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multifractal modelling and spectrum analysis: methods and applications to gamma ray spectrometer data from southwestern Nova Scotia, canada

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Science China Earth Sciences 2006年第3期49卷 283-294页

作者： CHENG Qiuming1,2.1. State Key Lab of Geological processes and mineral Resources, China university of Geosciences, Wuhan 430074, China 2. department of Earth and Space Science and Engineering,{2., york university, 4700 keele street, toronto, ontario, m3j 1p3, canada State Key Lab of Geological processes and mineral Resources China University of Geosciences Wuhan China department of Earth and Space Science and Engineering Department of Geography York University Toronto Canada

multifractal spectrum, autocorrelation/semivariogram and power spectrum are three dif- ferent functions characterizing a field or measure from different aspects. These functions are interre- lated in such that the autocorrelation/semivariogram and power spectrum are related to the low order statistical moments (0 to 2.nd) which may determine the local multifractality (τ ″(1)) of a multifractal measure. A better understanding of the interrelationships among these three functions is important because, on one hand, the multifractal modelling characterizes a multifractal measure in a more de- tailed manner since it involves moments of all orders. On the other hand, the commonly used semivariogram and power spectrum functions can be used as alternatives to study the dominant mul- tifractal properties around the mean measure. moreover, semivariogram and power-spectrum func- tions provide spatial and spectral information, which is highly valued in geological applications. A new fractal relation found between area and power-spectrum will be useful for investigation of new meth- ods of spatial-spectral analysis for pattern recognition, anomaly separation, classification, etc. These results have been demonstrated with the case study of modelling gamma ray spectrometer data from the mineral district, southwestern Nova Scotia, canada. The results have shown that the values of uranium (U), thorium (Th) and potassium (K) may possess monofractal properties whereas the ratios of these values show high multifractality. The values of the ratios U/K and U/Th show relatively large variances and may provide more information for distinguishing the distinct phases of the granites, country rocks as well as possible gold mineralization-associated regional hydrothermal alteration zones. In addition, the power spectra for U, Th, K, U/Th and U/K consistently show two distinct power-law relationships for two ranges of wave number 12.ω ≤160 km and 0≤ω ≤12.km. These properties might provide usefu

关键词： gamma ray spectrometer data, gold mineralization, alteration zones, multifractal modelling, spectral analysis, GIS.

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modified High-order Upwind method for Convection Diffusion Equation

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Acta mathematicae Applicatae Sinica 2002年第1期18卷 131-146页

作者： Wei-dong ZHAO, Dong LIANGSchool of mathematics and System Sciences, Shandong university, jinan 2.0100, China{2. of mathematics and Statistics,{2., 4700 keele street, toronto, ontario, m3j 1p3, canada School of mathematics and System Sciences Shandong University Jinan 250100 China department of mathematics and Statistics York University 4700 Keele Street Toronto Ont. M3J 1P3 Canada

In this paper, we study the high-order upwind finite difference method for steady convection-diffusion problems. Based on the conservative convection-diffusion equation, a high-order upwind finite difference scheme on nonuniform rectangular partition for convection-diffusion equation is proposed. The proposed scheme is in conversation form, satisfies maximum value principle and has second-order error estimates in discrete H1 norm. To illustrate our conclusion, several numerical examples are given.

关键词： Convection diffusion high-order upwind method error estimate

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Selection of multifractal Scaling Breaks andSeparation of Geochemical andGeophysical Anomaly

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journal of China university of Geosciences 2001年第1期12卷 54-59页

作者： Cheng Qiuming department of Earth and Atmospheric Science, department of geography,{{2., toronto, ontario, canada, m3j 1p3 department of Earth and Atmospheric Science Department of Geography York University Toronto Ontario Canada M3J 1P3

