Ground-roll separation of seismic data based on morphological component analysis in twodimensional domain

Ground roll is an interference wave that severely degrades the signal-to-noise ratio of seismic data and affects its subsequent processing and interpretation.In this study,according to differences in morphological characteristics between ground roll and reflected waves,we use morphological component analysis based on two-dimensional dictionaries to separate ground roll and reflected waves.Because ground roll is characterized by lowfrequency,low-velocity,and dispersion,we select two-dimensional undecimated discrete wavelet transform as a sparse representation dictionary of ground roll.Because of a strong local correlation of the reflected wave,we select two-dimensional local discrete cosine transform as the sparse representation dictionary of reflected waves.A sparse representation model of seismic data is constructed based on a two-dimensional joint dictionary then a block coordinate relaxation algorithm is used to solve the model and decompose seismic record into reflected wave part and ground roll part.The good effects for the synthetic seismic data and application of real seismic data indicate that when using the model,strong-energy ground roll is considerably suppressed and the waveform of the reflected wave is effectively protected.

Cross-scale characteristics of backfill material using NMR and fractal theory

This paper analyzed the pore structure, quantified the pore fractal dimension, calculated the grading index(GI) of mixed aggregate, and studied the relationship among GI, pore structure, and strength to describe the cross-scale characteristics of backfill, which is made from stone powder and cemented tailing. A series of experiments were conducted on stone powder cement tailings backfill(SPCTB). The GI formulas for mixed aggregates, containing stone powder and tailings, were derived based on the Füller theory. The nuclear magnetic resonance(NMR) fractal dimensions of backfills were derived using fractal geometry principles. Compared to the mesopore and macropore fractal dimensions, the correlation between micropore fractal dimension and macro-properties in terms of NMR porosity, pore structure complexity, uniaxial compression strength(UCS), and GI is the most significant. Macropore fractal dimension is generally correlated with UCS and GI and the other properties such as the shape of mixed aggregates also have an impact on fractal dimension. However, mesopore fractal dimension has no obvious relationship with macro-properties. Finally, the relationship between GI and UCS was studied, which contributed to improving backfill’s strength and optimizing gradation.

3-D fracture network dynamic simulation based on error analysis in rock mass of dam foundation

Accurate 3-D fracture network model for rock mass in dam foundation is of vital importance for stability,grouting and seepage analysis of dam foundation.With the aim of reducing deviation between fracture network model and measured data,a 3-D fracture network dynamic modeling method based on error analysis was proposed.Firstly,errors of four fracture volume density estimation methods(proposed by ODA,KULATILAKE,MAULDON,and SONG)and that of four fracture size estimation methods(proposed by EINSTEIN,SONG and TONON)were respectively compared,and the optimal methods were determined.Additionally,error index representing the deviation between fracture network model and measured data was established with integrated use of fractal dimension and relative absolute error(RAE).On this basis,the downhill simplex method was used to build the dynamic modeling method,which takes the minimum of error index as objective function and dynamically adjusts the fracture density and size parameters to correct the error index.Finally,the 3-D fracture network model could be obtained which meets the requirements.The proposed method was applied for 3-D fractures simulation in Miao Wei hydropower project in China for feasibility verification and the error index reduced from 2.618 to 0.337.

上游法筑坝尾矿沉积规律及固结情况预测

以马家田尾矿库为工程背景,通过现场钻探取样进行室内颗分实验,结合尾砂结构特征、“分形-分维”理论进行综合分析,研究尾矿颗粒在整体沉积过程中的沉积规律,并以研究的沉积规律为理论依据,将尾矿库划分为6个固结区,对尾矿库固结程度进行计算与预测。研究结果表明:尾矿库坝前多沉积尾粉砂,坝尾多沉积尾粉质黏土,呈“坝前粗、坝中粗细交替、坝尾细”的沉积特征。尾矿颗粒在垂向上呈“下细上粗”、水平上呈“由粗到细”的沉积规律。尾矿粗细颗粒含量整体分布均匀,其中,粗粒尾矿的中值粒径d_(50)变化有规律,细粒尾矿的中值粒径d_(50)变化规律不明显,尾粉土分选差异性较大。尾矿库的主固结已完成,次固结相对变形较小,且最小固结度为0.27。

Pest Detection Method Using Multi-Fractal Analysis

A novel method for pest detection is proposed based on the theory of multi-fractal spectrum to extract pests on plant leaves.Both local and global information of the image regularity were obtained by multi-fractal analysis.By applying fractal dimension,the spots on leaf images can be extracted without loosing or introducing any information.The different parts of images are re-analysis by morphology operations to determine the candidate regions of pests.The performance of multi-fractal analysis of whitefly detection is investigated through greenhouse experiments.The experimental results show that the proposed method is robust to noise from light and is not sensitive to the complex environment.

