Fractal and Multifractal Modeling of Hydrothermal Mineral Deposit Spectrum: Application to Gold Deposits in Abitibi Area, Ontario, Canada

A number of fractal/multifractal methods are introduced for quantifying the mineral deposit spectrum which include a number-size model, grade-tonnage model, power spectrum model, multifractal model and an eigenvalue spectrum model. The first two models characterize mineral deposits spectra based on relationships among the measures of mineral deposits. These include the number of deposits, size of deposits, concentration and volume of mineral deposits. The last three methods that deal with the spatial-temporal spectra of mineral deposit studies are all expected to be popularized in near future. A case study of hydrothermal gold deposits from the Abitibi area, a world-class mineral district, is used to demonstrate the principle as well as the applications of methods proposed in this paper. It has been shown that fractal and multifractal models are generally applicable to modeling of mineral deposits and occurrences. Clusters of mineral deposits were identified by several methods including the power spectral analysis, singularity analysis and the eigenvalue analysis. These clusters contain most of the known mineral deposits in the Timmins and Kirkland Lake camps.

Geochemical and Geophysical Data Processing Aided by“Multifractal-Spectrum”Filters for GIS-Based Mineral Exploration

A recently developed method, on the bases of “multifractal spectrum” filters for mineral exploration, is introduced in this paper. The “multifractal spectrum” filters, a group of irregularly shaped filters that are constructed on each processed datum, can be used to separate various types of geochemical and geophysical anomalies. The basic model, with an emphasis on the GIS based implementation and the application to the geochemical and geophysical data processing for mineral exploration in southern Nova Scotia, Canada, indicates its advantage in the separation of multiple anomalies from the background.

Multifractal Analysis of Element Distribution in Skarn-type Deposits in the Shizishan Orefield,Tongling Area,Anhui Province,China

A series of element concentrations sampled from four drill cores with a length about 1000 m into different skarn-type deposits were selected from the Shizishan orefield, central Tongling, southeastern part of Anhui Province. Using the multifractal method, the distribution and migration characteristics of the major and trace elements are analyzed. The multifractal spectrum of the major elements is left-skewed, whereas the spectrum of the trace elements is right-skewed, which shows that in the process of skarn formation, the trace elements were enriched only locally, and major elements transported within a much larger range. The correlation coefficients of the multifractal parameters Aa （width of the multifractal spectrum） of the four drill cores are relatively low, but the correlation coefficients of the multifractal parameters R （spectrum symmetry parameter） and Af are relatively higher, indicating that although the non-homogeneous intensity of the distribution of elements is inconsistent, their spatial accumulation patterns are almost the same during the ore-forming process. The statistics of the mnltifractal parameters of various elements in the different locations show that the ore-forming processes and element migration pattern in the Shizishan orefield are consistent, and that the migrations of trace elements and major elements exhibit some differences.

MULTIFRACTAL DECOMPOSITION OF FRACTALS WITH FINITE MEMORY

The authors study recursive structures with ＂finite memory＂ in Euclidean matric space and the multifractal decomposition of the corresponding fractals. For any two positive numbers q,β, and such a recursive structure, a linear operator V^q,β in finite dimensional space is defined. The multifractal spectrum is given by the spectral radius of Vq,^β.

Multifractal analysis of inclined oil-water countercurrent flow

Characterizing countercurrent flow structures in an inclined oil-water two-phase flow from one-dimensional measurement is of great importance for model building and sensor design.Firstly,we conducted oil-water two-phase flow experiments in an inclined pipe to measure the conductance signals of three typical water-dominated oil-water flow patterns in inclined flow,i.e.,dispersion oil-in-water pseudo-slug flow （PS）,dispersion oil-in-water countercurrent flow （CT）,and transitional flow （TF）.In pseudo-slug flow,countercurrent flow and transitional flow,oil is completely dispersed in water.Then we used magnitude and sign decomposition analysis and multifractal analysis to reveal levels of complexity in different flow patterns.We found that the PS and CT flow patterns both exhibited high complexity and obvious multifractal dynamic behavior,but the magnitude scaling exponent and singularity of the CT flow pattern were less than those of the PS flow pattern; and the TF flow pattern exhibited low complexity and almost monofractal behavior,and its magnitude scaling was close to random behavior.Meanwhile,at short time scales,all sign series of two-phase flow patterns exhibited very similar strong positive correlation; at high time scales,the scaling analysis of sign series showed different anti-correlated behavior.Furthermore,with an increase in oil flow rate,the flow structure became regular,which could be reflected by the decrease in the width of spectrum and the difference in dimensions.The results suggested that different oil-water flow patterns exhibited different nonlinear features,and the varying levels of complexity could well characterize the fluid dynamics underlying different oil-water flow patterns.

