分形方法在洪涝灾害预测中的应用：以广西梧州为例

洪涝灾害是由暴雨洪水形成的一种突发性、最常见的自然灾害,它发发生在时间序列上具有分形特征。以广西梧州解放以来发生的特大洪涝灾害年份建立灾变日期序列,运用分式布朗运动模型中的Ｒ／Ｓ分析对洪涝灾害发生的时间序列进行模拟,计算了Ｈ指数值,建立了（τ）／Ｓ（τ）的幂函数关系式等,并以此为依据,预测下次灾年将在１９９９年出现。     

分形理论在成矿预测中的应用

分形理论是人类进行思维和探索复杂性而定量描述的一种新方法，是研究大自然界中不规则现象的有力数学工具，在地质领域中的应用非常广泛。介绍Ｒ／Ｓ分析法原则，并结合实例来研究地质体和地质现象的分形特征，确定地质异常，建立地质异常分形模型。     

分形方法在地震序列类型早期判别中的应用

着重讨论了地震序列的空间分布随时间变化的特性，利用分形方法提取大震后余震的空间分维信息，从而达到早期判别地震序列类型的目的。以１９６６年以来定位精度较好、余震记录较全的１２个７级以上大震和大同６级强震序列为资料，计算了震后１个月内余震随时间变化的空间分维数。结果发现，不同类型的地震序列分维数不同。一般震后５－６天，主震型序列的分维数在１．１－１．２之间，多震型序列的分维数在１．３以上。利用前７天的     

数学形态学用于纹理图像的分维估计

首先介绍了灰度图像膨胀与腐蚀的定义，然后给出了数学形态学估计分维的数学模型，进而用于纹理图像的分维估计。实验结果表明：该方法原理简单，算法设计灵活，运算速度快捷，为纹理特征描述提供了一种有效的新途径。     

地震前兆吸引子的演化特征

用非线性动力学重建相空间的方法对唐山地震前后（１９７１～１９７８年）昌黎地电台和地应力台前兆观测资料分别进行了关联维的计算．结果表明，地电阻率和地应力前兆资料吸引子具有分数维结构，并且发现这两种不同前兆资料的吸引子具有相同的前兆动态变化特征．在计算中发现，地电阻率的分数维具有多层次性．对此还进行了简单的讨论     

The Fractal Feature of Granulometric Composition in Fault Gouges from the Yishu Fault Zone and Adjacent Northwest-Trending Faults and Its Seismo-geological Implications

In this work,the fractal dimension of granulometric composition in the fault gouge from the Yishu fault zone and northwest-trending faults on its west side is calculated and studied based on the fractal theory of rock fragmentation.The seismo-geological implications of the fractal dimension of granulometric composition in fault gouges are also discussed.The results show that the Yishu fault zone is more active than the northwest-trending faults and the Anqiu-Juxian fault is the most active in the Yishu fault zone.The fractal dimension of fault gouge is a parameter describing the relative active age and rupture mode of the fault and forming age of the fault gouge.The fractal dimension value is also related to the parent rock,thickness,structural position,and clay content of the fault gouge.     

宁夏灵武地震序列的分数维特征

本文从分数维几何学的观点出发,采用标度变换法分别计算了1984年至1988年6月宁夏灵武地区中强地震序列的时间分布分数维,结果表明,1988年1月4日灵武5.5级地震后,中小地震序列的分数维显著增高(D=0.44)。文中还结合本区断裂构造特点和地震活动性分析,初步探讨了灵武及其周围地区的地震趋势。     

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.