The fractal nature of the inhomogeneities in the lithosphere evidenced from seismic wave scattering

In this paper we show evidences of the fractal nature of the 3-D inhomogeneities in the lithosphere from the study of seismic wave scattering and discuss the relation between the fractal dimension of the 3-D inhomogeneities and that of the fault surfaces. Two methods are introduced to measure the inhomogeneity spectrum of a random medium: 1. the coda excitation spectrum method, and 2. the method of measuring the frequency dependence of scattering attenuation. The fractal dimension can be obtained from the inhomogeneity spectrum of the medium. The coda excitation method is applied to the Hindu-Kush data. Based on the observed coda excitation spectra (for frequencies 1–25 Hz) and the past observations on the frequency dependence of scattering attenuation, we infer that the lithospheric inhomogeneities are multiple scaled and can be modeled as a bandlimited fractal random medium (BLFRM) with an outer scale of about 1 km. The fractal dimension of the 3-D inhomogeneities isD ₃=31/2–32/3, which corresponds to a scaling exponent (Hurst number)H=1/2–1/3. The corresponding 1-D inhomogeneity spectra obey the power law with a powerp=2H+1=2–5/3. The intersection between the earth surface and the isostrength surface of the 3-D inhomogeneities will have fractal dimensionD ₁=1.5–1.67. If we consider the earthquake fault surface as developed from the isosurface of the 3-D inhomogeneities and smoothed by the rupture dynamics, the fractal dimension of the fault trace on the surface must be smaller thanD ₁, in agreement with recent measurements of fractal dimension along the San Andreas fault.     

A scale-invariant approach to flood-frequency analysis

In order to study historical flood-frequency records we plot the log of the number of floods on a river per unit time in which the peak discharge exceeds a specified value against the log of that value. For ten benchmark stations we find good correlations with scale-invariant (fractal) statistics. We suggest that the underlying physical processes associated with the generation of floods are sufficiently scale invariant over time scales from one to one hundred years that they provide a rational basis for the application of scale-invariant statistics. Our results fall within the range of flood-frequency estimates made by other statistical techniques. We propose that the ratio of the ten-year peak discharge to the one-year peak discharge is a quantitative measure of flood potential. With scale invariance is also the ratio of the one-hundred year flood to the ten-year flood. We find that the values of for ten stations on rivers throughout the country range from 2.04 to 8.11 and find strong regional variations that can be correlated in terms of climate. Our results are consistent with the observed fractal statistics in sedimentary sections. We have also carried out R/S analyses for the ten stations and have obtained values of the Hurst exponent. We find that the Hurst exponent cannot be used for flood-frequency forecasting.     

A scale-invariant approach to flood-frequency analysis

In order to study historical flood-frequency records we plot the log of the number of floods on a river per unit time in which the peak discharge exceeds a specified value against the log of that value. For ten benchmark stations we find good correlations with scale-invariant (fractal) statistics. We suggest that the underlying physical processes associated with the generation of floods are sufficiently scale invariant over time scales from one to one hundred years that they provide a rational basis for the application of scale-invariant statistics. Our results fall within the range of flood-frequency estimates made by other statistical techniques. We propose that the ratio of the ten-year peak discharge to the one-year peak discharge is a quantitative measure of flood potential. With scale invariance is also the ratio of the one-hundred year flood to the ten-year flood. We find that the values of for ten stations on rivers throughout the country range from 2.04 to 8.11 and find strong regional variations that can be correlated in terms of climate. Our results are consistent with the observed fractal statistics in sedimentary sections. We have also carried out R/S analyses for the ten stations and have obtained values of the Hurst exponent. We find that the Hurst exponent cannot be used for flood-frequency forecasting.     

某水电站库区泥石流发育特征及其非线性特性研究

通过对某水电站库区内12条主要的泥石流沟从沟道数与流域面积,沟道数与主沟长,沟道数与沟谷坡降关系上研究了库区内泥石流沟发育的非线性特征,并通过其双对数曲线方程得到了各自的分维数,其意义是在对泥石流危险度评判中为各因素权重的求取提供一个定量的手段,并据此可利用非线性技术来解决泥石流灾害研究中的预测及防治等主要问题,为泥石流灾害防治提供新的思路。     

分形方法在南麂岛土地覆盖类型分析中的应用

借助分形理论对南麂列岛国家级海洋自然保护区内的主岛---南麂岛的地面覆盖及其状况进行分析,把各地类图斑的复杂性、破碎性和形状等定性概念,用分维值和形状因子进行定量描述和比较,分析其形成机制。结果表明,灌木林地和草地等自然性较强的地类分维值较大,而晒场和居民地等人为干预较多的地类分维值较小,庄稼地的分维值则介于它们之间。     

基于遥感技术的无锡市城镇形态分形研究

城镇形态研究不仅是城镇规划、城镇建设和城镇土地利用的重要依据 ,也是城镇社会经济发展的理论基础。对地理现象形态的关注和研究早已成为地理学者的一项工作。从地貌学者所关注的地形到城市地理学家所关注的城市形态分类 ,都有形态问题。从 2 0世纪 90年代以来 ,我国在城市形态研究领域 ,无论在理论方面还是在应用方面 ,都取得了许多成就 ,但大多数研究主要集中在空间结构变化的机制和城镇内部结构形态的变化这两方面 ,对城镇形态的自身特征及其变化研究不多 ,对城镇形态的空间信息如何客观、准确地提取则涉及得更少。据此 ,本文的研究重点首先是解决如何客观、有效地提取城镇形态信息和空间数据 ;其次是根据提取出的空间信息和数据 ,对无锡市城镇外部形态特征进行分形研究 ,以揭示出城镇形态的复杂性和稳定性。     

QPOG技术及其应用研究

研究了地震资料的现场处理技术－－QPOG（Quickly Predicting Oil and Gas），提出利用QPOG技术右以在地震勘探中快速有效地进行油气预测，并给出了有井区和无进区的两种预测方法；有井区以人工神经网络、模糊相似优先比等方法为主，无井区以分形、混沌、突变等理论方法为主，通过对具体研究区的实际预测，证明了方法的实用性。     

基于DEM的流域水系分维估算方法探讨

分形理论是现代数学的一个新的分支，是一种新世界观和方法论。分形理论与地学的结合，极大地推动了地理学的发展。介绍了分形理论在水文学研究中的应用和发展，介绍了利用Arc/Info，以DEM为数据源提取流域信息的方法。提供了一种将分形理论、GIS技术和流域地貌模型巧妙耦合，分别用基于覆盖法的分维估算方法和基于Horton定理的分维估算方法计算了马连河流域水系分形维数。这种方法与传统方法相比，具有易于操作、高效等优点。     

地震断裂系统的分形和在地震预报中的应用

本文基于地震断层具有自相似结构,从分形概念出发,依据地震资料提出了适合于前震和余震的分形模型,在此基础上讨论了前震和余震的b值特征,提出了地震矩不均衡度的概念。本文还探讨了利用分数维和地震矩不均衡度进行地震预报的可能性。研究发现,正常情况下,地震矩不均衡度呈现低值,大震发生前出现高值异常,震后降低;在空间上,震前2—4年其异常范围大,震前一年异常区逐渐缩小,大震发生在异常集中区内或其边缘。     

苏锡常地区地裂缝分形的初步研究

利用分形理论对苏锡常地区地裂缝的空间分布特征进行了初步探讨,计算出该区地裂缝的分维值在0987～0996之间。分析认为,该区地裂缝在地质作用过程中自组织程度一致性较强,并具局部与整体的自相似性,这种自相似性,对研究该区地裂缝的进一步发展可能有一定的预测意义