地震前兆观测资料的分形处理方法

本文从自仿射分形的角度探讨地震兆汾观测资料的分形处理方法。在对自仿射分形的分维量测方法进行对比分析的基础上，给出了处理地震前兆观测资料较为适用的分形方法和满足计算需要的样本点数，从对部分水氡和地电阻率资料进行了处理分析中，得到了有益的启示：地震前兆时序观测资料可用分形方法处理分析，分维值可反映观测资料的结构变化特征，其作为一个无量纲量为综合对比分析各类前兆现象，探讨地震前兆场的复杂性特征提供了有效     

Hausdorff分数维识别地震道初至走时

地震波初至走时的识别在地震勘探、人工地震层析成像以及全球地震层析成像方法研究中起重要作用．初至走时拾取的精度在很大的程度上影响地震层析成像及演的精度．本研究以提高地震波初至走时拾取的精度及定量化程度为目标,利用计算地震道时间序列分数维的方法,实现了地震波初至走时的自动拾取．本文以分形理论为基础,进行了地震道时间序列Hausdorff分数维的计算．计算结果表明地震道时间序列的分数维在初至到达前后具有不同的数值,其变化点能够定量指示出初至走时的位置．本文还给出了利用该方法对实测数据进行初至走时拾取的实例．     

考虑非饱和特性的黄土湿陷性与微观结构分析

利用扫描电子显微镜测试技术对3个场地16个土样的微观结构进行观测,并使用图像处理软件对微观图像进行处理、对土样孔隙的几何特征参数和分维数进行了提取,土样孔隙分布分维数为1.816~1.936。利用分形几何学原理建立非饱和土的孔隙分布函数,对天然湿度下黄土中水分分布进行分析,运用回归分析的方法对孔隙的分维数、非饱和孔隙孔隙率和湿陷性的关系进行了分析。结果表明：孔隙分维数越大,孔隙结构越复杂;天然湿度下处于非饱和状态的黄土孔隙孔径均大于40μm,黄土的湿陷系数随着孔隙分维数、非饱和孔隙孔隙率的增大而增大,非饱和孔隙是造成黄土湿陷的主要原因。     

模糊空间分维在地震活动时空演化研究中的应用

本文把模糊分维方法应用于地震活动时空演化研究,当中.给出了强震和中强震活动模糊空间分维的确定方法,并通过计算不同小区的模糊空间分维随时间的变化曲线来研究地震活动的时空演化特征.以华北及西南地区地震活动性时空演化图象为例进行了具体分析研究.所得结果表明,大震前地震活动的模糊空间分维D_0~(2)要出现下降异常,并且大地震发生在D_0~(2)减小的地区(西南)或先减小而后达到高值(华北)的地区.     

Piecewise prediction model for watershed‐scale erosion and sediment yield of individual rainfall events on the Loess Plateau,China

Establishing a universal watershed‐scale erosion and sediment yield prediction model represents a frontier field in erosion and soil/water conservation. The research presented here was conducted on the Chabagou watershed, which is located in the first sub‐region of the hill‐gully area of the Loess Plateau, China. A back‐propagation artificial neural model for watershed‐scale erosion and sediment yield was established, with the accuracy of the model, then compared with that of multiple linear regression. The sensitivity degree of various factors to erosion and sediment yield was quantitatively analysed using the default factor test. On the basis of the sensitive factors and the fractal information dimension, the piecewise prediction model for erosion and sediment yield of individual rainfall events was established and further verified. The results revealed the back‐propagation artificial neural network model to perform better than the multiple linear regression model in terms of predicting the erosion modulus, with the former able to effectively characterize dynamic changes in sediment yield under comprehensive factor conditions. The sensitivity of runoff erosion power and runoff depth to the erosion and sediment yield associated with individual rainfall events was found to be related to the complexity of surface topography. The characteristics of such a hydrological response are thus closely related to topography. When the fractal information dimension is greater than the topographic threshold, the accuracy of prediction using runoff erosion power is higher than that of using runoff depth. In contrast, when the fractal information dimension is smaller than the topographic threshold, the accuracy of prediction using runoff depth is higher than that of using runoff erosion power. The developed piecewise prediction model for watershed‐scale erosion and sediment yield of individual rainfall events, which introduces runoff erosion power and runoff depth using the fractal information dimension as a boundary, can be considered feasible and reliable and has a high prediction accuracy. Copyright © 2013 John Wiley & Sons, Ltd.     