A Class of Fractal Functions and Their Dimension Estimates

本文作者首先借助于b进制分数及无穷级数构造了一类分形函数，然后研究了这些函数图象的分形维数及其Hoelder性质，得到了一些维数结果。

Math Imitation of the Texture of Particle Cluster Emitted from Diesel Engine

Aim The particle texture from diesel engine was imitated by use of computer. Methods The theory of fractal geometry and the diffusion limited aggregation model were used to simulate the micron texture. Results The fractal dimensions of granule distribution and corpuscle superficial area are quite conformed with those of measurement. Conclusion The texture parameters of engine particle cluster can be obtained precisely by use of fractal theory.

Fractal features of size distribution of Chinese intercity bus hubs

Size distribution characteristics of intercity bus hubs in China from 1997 to 2（104 were analyzed regarding highway passenger volume as a size index of intercity bus hubs. Yearly fractal dimensions of intercity bus hub sizes were exactly calculated by a novel model. Fractal dimensions of the 200 biggest intercity bus hubs from 2000 to 2004 were 1. 486 2 to 1. 511 8, and that is consistent with fractal dimensions of Chinese urban system sizes. It showed that the size distribution of intercity bus hubs had fractal structure. Fractal dimensions from 1997 to 2004 indicated that intercity bus hub size distribution grew from bi-fractal to single fractal. It is concluded that the intercity bus hub system is in evolutionary progress, and the Central Government should support large intercity bus hubs more to optimize system structure.

THEORETICAL VERIFICATION OF THE SCALING RELATION TO DETERMINE SURFACE FRACTAL DIMENSION OF POROUS MEDIA

A simplified procedure is developed to acquire the surface fractal dimension of porous media utilizing the PSD information from mercury porosimetry or other analyses.The self similarity of the inner surface of Sierpinski sponge is analyzed,the result of which demonstrates that the inner surface of Sierpinski sponge is not scale invariant over the whole range of scale transformations.By applying the simplified procedure to analyze and treat the PSD information of Sierpinski sponge over the scale invariant range,it is found that the surface fractal dimension calculated by the scaling relation is in very good agreement with its theoretical value,which virtually provides a theoretical affirmation of the method.

Characterizations of PSD Fractal of Porous Medium

A volume-based method for measuring particle-size distribution (PSD) fractal dimensions of porous mediums was developed by employing laser size-analyzing technology. Compared with conventional approaches of using hydrometer or screen to determine PSD, this method can avoid calculation errors and measure smaller size-scale porous medium. In this paper the experimental porous mediums were brown soil, kaolin and sand soil. A micro-order of magnitude (10 -5 m) in particle-size interval could be shown in PSD results of brown soil and kaolin. The experiments indicated that brown soil had a nearly mono-fractal PSD character, while kaolin and sand soil showed multi-fractal PSD characters. By the adsorption isotherm experiments, the PSD fractal dimensions of the sand soil were also found to keep a linearly increasing relation with the linear adsorptive parameters of the soils in different intervals to adsorb benzene from aqueous solution.

Implication of Surface Fractal Analysis to Evaluate the Relative Sensitivity of Topography to Active Tectonics,Zagros Mountains, Iran

Fractal geometry is increasingly becoming a useful tool for modeling and quantifying the complex patterns of natural phenomena. The Earth's topography is one of these phenomena that have fractal characteristics. This paper investigates the relative sensitivity of topography to active tectonics using ASTER Global Digital Elevation Model. The covering divider method was used for direct extraction of surface fractal dimension(D surf) to estimate the roughness-surface of topography with aid of geographic information system(GIS)techniques. This evaluation let us highlight the role of the geomorphic and tectonic processes on the spatial variability of fractal properties of natural landforms.Geomorphic zones can be delineated using fractal dimension mapping in which variability of surface fractal dimension reflects the roughness of the landform surface and is a measure of topography texture. Obtained results showed this method can be a quick and easy way to assess the distribution of land surface deformation in different tectonic settings. The loose alluvial deposits and irregularities derived by tectonic activity have high fractal dimensions whereas the competent formations and higher wavelength folded surfaces have lower fractal dimensions.According to the obtained results, the Kazerun Fault Zone has a crucial role in the separation of the Zagros Mountain Ranges into the different lithological,geomorphological and structural zones.

An image retrieval system based on fractal dimension

This paper presents a new kind of image retrieval system which obtains the feature vectors of images by estimating their fractal dimension; and at the same time establishes a tree structure image database. After preprocessing and feature extracting, a given image is matched with the standard images in the image database using a hierarchical method of image indexing.

Texture image classification using multi fractal dimension

This paper presents a supervised classification method of sonar image, which takes advantages of both multi-fractal theory and wavelet analysis. In the process of feature extraction, image transformation and wavelet decomposition are combined and a feature set based on multi-fractal dimension is obtained. In the part of classifier construction, the Learning Vector Quantization (LVQ) network is adopted as a classifier. Experiments of sonar image classification were carried out with satisfactory results, which verify the effectiveness of this method.