Spatially superimposed multiple processes such as multiplicative cascade processes often generate multifractal measures possessing so-called self-similarity or self-affinity that can be described by power- law type of functions within certain scale ranges The multifractalities can be estimated by applying multifractal modeling to the measures reflecting the characteristics of the physical processes such as the element concentration values analyzed in rock and soil samples and caused by the underlying mineralization processes and the other geological processes. The local and regional geological processes may result in geochemical patterns with distinct multifractalities as wall as variable scaling ranges. Separation of these multifractal measures on the basis of both the distinct multifractalities and the scaling ranges will be significant for both theoretical studies of multifractal modeling and its applications. multifractal scaling breaks have been observed from various multifractal patterns. This paper introduces a technique for separating multifractal measures on the basis of scaling breaks. It has been demonstrated that the method is effective for decomposing geochemical and geophysical anomalies required for mineral exploration. A dataset containing the element concentration values of potassium and phosphorus in soil samples was employed for demonstrating the application of the method for studying the fertilizer and yield optimization in agriculture

关键词： mineralization processes self-similarity geochemical anomaly separation multifractal scaling breaks.

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GIS-Based Hydrogeological-parameter modeling

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journal of Earth Science 2000年第2期19卷 39-41页

作者： Han Shujie Cheng Qiuming department of Earth and Atmospheric Science york university,{{2., m3j 1p3 canada

A regression model is proposed to relate the variation of water well depth with topographic properties (area and slope), the variation of hydraulic conductivity and vertical decay factor. The implementation of this model in GIS environment (ARC/TNFO) based on known water data and DEm is used to estimate the variation of hydraulic conductivity and decay factor of different lithology units in watershed context.

关键词： hydraulic conductivity GIS modeling.

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Geochemical and Geophysical Data processing Aided by“multifractal-Spectrum”Filters for GIS-Based mineral Exploration

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journal of Earth Science 2000年第2期19卷 36-38页

作者： Xu Yaguang Cheng Qiuming department of Earth and Atmospheric Science, york university, North {{2., ontario, m3j 1p3 canada

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.

关键词： multifractal spectrum GIS based mineral exploration geochemical and geophysical anomalies.

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Fractal Correction of Well Logging Curves

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journal of China university of Geosciences 2001年第3期12卷 272-275页

作者： Li Qingmou Cheng Qiuming Institute of Geology & Geophysics, Chinese Academy of Sciences, Beijing 100101 department of Earth and Atmospheric Science, york university,{{2., ontario, canada, m3j 1p3 Institute of Geology & Geophysics Chinese Academy of Sciences Beij ing 100101 department of Earth and Atmospheric Science York University Toronto Ontario Canada M3J 1P3

It is always significant for assessing and evaluation of oil bearing layers, especially for well logging data processing and interpretation of non marine oil beds to get more accurate physical properties in thin and inter thin layers. This paper presents a definition of measures and the measure presents power law relation with the corresponded scale described by fractal theory. Thus, logging curves can be reconstructed according to this power law relation. This method uses the local structure nearby concurrent points to compensate the average effect of logging probes and measurement errors. As an example, deep and medium induced conductivity (ImpH and IDpH) curves in ODp Leg 12. Hole 797C are reconstructed or corrected. Corrected curves are with less adjacent effects through comparison of corrected curves with original one. And also, the power spectra of corrected well logging curve are abounding with more resolution components than the original one. Thus, fractal correction method makes the well logging more resoluble for thin beds.

关键词： fractal thin bed well logging singularity of well logging well logging correction.

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Edge Effect Correction in the S-A method for Geochemical Anomaly Separation

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journal of China university of Geosciences 2004年第4期15卷 379-387页

作者： Ge Yong department of Earth and Atmospheric Science, york university,{{2., ON, m3j 1p3, canada State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences & Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China Cheng Qiuming department of Earth and Atmospheric Science, york university,{{2., ON, m3j 1p3, canada Earth Systems and mineral Resource Engineering Lab, China university of Geosciences, Wuhan 430074, China Zhang Shenyuan department of Earth and Atmospheric Science, york university,{{2., ON, m3j 1p3, canada department of Resource and Earth Science, China university of mining & Technology, Beijing 100083, China department of Earth and Atmospheric Science York University Toronto ON M3J 1P3 Canada State Key Laboratory of Resources and Environmental Information System Institute of Geographic Sciences & Natural Resources Research Chinese Academy of SciencesBeijing 100101China department of Earth and Atmospheric Science York University Toronto ON M3J 1P3 Canada Earth Systems and mineral Resource Engineering Lab China University of Geosciences Wuhan 430074 China department of Earth and Atmospheric Science York University Toronto ON M3J 1P3 Canada department of Resource and Earth Science China University of Mining & Technology Beijing 100083 China