饱和砂土地震液化判别的分形插值模型

借鉴分形基本理论,提出了基于分形插值模型的饱和砂土地震液化判别方法.该方法首先选取影响饱和砂土地震液化判别的7个主要因素,根据分类标准,采用在每级标准中随机内插的方法,得到40个标准样本,用于构建饱和砂土地震液化判别的分形插值模型;其次根据最大似然分类原则确定每个饱和砂土地震液化判别指标的评价分维数;然后利用加权求和法计算样本的综合评价值,并根据样本综合评价值与经验等级之间的关系建立分形插值评价模型;最后,进行了实例分析结果表明:该模型的评价结果合理、客观,计算得到的每个样本具体得分值,即使对属于同一级的样本也可以给出其地震液化程度的顺序,为饱和砂土地震液化评价工作提供了一种新的研究方法与思路.     

Fractal generation of surface area of porous media

Many natural porous geological rock formations, as well as engineered porous structures, have fractal properties, i.e., they are self-similar over several length scales. While there have been many experimental and theoretical studies on how to quantify a fractal porous medium and on how to determine its fractal dimension, the numerical generation of a fractal pore structure with predefined statistical and scaling properties is somewhat scarcer. In the present paper a new numerical method for generating a three-dimensional porous medium with any desired probability density function (PDF) and autocorrelation function (ACF) is presented. The well-known Turning Bands Method (TBM) is modified to generate three-dimensional synthetic isotropic and anisotropic porous media with a Gaussian PDF and exponential-decay ACF. Porous media with other PDF's and ACF's are constructed with a nonlinear, iterative PDF and ACF transformation, whereby the arbitrary PDF is converted to an equivalent Gaussian PDF which is then simulated with the classical TBM. Employing a new method for the estimation of the surface area for a given porosity, the fractal dimensions of the surface area of the synthetic porous media generated in this way are then measured by classical fractal perimeter/area relationships. Different 3D porous media are simulated by varying the porosity and the correlation structure of the random field. The performance of the simulations is evaluated by checking the ensemble statistics, the mean, variance and ACF of the simulated random field. For a porous medium with Gaussian PDF, an average fractal dimension of approximately 2.76 is obtained which is in the range of values of actually measured fractal dimensions of molecular surfaces. For a porous medium with a non-Gaussian quadratic PDF the calculated fractal dimension appears to be consistently higher and averages 2.82. The results also show that the fractal dimension is neither strongly dependent of the porosity nor of the degree of anisotropy assumed.     

Fractal generation of surface area of porous media

Many natural porous geological rock formations, as well as engineered porous structures, have fractal properties, i.e., they are self-similar over several length scales. While there have been many experimental and theoretical studies on how to quantify a fractal porous medium and on how to determine its fractal dimension, the numerical generation of a fractal pore structure with predefined statistical and scaling properties is somewhat scarcer. In the present paper a new numerical method for generating a three-dimensional porous medium with any desired probability density function (PDF) and autocorrelation function (ACF) is presented. The well-known Turning Bands Method (TBM) is modified to generate three-dimensional synthetic isotropic and anisotropic porous media with a Gaussian PDF and exponential-decay ACF. Porous media with other PDF's and ACF's are constructed with a nonlinear, iterative PDF and ACF transformation, whereby the arbitrary PDF is converted to an equivalent Gaussian PDF which is then simulated with the classical TBM. Employing a new method for the estimation of the surface area for a given porosity, the fractal dimensions of the surface area of the synthetic porous media generated in this way are then measured by classical fractal perimeter/area relationships. Different 3D porous media are simulated by varying the porosity and the correlation structure of the random field. The performance of the simulations is evaluated by checking the ensemble statistics, the mean, variance and ACF of the simulated random field. For a porous medium with Gaussian PDF, an average fractal dimension of approximately 2.76 is obtained which is in the range of values of actually measured fractal dimensions of molecular surfaces. For a porous medium with a non-Gaussian quadratic PDF the calculated fractal dimension appears to be consistently higher and averages 2.82. The results also show that the fractal dimension is neither strongly dependent of the porosity nor of the degree of anisotropy assumed.     

储层微观非均质性定量表征的分形模型

储层非均质性是影响油气田勘探和开发的重要因素.储层岩石孔隙具有分形特征,分形维数可以定量地表征储层的微观非均质性.本文简述了孔隙分布概率密度函数、分形判据等分形理论基础,系统分析了利用压汞测试法,毛细管力曲线法和计盒法等计算分形维数的方法,以及分形维数解析研究的进展,并对进一步研究做了展望.     

