地震空间分布多分维数的计算及初步应用

本文简要介绍了计算多分维数的推广G-P法;讨论了无标度区的选取,认为无标度的上限受边界效应的影响,下限受定位精度的限制;最后给出中国东部几个地区的地震多分维谱及其随时间的变化,结果表明,这些地区的中强震之前多分维数D_q(q=-2,0,2)均有下降过程,特别是q<0的D_q值在震前有明显变化(变化幅度在0.4以上)。这显示D_q谱较好地揭示了震前地震空间分布的演化。     

多分形断层模型与地震序列研究

本文提出形成地震序列的多分形断层模型并利用分形分维理论讨论该模型及其序列。给出本模型的震级—频度关系、余震序列中强余震预报公式和多分维D_q—q关系式,探讨了利用多分维预报地震的有效性。     

玛纳斯地震前后地震活动信息熵及分维的动态变化

根据耗散结构理论及Mandelbort提出的分形几何学观点,研究了玛纳斯5.8级地震前后地震(M_s≥1.5)序列的时空分布特征、地震活动信息熵及分维的动态变化。发现玛纳斯5.8级地震前存在减熵和降维。认为,地震熵或分维可以定量描述地震时空分布变化过程,并量度变化过程从无序向有序的演化。     

华北地区地震分布多标度分形特征的初步研究

依据“固定质量法”的定义及原理,本文给出了一种判断地震空间分布分形结构及计算D_q的方法。利用该方法对华北地区地震的空间分布特征进行了初步研究。结果表明,在满足一定的统计条件下,不同区域范围内、不同时间段的地震分布均具有分形结构。围绕海城、唐山大震区分别选择4个大小不同的区域,分不同时段计算其D_q—q谱。结果表明,强震前后其形态无显著变化。强震前在较大的区域范围内,D_o值有降低的趋势,震后回升;在震源区周围较小区域内,D_o的变化相反;而有的区域强震前后D_o值没有变化。     

地震时空分布结构的多重分形特征的研究

地震作为地壳内的大尺度破裂被认为是分形的，具有分数维的特征。根据多重分形的观点，本文研究了部分曾发生过中强以上地震地区小震时空分布特征，应用固定质量法计算了地震时空分布的广义分维Ｄｑ，并得到了分形奇异谱ｆ（α）－α。初步分析结果表明：地震空间分布具有非均匀的分形结构，Ｄ∞的分维值比Ｄ０和负ｑ的Ｄｑ值稳定。Ｄ∞的时间变化实例表明：Ｄ∞在大震发生前降低。这意味着地壳应力场非均匀程序的变化，进而简略地讨     

1989年大同6.1级地震前山西带小震活动时间分布结构多重分形维数的变化特征

本文应用多重分形理论研究了1989年大同6.1级地震前山西地震带(简称山西带,下同)小震活动时间分布结构的变化特征,发现震前各D_q值均有降维异常出现,且D_(+q)(q>0,下同)的异常尤为突出,取不同层次的地震样本进行计算其异常形态基本一致,表明震前小震活动时间分布从无序向有序转变所显示的内在结构异常变化是真实可靠的,这对我们今后地震分析预报的研究或许是有所裨益的.     

四川西部地区地震活动的空间分维特征

本文采用多分形的方法研究了四川西部地区20年来的地震活动的空间分布特征.对D_q谱与D_(-1),D_(-2)曲线结合震例进行分析,指出其变化与强震活动有密切联系。并结合空区理论,认为D_q(q<0)主要描述了地震空区的情况,该方法在地震前兆信息提取有中重要意义。     

多重分形与地震

本文介绍了多重分形理论的主要内容、广义维数D_q和f(a)谱的测算方法,评述了国外对地震空间分布多重分形研究的最新进展,指出地震多重分形的相变是当前急待解决的重要问题。     

模糊空间分维在地震活动时空演化研究中的应用

本文把模糊分维方法应用于地震活动时空演化研究,当中.给出了强震和中强震活动模糊空间分维的确定方法,并通过计算不同小区的模糊空间分维随时间的变化曲线来研究地震活动的时空演化特征.以华北及西南地区地震活动性时空演化图象为例进行了具体分析研究.所得结果表明,大震前地震活动的模糊空间分维D_0~(2)要出现下降异常,并且大地震发生在D_0~(2)减小的地区(西南)或先减小而后达到高值(华北)的地区.     

