地震记录的广义分维及其应用

根据分形理论,对不同信噪比地震记录的分维特征进行了分析,指出地震记录中噪声背景与信号部分具有不同的分维尺度,地震道时间序列的分维数值与计算时所用的测量尺度有关,因此,可利用广义分维的概念计算地震记录的分数维.地震记录广义分维大大提高了分形算法在计算机自动识别地震波震相时的抗噪声能力.最后用本文方法对实际地震记录进行了有效的初至波自动拾取.     

空隙介质水动力弥散尺度效应的分形特征及弥散度初步估计

通过时空隙介质中水动力弥散尺度效应近期研究成果的总结和分析，阐述了不同尺度下空隙介质的空间非均质的自相似性，提出了水动力弥散的尺度效应在统计意义上具有分形特征，按计算方法（解析模型与数值方法）与岩性特征（孔隙介质与非孔隙介质）及计算模型维数的不同，对世界范围内所收集到的百余个纵向弥散度数据求出了尺度效应的分维数并进行了分析与讨论，为地下水污染模型研究提供了一种参数的初步估计方法。     

Wavelet analysis of the hydrological time series of Dalai Lake, Inner Mongolia, China

An important new development in hydrological data analysis in the last decade is the application of wavelet analysis. Here, wavelet theory is used to study the complexity and multi-scale periodicity of the hydrological time series of the Dalai Lake Basin in Inner Mongolia. Two large rivers, the Kelulun and the Wurxun, are the main inflows to Dalai Lake, which is currently shrinking. The annual and monthly flows of the Kelulun River are shown to vary more than those of the Wurxun River, and the monthly flows of the two rivers vary much more than their annual flows. Db5 wavelets are shown to be more suitable for annual flow calculations, whereas Db4 wavelets are more suitable for monthly flow calculations. Multi-scale wavelet analysis of the annual and monthly flows of the Kelulun and Wurxun rivers shows that the variation of the two rivers is similar and has a 25-year cycle, 12 years of wet and 12 years of drought periods, and our results show that both rivers are expected to transition into a wet period beginning in 2012. Therefore, the Dalai Lake Basin, which has been in a drought period since 2000, is expected to gradually transit into a wet period from 2012 onward.     

Empirically derived relationships between fractal dimension and power law form frequency spectra

Fractal analysis and Fourier analysis are independent techniques for quantitatively describing the variability of natural figures. Both methods have been applied to a variety of natural phenomena. Previous analytical work has formulated relationships between the fractal dimension and power law form frequency spectrum.Mandelbrot (1985) has shown that difficulties arise when the ruler method for measuring dimensionality is applied to other than self-similar figures. Since an investigator presumably does not know in advance the dimensionality of a natural profile, it is essential to quantify the nature of the discrepancy for self-affine cases. In this study, a series of experiments are conducted in which discrete random series of specified spectral forms are analyzed using the fractal ruler method. The various parameters of the fractal measurement are related to the parameters of the spectral model. In this way, empirical relationships between the techniques can be derived for discrete, finite series which simulate the results of applying the fractal method to observational data.The results of the study indicate that there are considerable discrepancies between the results predicted by theory and those derived empirically. The fundamental power law form of length versus resolution pairs does not hold over the entire region of analysis. The predicted linear relationship between fractal dimension and exponent of the frequency spectrum does not hold, and the spectral signals can be extended beyond the limits of dimension inferred by theory. Root-mean-square variability is also shown to be linearly related to the fractal intercept term. An investigation of the effect of nonstationary sampling is conducted by generating signals composed of segments of differing spectral characteristics. Fractal analyses of these signals appear identical to those conducted on stationary series.The discrepancies between theoretical prediction and empirical results described in this study reflect the difficulties of applying analytically derived techniques to measurement data. Both Fourier and fractal techniques are formulated through rigorous mathematics, assuming various conditions for the underlying signal. When these techniques are applied to discrete, finite length, nonstationary series, certain statistical transformations must be applied to the data. Methods such as windowing, prewhitening, and anti-aliasing filters have been developed over many years for use with Fourier analysis. At present, no such statistical theory exists for use with fractal analysis. It is apparent from the results of this study that such a statistical foundation is required before the fractal ruler method can be routinely applied to observational data.     

矿床储量规模分布的分形模型及其分维的数理分析

矿床储量规模预测在矿产勘查和评价中占有十分重要的位置,而其预测的最主要手段是建立矿床储量规模分布的数学模型.根据矿床储量的统计自相似性,应用概率统计方法建立了矿床储量规模的分形模型.同时,通过模型及其分维值的数理分析,得出不同分维值的地学解释,讨论了分维的线性与非线性最小二乘回归估计法.     

GIS approach to scale issues of perimeter-based shape indices for drainage basins

Abstract

Shape indices have been in use for several decades to describe the characteristics and hydrological properties of drainage basins. Due to the fractal behaviour of the basin boundary, perimeter-based shape indices depend on the scale at which they are determined. Therefore, these indices cannot objectively compare drainage basins across a range of scales and basin sizes. This paper presents an objective GIS-based methodology for determining scale-dependent shape indices from gridded drainage basin representations. The scale effect is addressed by defining a representative scale at which the indices should be determined, based on a threshold symmetric difference between two grids representing the drainage basin at different resolutions.     

一种测量断裂构造信息维的方法及其应用

基于分形理论,提出了一种快速测量单区和多区断裂构造信息维的方法。按直线、正方形、Koch曲线及Sierpinski垫片4种图形的测量结果,信息维测量值与其理论值之间最大的相对误差绝对值仅为0.5%,表明采用该方法测量出的信息维具有较高的可靠性和准确度。在某火山岩型铀矿田开展了该方法的应用试验。该铀矿田内有超过92%的铀矿床均位于断裂信息维大于1.24的区域内,说明断裂构造信息维越大,越有利于火山岩型铀矿成矿,从而为建立新的铀矿预测标志提供了新的思路和方法。     

形变时序数据性态特征确定方法研究

提出变异函数、主分量分析及关联维的方法分析形变时序数据序列的性态特征,特别是针对沉降数据序列进行实例试算.结果表明,这三种方法用于形变数据序列的性态特征分析是可行的,可以用来确定沉降数据序列的变异性、混沌性及分形维特征.     

杆系有限元法求解复合土钉支护结构的位移

复合土钉支护位移计算尚未有成熟的分析方法。本文采用杆系有限单元法,结合支护土钉滞后的施工动态分析,来求解施工超前桩墙的复合土钉支护结构的水平位移。坑外侧主动土压力,由于受到密集土钉作用和坡角的影响,考虑折减计算。本分析方法简便,易于计算机编程。通过工程实例计算和分析,结果表明水平位移计算值与实测值较为接近。     

分形理论在贝尔凹陷基岩潜山裂缝预测中的应用

断裂与裂缝多为统一的应力场下破裂程度和相对位移量不同的破裂构造,都具有自相似性,满足分形理论。应用分形几何理论研究了贝尔凹陷布达特群潜山顶面断裂发育的平面分形特征和布达特群取心井段上裂缝的分形特征,并建立了二者之间的定量关系。基于断裂的分形特征尝试性地去预测有利的裂缝发育带,以期为裂缝的预测提供新的途径。研究结果表明,断裂信息维越高,裂缝信息维也越高,裂缝越发育。裂缝信息维大于1.4的区域是布达特群裂缝发育的有利区。