Fractal analysis of the Oyo River, cave systems, and topography of the Gunungsewu karst area, central Java, Indonesia

Gunungsewu, the southernmost subzone of the Southern Mountains, central Java, is a classic karst terrain, bounded by the Oyo River on the north and the Indian Ocean on the south. In this study, the Oyo River, the main drainage in the area, is divided into 14 segments, and the fractal dimension of each segment is determined by the box-counting method. The 14 segments show various values of fractal dimensions, which are controlled by lithology and geologic structures of the area that is being dissected by the river. Easily eroded lithologies have larger fractal dimensions, and the value changes abruptly when the river crosses faults. Fractal dimensions of six underground rivers in the Bribin, Sodong, Semuluh, Jomblang, Soga, and Sumurup caves, and the surface topography above the caves were also determined. The caves have fractal dimensions that range from 1.043 ±0.01 to 1.08±0.01; the surface topography has fractal dimensions that range from 1.49±0.01 to 1.732±0.01. The fractal dimension of an underground river is proportional to the fractal dimension of the surface topography over the passage. Larger fractal dimensions of underground rivers are associated with smaller flow rates of the rivers. Received, June 1998Revised, March 1999, August 1999, February 2000Accepted, February 2000     

从时间序列中提取维数信息

作者介绍了分形和分维的概念、性质和意义，重点讨论了从一维时间序列中提取维数信息的方法，并给出了一些在天气和气候中的应用。     

基于引力模型的城市空间互相关和功率谱分析——引力模型的理论证明、函数推广及应用实例

空间相互作用是先于城市体系而存在的重要概念 ,引力模型是描述空间相互作用的基本函数之一 ,但引力模型的理论基础不明确而且实际应用有局限。本文首先从城市地理系统的广义分形假设出发 ,推导出引力模型的幂函数形式 ,使其从一个经验模型上升为理论模型 ;进而引入时变函数和时滞参数将引力模型推广为更为一般和更加实用的形式 ,为发展城市引力过程的空间互相关分析和功率谱分析方法奠定了理论基础。借助 194 9～ 1998年 5 0年的人口演化数据 ,以北京 -天津的空间相互作用为实例 ,对基于城市引力关系的空间作用进行了相关分析和波谱分析 ,从而提供了城市网络空间相互作用广义引力分析的典型范例。     

城市形态的分维估算与分形判定

城市形态的分形是城市发育到一定阶段涌现出的有序格局和复杂结构,其基本特征是空间分布的无尺度性质。当研究者基于某个显著性水平推断城市分维存在时,实际上就是基于相应的置信度判断分形特征。虽然分形城市研究已经多年,但大量有关维数测算的基础问题依然悬而未决。本文根据分形几何学的基本思想论证城市形态分维测算的若干问题。分维测量的准则是最佳覆盖——不多不少、恰到好处的覆盖。盒子覆盖是最容易理解的测量方法。采用盒子覆盖法测量城市形态分维时,应考虑三个标准：一是快速逼近,二是简便操作,三是稳定拟合。直观估计分维的办法是利用双对数坐标图。由于城市形态不是严格意义的分形,而是类似于文献中的“前分形”,测量尺度与相应测度的幂律关系通常仅在一定尺度范围内有效,从而形成所谓标度区。本文围绕城市形态的分维测量和分形判断开展一系列讨论,包括尺度选取、标度区识别和统计标准等问题,对今后城市分形研究具有理论启示和方法论的参考价值。     

Electrical anisotropy and conductivity distribution functions of fractal random networks and of the crust: the scale effect of connectivity

All explanations of the high-conductivity layers (HCL) found by magnetotellurics in the middle or lower crust incorporate a mixture of a low-conductivity rock matrix and a highly conductive phase, for example graphite or saline fluids. In most cases the bulk conductivity of the mixture does not depend on the conductivity of the rock matrix but rather (1) on the amount of high-conductivity material and, in particular, (2) on its geometry. The latter is quantitatively described by the parameter 'electrical connectivity'. Decomposition of the observed bulk conductivity of the mixture into these two parameters results in an ill-posed problem. Even if anisotropy occurs in the HCL, three output parameters (highly conductive phase fraction, connectivity with respect to the X direction, connectivity with respect to the Y direction) have to be estimated from the two bulk conductivities of the anisotropic HCL. The additional information required for solving this problem is provided if instead of single-site data the conductivities from many field sites are evaluated: a sample distribution of the conductivity can then be obtained. Ensembles of random networks are used to create theoretical distribution functions which match the empirical distribution functions to some extent. The use of random resistor networks is discussed in the context of other established techniques for the treatment of two-phase systems, such as percolation theory and the renormalization group approach. Models of embedded networks explain the discrepancy between 'small' anisotropy (2-3) on the laboratory scale and large anisotropy (10-100) found in electromagnetic field surveys encompassing volumes of several cubic kilometres. Strong anisotropy can indicate low electrical connectivity, and a possible explanation is that a network stays close to the percolation threshold.     

滑坡频度-降雨量的分形关系

降雨-滑坡关系是对降雨引发的滑坡进行预报的一个重要基础。本文根据中国浙江省1990～2003年期间有明确日期和坐标记录的1414个滑坡数据和基本覆盖浙江全部陆地区域的1257个雨量站记录的日降雨量数据,研究了滑坡频度-降雨关系。研究结果表明,降雨引发滑坡的频度与降雨量之间遵循分形的幂指数关系,并且在两个尺度的降雨量范围内具有不同的标度指数。按照幂指数关系拟合的两条滑坡累计频度-降雨关系线交点(拐点)处的降雨量(Rin)指出了引发75%左右滑坡的累计降雨阀值的上边界(以THCR表示)。对1d、4d、6d和11d这4个累计降雨时段的研究表明,引发75%左右滑坡的累计降雨阀值分别为205mm(1d)、273mm(4d)、294mm(6d)、315mm(11d)。     

阔克沙勒—吉萨尔地震活动时间的多重分形研究

应用多重分形的标度指数谱f(α)～α方法分析阔克沙勒——吉萨尔地区地震活动时间序列,发现一定范围内地震多重分形f(α)～α在大震前有明显的异常显示。说明f(α)谱研究地震的多重分形,简单、有效、能全面地描述地震时间分布这类不均匀分形集。