测井数据分维计算及其应用条件研究

分形几何已成功地应用于储层表征,分维是储层一征和随机建模的控制参数,为了准确表征储层,必须精确地估计分维值。本文介绍了利用测井数据计算储层分维值的三种方法：变尺度分析法（Ｒ／Ｓ分析）,变异函数分析法、功率谱分析法,研究发现分维计算中对数据的分级处理实际上就是对数据进行灰色累加生成。研究表明影响分维估计精度的主要因素有四种：数据点数、数据概率分布、数据平稳性,无标度区,研究认为,现有的３种方法不能用     

地震活动前兆的三种广义分形维

地震研究及其预报是多学科的交叉,而非线性科学即分形学和混浊理论给人以新启示。本文叙述了地震的广义能量分维,广义时间分维和广义空间分维,探讨了三种广义分维在地震的前兆和余震中的变化规律,进而指出三种广义分维由主震前的低层异常变为震后再度回升现象,作者对第５个地震活跃期的特点提出了一些看法。     

Influence of pore size and geometry on peat unsaturated hydraulic conductivity computed from 3D computed tomography image analysis

In organic soils, hydraulic conductivity is related to the degree of decomposition and soil compression, which reduce the effective pore diameter and consequently restrict water flow. This study investigates how the size distribution and geometry of air‐filled pores control the unsaturated hydraulic conductivity of peat soils using high‐resolution (45 µm) three‐dimensional (3D) X‐ray computed tomography (CT) and digital image processing of four peat sub‐samples from varying depths under a constant soil water pressure head. Pore structure and configuration in peat were found to be irregular, with volume and cross‐sectional area showing fractal behaviour that suggests pores having smaller values of the fractal dimension in deeper, more decomposed peat, have higher tortuosity and lower connectivity, which influences hydraulic conductivity. The image analysis showed that the large reduction of unsaturated hydraulic conductivity with depth is essentially controlled by air‐filled pore hydraulic radius, tortuosity, air‐filled pore density and the fractal dimension due to degree of decomposition and compression of the organic matter. The comparisons between unsaturated hydraulic conductivity computed from the air‐filled pore size and geometric distribution showed satisfactory agreement with direct measurements using the permeameter method. This understanding is important in characterizing peat properties and its heterogeneity for monitoring the progress of complex flow processes at the field scale in peatlands. Copyright © 2010 John Wiley & Sons, Ltd.     

Optimal Design of a Gravity Survey Network and its Application to Delineate the Jabera-Damoh Structure in the Vindhyan Basin,Central India

Fractal dimension analysis was carried out for optimal designing of 2-D gravity survey network and to determine an optimum range of gridding interval to generate least aliased Bouguer anomaly maps. As a test case, this method has been successfully applied to the Jabera-Damoh region of the Vindhyan Basin, which is considered as a potential hydrocarbon bearing area. In particular, we aim to delineate accurately the lateral extent of a possible hydrocarbon bearing structure. To achieve this aim, fractal dimension of survey network was computed using 2-D distributions of observation points in the planning phase of the survey so that the optimum station spacing for gravity survey can be obtained. A range of optimum gridding interval for the gravity data set was suggested using the box-counting method of fractal dimension determination. Bouguer anomaly maps of the region are prepared utilizing the optimum gridding interval. For the first time, these anomaly maps clearly outline the gravity evidence of an anomalous rifted structure, which is bounded by parallel faults on either side. This structure is interpreted as a favorable basin for the occurrence of hydrocarbons. Another finding of this study has been the delineation of an apparently small ridge-like structure running east-west, dividing this basin in two parts. A subsurface geological model along a profile across the Jabera structure has also been presented.     

Impact of fractal characteristics on evaporation and infiltration in unsaturated heterogeneous soils

ABSTRACT

In this study, an approach is developed to investigate the impact of fractal characteristics of unsaturated soil between the water table and land surface on the steady-state evaporation and infiltration across a heterogeneous landscape. The soil domain is conceptualized as a collection of stream tubes of soils and the particle diameters in various stream tubes follow a fractal distribution. The saturated hydraulic conductivity of each stream tube is related to the representative particle diameter in the tube. The effective specific discharge is then integrated from the specific discharge for each stream tube and the fractal distribution. The effective evaporation and infiltration in unsaturated soils increase with the fractal dimension. The ratio of minimum over maximum diameters does not significantly affect the specific discharge in the fractal soil. The specific discharge in unsaturated fractal soils calculated by using the simple average particle diameter mostly over-predicts the actual effective specific discharge.     

RESEARCH ON THE RELATIONSHIP BETWEEN FRACTAL FACTORS AND TECTONIC ACTIVITY——A CASE STUDY OF SOUTHWESTERN YUNNAN BLOCK

Geomorphology could record long-term accumulation of tectonic movement and quantify it by relevant parameters.But because the influences of other factors such as climate and lithology,how to use the relevant parameters to reveal the relationship between geomorphology and tectonics is a research hot spot.In this paper,we utilize the variogram method and the cellular fractal model to estimate parameters such as the fractal dimension (D) and ordinate intercept (γ) from the SRTM3 DEM using a moving window operation.We compare the distribution characteristics of the parameters in different climate and lithology.The results indicate that the correlation between the parameters and lithology or climate is very poor.The fractal dimension (D) reveals a very good correlation with tectonics,which is low in tectonically inactive areas and high in active areas.It implies that fractal dimension (D) may be a new method for research of regional tectonic movement.     

