, all discoveredlarge, especially superlarge, mineral deposits generally have a complete census in the geologicalliteratures. On the other hand, not all discovered small mineral deposits are recorded in thegeological literatures because for economic reasons people have not much interest in them-this iscalled 'not all recorded'. This practice often results in the observation truncations, that is, thedata points near the two ends in an observable population, which is obtained by fitting a power lawsize-frequency distribution to discovered mineral deposits in a given region, show concave-downdeparture from the correlation line fitted. The authors suggest that the size and number ofundiscovered deposits may be forecast by fitting a fractal size distribution to discovered mineraldeposit sizes between the upper and lower truncation observations and then extrapolating thescale-independent area to deposit sizes larger than the upper truncation limit. Based on thestatistical results obtained by the fractal size-frequency distributions of 394 discovered golddeposits with sizes greater than 2 t Au in China and 83 known gold deposits with sizes over 0.3 t Auin the Jiaodong area of China, the authors forecast according to the present commercial standardsfor gold ores that the total resources of undiscovered gold deposits ranging in tonnage from 50 to2000 t Au are more than 4500 tin China, and that in the Jiaodong area of China the total resourcesof potential gold deposits with sizes in the range of 30 to 650 t Au are about 700 t.
基金Project(52130501)supported by the National Natural Science Foundation of ChinaProject(LY20E050012)supported by the Natural Science Foundation of Zhejiang Province,ChinaProject(Y201942581)supported by the Scientific Research Project of Education Department of Zhejiang Province,China。
文摘Without considering the influence of heat,existing fractal contact models are not applicable to analyze the contacts when the temperature changes.For this problem,the normal load model and the normal stiffness model of thermal elasto-plastic contact of rough surfaces are developed respectively in this paper.The proposed model is based on the normal contact mechanics model of fractal theory of anisotropic and thermal elasto-plastic contact theory which can be used to characterize the rough surface thermodynamic properties.Then the validity of the model is verified.Finally,the influence of main parameters on the total normal load and the whole normal stiffness of thermal elasto-plastic contact at the interface is analyzed by contact simulation.The results show that the total normal load of thermal elasto-plastic contact increases with the increases of temperature.The whole normal stiffness of thermal elasto-plastic contact increases with increasing coefficient of linear expansion,scale factor,temperature difference or fractal dimension,but decreases with increasing fractal roughness.This model expands basic theory and applications of traditional models,and can be used to calculate and analyze the contacts when the temperature changes.