Fractal Dimension Analysis Based Aging State Assessment of Insulating Paper with Surface Microscopic Images

The insulating paper of the transformer is affected by many factors during the operation,meanwhile,the surface texture of the paper is easy to change.To explore the relationship between the aging state and surface texture change of insulating paper,firstly,the thermal aging experiment of insulating paper is carried out,and the insulating paper samples with different aging times are obtained.After then,the images of the aged insulating paper samples are collected and pre-processed.The pre-processing effect is verified by constructing and calculating the gray surface of the sample.Secondly,the texture features of the insulating paper image are extracted by box dimension and multifractal spectrum.Based on that,the extreme learning machine(ELM)is taken as the classification tool with texture features and aging time as the input and output,to train the algorithm and construct the corresponding relationship between the texture feature and the aging time.After then,the insulating paper with unknown aging time is predicted with a trained ELMalgorithm.The numerical test results show that the texture features extracted from the fractal dimension of the micro image can effectively characterize the aging state of insulating paper,the average accuracy can reach 91.6%.It proves that the fractal dimension theory can be utilized for assessing the aging state of insulating paper for onsite applications.

Multifractal Analysis of Geochemical Stream Sediment Data in Bange Region, Northern Tibet

The aim of this study is to quantify the geochemical elements distribution patterns analyzed from stream sediment data and then to delineate favorable areas for mineral exploration. A total of 7 270 stream sediment samples were collected from four subareas and 37 rock（ore） chip samples from five different locations in the Bange region, northern Tibet（China）. The multifractal spectra of 12 elements including Au, Ag, As, Cu, Mo, Pb, Zn, W, Sn, Bi, Sb and Hg are represented by the method of moments, and characterized by five quantitative multifractal parameters. The results show that the multifractality for Cu and Bi in the Gongma area is much stronger than those in other subareas. Both the asymmetry index of multifractal spectra and the variance coefficients of Cu and Bi in this area are the highest, which imply that the distribution pattern of Cu and Bi in the Gongma area is the most heterogeneous. These multifractal parameters indicate that the Gongma area is the most favorable for prospecting Cu and Bi. The results obtained by the method of moments are in agreement with petrochemical analysis and field observation. It is suggested that multifractal analysis can be used as an effective tool to evaluate the ore-forming potential in the study area and to provide new approaches for geochemical exploration.

Multifractal characteristics of cylindrical sludge drying

This paper analyzes dewatered sludge drying using the multifractal theory.The drying rates of cylindrical sludge with equal masses but different crosssectional diameters was studied,from which multifractal parameters such as partition function and quality exponent were obtained.The parameters acquired were used to calculate the multifractal singularity spectrum and indicate the presence of multifractal characteristics.The smaller cross-sectional diameters of the sludge were found to be non-homogeneous,and required quantitative methods to analyze.

Improved multi-fractal network traffic model and its performance analysis

This paper demonstrates the limitation of the traditional multi-fractal wavelet model （MWM）. Through analyzing the multi-resolution behaviors of the real video traffic, we propose an improved MWM model. It synthesizes the traffic traces using another wavelet basis, and can adjust wavelet coefficients and multiplicative coefficients at each time scale, based on the network measurement. Subsequently, multifractal spectra and queue performances of the new model have been analyzed. The simulation proves it can capture the multifractal behaviors of network traces.