Anomaly separation using geochemical data often involves operations in the frequency domain, such as filtering and reducing noise/signal ratios. Unfortunately, the abrupt edge truncation of an image along edges and holes (with missing data) often causes frequency distribution distortion in the frequency domain. For example, bright strips are commonly seen in frequency distribution when using a Fourier transform. Such edge effect distortion may affect information extraction results; sometimes severely, depending on the edge abruptness of the image. Traditionally, edge effects are reduced by smoothing the image boundary prior to applying a Fourier transform. Zero-padding is one of the most commonly used smoothing methods. This simple method can reduce the edge effect to some degree but still distorts the image in some cases. moreover, due to the complexity of geoscience images, which can include irregular shapes and holes with missing data, zero-padding does not always give satisfactory results. This paper proposes the use of decay functions to handle edge effects when extracting information from geoscience images. As an application, this method has been used in a newly developed multifractal method (S-A) for separating geochemical anomalies from background patterns. A geochemical dataset chosen from a mineral district in Nova Scotia, canada was used to validate the method.

关键词： edge effect correction fractal modeling spatial information extraction zero-padding decay functions.

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Fractal and multifractal modeling of Hydrothermal mineral Deposit Spectrum: Application to Gold Deposits in Abitibi Area, ontario, canada

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journal of China university of Geosciences 2003年第3期14卷 199-206页

作者： Cheng Qiuming department of Earth and Atmospheric Science, department of geography,{{2., toronto, canada m3j1p3 Faculty of Earth Resources, China university of Geosciences, Wuhan 430074 department of Earth and Atmospheric Science Department of Geography York University Toronto Canada M3J1P3 Faculty of Earth Resources China University of Geosciences Wuhan 430074

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.

关键词： mineralization spectrum power-spectrum multifractal spectrum eigenvalue spectrum and GIS modeling

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B(0,N)-graded Lie superalgebras coordinatized by quantum tori Dedicated to professor Sheng GONG on the occasion of his 75th birthday

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Science China mathematics 2006年第11期 1740-1752页

作者： CHEN Hongjia, GAO Yun, & SHANG Shikui department of mathematics, university of Science and Technology of China, Hefei {2.00{2., China department of mathematics and Statistics, york university, toronto, ontario, canada m3j 1p3

We use a fermionic extension of the bosonic module to obtain a class of B(0, A)graded Lie superalgebras with nontrivial central extensions.

关键词： graded Lie superalgebras quantum tori bosons and fermions.

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CRITERION　OF　STOCHASTIC　LAYER　NEAR　A　pLANAR　HOmOCLINIC　ORBIT　OF　NONLINEAR　DYNAmICAL　SYSTEm

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journal of Hydrodynamics 1995年第2期7卷 35-50页

作者： Albert C. j. Luo(department of mechanical & Industrial Engineering university of manitoba. Winnipeg, manitoba, R3T {2.{2.{{2.) Univ of manitoba Winnipeg Canada

A new analytic method is developed for nonlinear dynamical system, to investigate the mathematical structure and physical characteristics of the stochastic layer near a homoclinic or heteroclinic orbit. This method is based on the subharmonic resonant condition and an energy increment along the separatrix of the system. The critical conditions for the disappearance of stochastic layer are presented, which are associated with all control parameters of the system including initial conditions, excitation frequencies excitatiom amplitudes ***, using this method, we analyze two simple nonlinear dynamical systems, namely,Duffing-Holmes's equation and a forced planar pendulum. As their stochastic layers begin to disappear, their critical amplitudes are also obtained for the given excitation frequency and other chosen parameters. By means of these conditions, we carry out numerical simulations for the two simple models. Their stochastic layer will be shown using poincare mapping section. Our theoretical results are subeequently shown to be in a good agreement with numerical simulations.

关键词： nonlinear dynamical system stochastic layer numerical simulation

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