Numerical analyses of pile performance in laterally spreading frozen ground crust overlying liquefiable soils

Lateral spread of frozen ground crust over liquefied soil has caused extensive bridge foundation damage in the past winter earthquakes. A shake table experiment was conducted to investigate the performance of a model pile in this scenario and revealed unique pile failure mechanisms. The modelling results provided valuable data for validating numerical models. This paper presents analyses and results of this experiment using two numerical modeling approaches: solid-fluid coupled finite element (FE) modeling and the beam-on-nonlinear-Winkler-foundation (BNWF) method. A FE model was constructed based on the experiment configuration and subjected to earthquake loading. Soil and pile response results were presented and compared with experimental results to validate this model. The BNWF method was used to predict the pile response and failure mechanism. A p-y curve was presented for modelling the frozen ground crust with the free-field displacement from the experiment as loading. Pile responses were presented and compared with those of the experiment and FE model. It was concluded that the coupled FE model was effective in predicting formation of three plastic hinges at ground surface, ground crust-liquefiable soil interface and within the medium dense sand layer, while the BNWF method was only able to predict the latter two.     

Unsaturated flows in soils with self-similar hydraulic conductivity distribution

In this article, we are concerned with the statistics of steady unsaturated flow in soils with a fractal hydraulic conductivity distribution. It is assumed that the spatial distribution of log hydraulic conductivity can be described as an isotropic stochastic fractal process. The impact of the fractal dimension of this process, the soil pore-size distribution parameter, and the characteristic length scale on the variances of tension head and the effective conductivity is investigated. Results are obtained for one-dimensional and three-dimensional flows. Our results indicate that the tension head variance is scale-dependent for fractal distribution of hydraulic conductivity. Both tension head variance and effective hydraulic conductivity depend strongly on the fractal dimension. The soil pore-size distribution parameter is important in reducing the variability of the unsaturated hydraulic conductivity and of the fluxes.     

新疆天山地区地貌分形与多重分形特征研究

利用投影覆盖法和投影覆盖概率对新疆天山地区不同构造地貌类型进行了分形与多重分形特征的研究。结果表明：在所研究的标度范围内，不同地貌区均表现出明显的多度域分形，分维值总体上呈现出高山区＞中低山区＞盆地区特点，多重分形谱Dq的形态和值域范围也表现出不同特征。研究认为，地貌表面的分维值与地貌形成的内外力地质作用方式和强度密切相关，并提出5-6km的尺度可作为地貌学研究中宏观与微观作用的分界点。     

Quantitative analysis of soil pores under natural vegetation successions on the Loess Plateau

Soil pore is a key attribute of the soil structure that affects soil reservoir under natural vegetation recovery on the Loess Plateau.This study is to quantitatively analyze soil pore parameters,measured with Computed Tomography(CT) at 15-57 mm depths under five different vegetation succession stages using a concept of substituting space for time in the Ziwuling Forest Region of the Loess Plateau.The results showed that the soil pore parameters,such as pore number,porosity,circularity,and fractal dimension,...     

Clustering of mining-induced seismic events in equivalent dimension spaces

High energy release during seismic events induced by mining operation is one of the major dangers perturbing production in underground mines. In this work, temporal changes of seismic event parameters for one of the Rudna Mine (Poland) panels are investigated. The study aim was to find whether the temporal clustering of smaller events in different parameters can be observed before and after the high energy events (M_l?≥?3) in the mining panel. The method chosen for analysis was the study of temporal variation of fractal dimension of the seismic events parameter sets composed from: the interevent epicentral distance (dr), logarithm of seismic energy (lE), and interevent energy coefficient (dlE), which is the absolute difference between logarithms of energy of two consecutive events. Temporal variations study was performed in equivalent dimension (ED) space. The transformation of the seismic source parameters into ED space allowed to estimate and compare the temporal changes of the fractal dimension of different parameter spaces using the same method—correlation fractal dimension, and then easily compare the obtained temporal changes of fractal dimension of different parameter sets. The effect of grouping is expressed by decrease of fractal dimension, which is connected with the similarity of events parameter values. The temporal changes of the fractal dimension of seismicity before the strong induced events would indicate some initiation phase of the process leading to the high energy release. In the case of the studied Rudna Mine panel, the temporal behavior of the fractal dimension values in different parameter spaces before seismic events showed significant changes before three out of four events with CLVD dominant source mechanisms.