本文介绍了分形与分维的基本概念，并综述了地球物理学中分形研究的最新进展。
In the paper, the basic concepts of fractals and fractal dimensions are introduced, and the new advances in the research of fractals in geophysics are also reviewed.
通过对工作面顶板的分形研究，得到了该工作面的分维。
Based on the study of roof fractal, the fractal dimension of roof is obtained.
人们所熟知的常用以代替分形维数的各种度量将在分维谱意义下加以统一，最后讨论多重分形及其分维谱的应用。
The usual fractal dimensions familiar to all us will be united by the multifractal dimension spectrum. Finally, the applications of the multifractal and its dimension spectrum will be discussed.
该文简要介绍了混沌理论的四个主题：有界、极为有限的可预测性、分形与分维、普适性。
This paper gives a brief account of four themes of chaos theory, bound, fractal geometry fractal dimension, too limited predictability, universality.
根据土体具有的非线性特征，运用分形几何理论提出了7项定量表征土体微结构状态的分维指标。
According to the nonlinear features of soil, 7 fractal dimension parameters to identify structure state of soil are suggested with the help of fractal theory.
然后用结构函数和均方根两种方法对理论和实际的轮廓曲线进行了分形表征和分维计算。
And then, fractal characterizations and dimension calculations were conducted in two kinds of profile curves with the methods of the structure function and the mean square root.
应用分形理论计算的埕北30太古界潜山储集体花岗片麻岩和煌斑岩岩心构造裂缝的分维数分别为1。
Using calculation of fractal theory, the fractal dimensions of the core structure fracture in granite gneiss and lamprophyre in Chengbei 30 Archaean group buried hill reservoir are1.
额外短切纤维的加入，使分形范围减小，降低质量分维。
Mass fractal dimension and fractal range decrease with the adding of additional short fibers.
本文建立了土体孔隙分布的分形模型，导出用分维和进气值表示的水分特征曲线和渗透系数的理论表达式。
By using this model the soil-water characteristics and permeability coefficient of unsaturated soil are deduced and expressed in fractal dimension and air-entry value.
结果表明，两者都具有显著的分形特征，起绉纹理的分维数与绉织物的视觉风格密切相关。
The result shows that both of them are fractals. And the fractal dimension of crepe texture is well correlated with the visual effect of the fabric.
运用分形和分维理论，用半方差法和功率谱密度法分别计算土壤强度的分维，其值接近2。
The fractal dimensions of soil cone indices were estimated in semi-variograms and power, spectral densities, which were all very close to 2.
将分形用于自然纹理描述，指出了单一分形维数测度用于纹理分析的局限性，并提出了尺度分维的新概念。
The limitations of single fractal dimension for texture analysis are pointed out and a new concept of scale fractal dimension is proposed.
结合国内外海岸线分形研究进展，以江苏省海岸线为例，系统地探讨了不同比例尺地图上海岸线长度与分维的变化及其规律。
Taking the Jiangsu coastline as an example, the authors systematically explore the changes and regularities of coastline length and fractal dimension on the maps on different scales.
利用分形分维方法对黄河三角洲潮滩和潮沟的地貌特征进行了定量研究。
The morphologic characteristics of tidal flat and ti dal creek system in the Huanghe River Delta was studied by fractal geometry method.
文中解释了砂岩碎屑分维增大的原因，研究了碎屑分形分布的物理机制。
The physical mechanism of fragment distribution and the fractal model on the increasing of fractal dimension are studied in this paper.
通过演化曲线可以看出，分形维数与损伤变量随应力的递增均呈非线性增加，但分维的变化较平缓；
The evolution curve show known that fractal dimension and damage variable present nonlinear increase with the increment of stress, and the change of fractal dimension is relatively smooth.
探讨了日流量过程的分形特性，重点研究了分维估计方法。
The methods for estimating fractal dimensions of daily flow hydrograph in a river are mainly presented.
利用分形学方法，计算图像的分维数，然后比较其分形特征。
Using fractal method, the fractal dimensions of these images are calculated to compare their fractal characteristics.
利用分形和分维理论研究DNA的复制机理并计算BDNA共聚物中氢键的解链温度。
The copy principle of DNA is studied by using fractal and fractal dimension theory and hydrogen-bond melting temperature in BDNA copolymers calculated.
本文以分形作为工具，分维值作为度量参数，研究制图综合中地图目标的分形衰减现象。
This paper uses fractal geometry as a tool and fractal dimension as a measurement parameter to analyze the phenomena of fractal attenuation of cartographic object on cartography generalization.
用分形对3604S4工作面和回采巷道顶板进行了研究，得到了该工作面下沉速度的几种分维值。
Study was conducted on the roof of No. 3604S4 coal face and the actual mining roadway with fractals, and a few kinds of functional values of subsidence velocity of this face were obtained.
应用分形理论初步分析了分形块度、表面裂隙分维与爆破能量密度的关系；
The relations between the size of coal lump fractal, surface cranny fractal and density of blasting energy were roughly analyzed by means of the fractal geometry theory.
另一方面，传统的单一分维估值方法不能够充分地描述一个地图目标的分形特征，扩展分维分析成为现在分形理论研究的一个热点。
On the other hand, the traditional fractal analysis methods of a single fractal dimension has limitation on describing characters of the objects.
这对于混凝土无损检测提出了新的思路，对于分形分维在混凝土研究中的广泛应用具有积极作用。
This proposed a new idea on the concrete non-destructive inspection, and had a positive role on wide application of the concrete research with the fractal dimension.
分析了不同分维下分形海面双站散射截面的角分布情况。
The angular distribution of the bistatic scattering cross-section from fractal sea surface for different fractal dimension and different spatial frequency is analyzed.
研究结果表明，突出与非突出井田的断层分布均服从分形规律；井田中断层分布的分维值与瓦斯突出之间存在着正相关关系等重要结论。
The study results indicate that the fault distribution in both outburst and non outburst mine fields are all follow the fractal la.
针对复杂背景及目标的分形特性差异，提取图像四个方向的灰度梯度，选择最小梯度大于阈值的区域进行平滑滤波，最后对分维参数进行分段线性拉伸。
Aiming at characteristic differences of background and target, four-direction gradient is extracted out and areas with large gradient are smoothed by a linear threshold filter.
依据分形理论，研究了膨胀土裂隙结构的分形特征，分析了膨胀土裂隙网络分维和裂隙面分维的力学效应。
In this paper, the fractal characteristics of fissure structure in expansion soil are studied based on fractal theory.
本文扼要介绍了分形和分维的基本概念和最新进展；
The basic. concepts and the modern advances of fractals and fractal dimension are introduced briefly in this paper.
客观确定分形的“无标度区”是分维测算中的关键问题之一。
Determining Scaling Range is a key problem to calculate fractal dimension.
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