RESEARCH ON SOME THEORETICAL PROBLEMS OF MAP DATA HANDLING USING FRACTAL APPROACH

Some theoretical problems of fractal geographical map data handling are dis- cussed and some new methods about fractal dimension introducing, developing, comparing and estimating are proposed in this paper.

Effect of Fiber Properties on Nonwovens' Pore Structures with Fractal Geometry Analysis

Nonwovens＇ pore structures are very important to their mechanical and physical properties. And the pore structures are influenced by the fiber properties and fibers arrangement in web. In this paper, the fractal geometry, in combination with computer image anaysis, is used to express the irregularity of pore size distribution in nonwovens, and the effect of fiber properties on fractal dimension of pore size distribution is discussed by using simulated images which are composed of nonlinear staple fibers. The results show that the fiber properties, such as crimp, diameter, angular distribution, and especially the number of fibers prominently influence the pore structure.

Fractal character of lenticles and its influence on sediment state in tailings dam

The distribution of tailings lenticles reflects the sediment state of tailing dam, and has a great influence on the stability of the dam. In order to disclose the distribution law of tailings lenticles in theory, 12 geological cross-sections, including 7 cross-sections of tailings dam constructed by the upstream method and 5 cross-sections by the middle line method, were analyzed with box dimension method. The results show that the distribution of tailings lenticles has better fractal character with box dimension from 1.290 7 to 1.513 6. The box dimension of the tailings dam constructed by upstream method is nearly 1.50 and that by middle line method is 1.30. Thereby the values of lenticles dimension have obvious relation to the method of constructing dam, and reflect the sediment state of tailings dam with the rule that smaller value means better state.

Fractal Dimension of Graph of Weierstrass Function and Its Derivative of the Fractional Order

In this paper,we obtain the fractal dimension of the graph of the Weierstrass function, its derivative of the fractional order and the relation between the dimension and the order of the fractional derivative.

Fractal Characteristics of Population Canopy Structure of the Mangrove,Bruguiera gymnorrhiza (L.) Lamk

The fractal characteristics of the canopy structure of B. gymnorrhiza population are investigated by fractal dimension analysis in the National Shankou Mangrove Nature Reserve. The 3-year-old branches have box dimensions between 1.22 and 1.55, showing the complexity degree of branching structure and the ability of occupying and utilizing ecological space. It may be considered that fractal dimension provides a useful index for the study of light utilization efficiencies and growth processes of B. gymnorrhiza. Calculated by using the two-surface method, the fractal dimensions for the crown pattern of individuals with ages of 20 to 50 years range from 2.21 to 2.54, indicating that the filling degree of foliage to a tree crown is relatively low and B. gymnorrhiza has the property of a sun plant. Along with the increase of ages of individuals, the filling degree of foliage to a tree crown changes from high to low, and so does the fractal dimension. The box dimensions obtained from the grayscale curves of population canopy are between 1.47 and 1.61. The greater the box dimension, the more loosely organized the canopy spatial structure, and the more the light spots. The canopy structural information and complexity of a population can be effectively captured by box dimensions obtained from canopy grayscale curves.

A numerical simulation of seepage structure surface and its feasibility

According to Cubic law and incompressible fluid law of mass conservation, the seepage character of the fracture surface was simulated with the simulation method of fractal theory and random Brown function. Furthermore, the permeability coefficient of the single fracture was obtained. In order to test the stability of the method, 500 simulations were conducted on each different fractal dimension. The simulated permeability coefficient was analyzed in probability density distribution and probability cumulative distribution statistics. Statistics showed that the discrete degree of the permeability coefficient increases with the increase of the fractal dimension. And the calculation result has better stability when the fractal dimension value is relatively small. According to the Bayes theory, the characteristic index of the permeability coefficient on fractal dimension P（Dfi｜ Ri） is established. The index, P（Dfi｜ Ri）, shows that when the simulated permeability coefficient is relatively large, it can clearly represent the fractal dimension of the structure surface, the probability is 82%. The calculated results of the characteristic index verify the feasibility of the method.

Analysis of microscopic pore structures of rocks before and after water absorption

Hydrophilic characteristics of rocks are affected by their microscopic pore structures,which clearly change after water absorption.Water absorption tests and scanning electron microscopic（SEM） experiments on rock samples,located at a site in Tibet,China,were carried out Changes of rock pore structures before and after water absorption were studied with the distribution of pore sizes and fractal characteristics of pores.The results show that surface porosities,fractal dimensions of pores and the complexity of pore structures increased because the number of new small pores produced increased or the original macropore flow channels were expanded after rocks absorbed water.There were points of inflection on their water absorption curves.After water absorption of other rocks,surface porosities and fractal dimensions of pores and complexity of pore structures decreased as the original pore flow channels became filled.Water absorption curves did not change.Surface porosity and the pore fractal dimensions of rocks have good linear relationships before and after water absorption.