马尔柯夫场在影像纹理模拟中的应用

本文介绍了马尔柯夫随机场（简称ＭＲＦ）模拟影像纹理的原理和算法，用本文提出的算法，作了模拟分形纹理的许多实验：模拟纹理的自相似性试验；ＭＲＦ模型参数对影像纹理的控制作用等试验。试验结果表明算法正确，ＭＲＦ是模拟影像纹理的一个好模型。     

利用分维向量改进神经网络在遥感模式识别中的分类精度

本文介绍了基于ＢＰ神经网络的遥感模式识别方法的特点，同时引入分形维数的概念及其在图像中的计算和应用，并将分维作为反映各类别数据纹理特征的附加波段分量，加到网络的输入层，明显地提高了分类精度。     

Self-Affine Fractals and the Fractal Dimension of Fractured Rock Profiles

The measured profiles of laboratory fractured rocks should be self-affine fractal.The scaling properties of these profiles are described by two parameters-the fractal dimension D and the crossover length tc The D values of eight profiles are calculated by the ruler method and by the standard deviation method respectively.It is shown that if tc is far greater than the sampling step tc two methods yield the same results,although if it is far smaller than r,the D by the standard method will be about 1.20,while D by the ruler method will very close to 1.0,because two fractal dimensions,local and global,exist on two sides of tc In order to obtain the local fractal dimension which may be close to that of the standard deviation method,the ruler method must be modified.We propose a way to estimate the tc and to modify the ruler method.Finally,a profile having given D is generated in terms of the principle of non-integer order differential,through which the above two methods are verified and lead to the same res     

青海高原地震时空免疫性及分形特征

本文详细研究了一次地震发生后其继发地震的时空免疫性特征、研究结果表明，青海地震的免疫性特征是十分明显的，它对进一步认识地震发生的时空特征有着重要的意义。相邻两次地震的时间间隔，和空间距离ｄ的临界直线关系为ｄ∞τ（－１．０），其迁移速率ｖ的关系为ｖ∞τ（－２．０）。这也是齐夫（ｚｉｐｆ）法则所约定的分维值，十分类似于１／ｆ谱。我们形象的称ｄ∞τ（－１．０）分布是“随机音乐”；ｖ∞τ（－２．０）分布是“布朗音乐”。     

地震主压应力轴分布的分形特征研究

本文通过对全国许多地区大量的小震及中、强地震主压应力轴分布情况的详细研究，发现地震主压应力轴的分布具有分形结构特征，并满足幂函数关系式ｌｇＮ＝ａ＋ｂＪ，其特征值ｂ与分数维大致成反比，无标度区约为２°－８°。中强以上地震的前震序列的地震主压应力轴分布的特征值似乎明显比小震群活动的地震主压应力轴分布的特征值大。     

节理岩体的分维特征及其工程地质意义

本文用分形理论,对节理网络分布和粗糙度曲线进行分形分析。结果表明,节理的空间分布和粗糙度曲线具自相似性;分维是一个表征岩体强度、岩体损伤程度、岩体质量及节理粗糙程度的几何参数,并可用于评价岩体稳定性、断裂体系活动性及划分风化卸荷带等。     

Fractal analysis of tidal channels in the Bahía Blanca Estuary (Argentina)

The fractal dimension (D) was estimated for nine tidal channels depicted in thematic mapper (TM) Landsat-5 imagery to derive information about the degree of geomorphological control on a tidal channel network characteristic of the Bahía Blanca Estuary (Argentina). Two methods, box counting and contiguity, were used to estimate fractal dimensions for each tidal channel. All channels produced D values close to 1, meaning that they are self-affine fractal features. However, these fractal dimensions do not represent the meandering pattern complexity characteristic of the tidal channels analysed. Although both methods allowed for estimation of D, the contiguity method showed that three of the channels actually are not fractal but have sinusoidal characteristics, a condition that was not detected by the former method.     

Delineation of arsenic-contaminated zones in Bengal Delta, India: a geographic information system and fractal approach

Groundwater extracted from shallow aquifers in the Bengal Delta is contaminated with arsenic. The fluviodeltaic process that creates aquifers, ironically, extends its role to also contaminating them with arsenic. The arsenic distribution maps show a spatial association of arsenic-contaminated wells with palaeo/cut-off/abandoned channels. Weight-on-evidences analysis indicates that the zones of contamination occur around palaeo-channels within a corridor of 500–700 m that contains most of the contaminated wells. These corridors are interpreted to be the zone of channel shifting. Contaminated wells represent point fractal geometry that can be separated into isolated points and clusters. Clusters occur within the zone of channel shifting as obtained by weight-on-evidences analysis. Isolated points occur within floodplain or back swamp areas. Clusters and isolated point fractals are interpreted to reflect the process of arsenic release into groundwater. The migration of biomass within the permeable sandy domain of channel deposits is proposed to be the predominant process in generating clusters. The isolated points represent restricted biomass spreading in less permeable clay-silt dominated floodplains.     

分形几何在激电时间谱中的应用

本文首次把分形维技术应用到岩石激发极化时间谱资料的处理中,并建立了相应的分形分维弛豫模型,通过大量和系统的理论与实验研究,得出了一些有意义的结论和认识。     

分形统计模型的理论研究及其在地质学中的应用

本文提出了一般分形模型和一般分维数的概念,认为许多地质模型是一般分形模型的特例,指出幂函数分布和帕累托分布是分形统计模型的数学基础,论证了幂函数分布在高端截尾条件下具有尺度不变的分形性质,根据非线性回归模型参数估计的方法,提出了求分维数的新方法,该方法具有许多优点。通过在计算机上产生随机数对分形统计模型进行模拟研究,以及通过实例说明分形统计模型应用的方法及步骤,并解释了分维数的实际意义。