台湾地区地震活动的时间多分形特征研究

利用板块构造、活断层分布、地壳运动这三个方面的最新资料将台湾地区划分为东、西两个地震区和六个地震带。对各地震带11a来的地震目录计算了广义维数Dq和多标度分形谱f(α)，然后绘制成Dq—q曲线和多标度分形谱f(α)—α以及分维时程曲线。综合分析后发现：(1)地震活动的时间结构是多分形而非单一分形结构；(2)台湾地区在大震前后的1～2a内，大震所在的地震带内地震时间结构的Dq—q曲线和多标度分形谱f(α)—α大都出现异常形态；(3)功时程曲线分析可以为强震的时间预报提供有效的客观依据。     

Multifractal analysis of earthquakes

Multifractal properties of the epicenter and hypocenter distribution and also of the energy distribution of earthquakes are studied for California, Japan, and Greece. The calculatedD _q-q curves (the generalized dimension) indicate that the earthquake process is multifractal or heterogeneous in the fractal dimension. Japanese earthquakes are the most heterogeneous and Californian earthquakes are the least. Since the earthquake process is multifractal, a single value of the so-called fractal dimension is not sufficient to characterize the earthquake process. Studies of multifractal models of earthquakes are recommended. Temporal changes of theD _q-q curve are also obtained for Californian and Japanese earthquakes. TheD _q-q curve shows two distinctly different types in each region; the gentle type and the steep type. The steeptype corresponds to a strongly heterogeneous multifractal, which appears during seismically active periods when large earthquakes occur.D _q for smallq or negativeq is considerably more sensitive to the change in fractal structure of earthquakes thanD _q forq2. We recommend use ofD _q at smallq to detect the seismicity change in a local area.     

Temporal characteristics of seismicity in the Alborz and Zagros regions of Iran, using a multifractal approach

Multifractal characteristics of the temporal distribution of earthquakes in the Zagros and Alborz regions of Iran were analyzed using the fixed-mass method. The generalized multifractal dimensions, singularity spectrum, mass exponents, and the asymmetry factor were calculated for these regions. The results indicate that the temporal distributions of earthquakes in the Zagros and Alborz regions are likely to be chaotic and have multifractal structures. Although both of the study areas show heterogeneous structures, the D_q and f(α_q) spectra for the Zagros region indicate that densely populated time domains are as heterogeneous as the sparsely populated ones. On the other hand, the multifractal spectra of the Alborz region show that the densely clustered time domains are more heterogeneous than the sparsely populated ones. Such a multifractal spectrum shows that there are many more sparsely populated time domains (i.e. seismic gaps) within the multifractal structure than densely populated ones.     

Multifractal analysis of three large earthquakes in Chile: Antofagasta 1995, Valparaiso 1985, and Maule 2010

A multifractal analysis of seismicity of three large earthquakes in Chile is made: the Central Zone 1985 (M _W = 8.0), Antofagasta 1995 (M _W = 8.1), and Maule 2010 (M _W = 8.8) earthquakes. The analysis shows that the fractal dimension spectrum D _q decreases with time before an earthquake. This fact suggests that the spatial distribution of seismic events could form a cluster before a main shock.     

Multifractal of spatial distribution of seismicity in Liaoning area

Making use of multifractal theory and corresponding computational method and according to the feature of evolution of spatial distribution with respect to seismicity by earthquake data in Liaoning area, earthquake activity of the area has been studied in detail. The results show that the evolution of increase in seismicity and distributive process in space are a multifractal structure. Whole characteristic of evolution in fractal increasing process of seismicity is described by obvious variation in regard toτ(q)-q curve,f(α) spectrum and other parameters before and after moderate and strong earthquakes.     

A study on the characteristics of the information dimensionD 1 of the temporal and spatial distributions of earthquakes in an active fault zone

The research of the information dimension (D ₁) in an active fault zone considers the contribution of each seismic event to information and reflects the characteristics of the temporal and spatial distributions of earthquakes from a new point of view, avoiding some short-comings of the research about the capacity dimension (D ₀). The results of calculation show that the information dimension of the temporal distribution in Xianshuihe active fault zone before Luhuo large earthquake isD ₁=0.1051. It is a consult creterion of large earthquakes in future in the fault zone. The information dimensions of the temporal distribution of the earthquakes in Anninghe active fault zone are respectivelyD ₁(t _N)=0.1363 (for the north section) andD ₁(t _S)=0.06710 (for the south section). The information dimensions of the spatial distribution are respectivelyD ₁(K _N)=1.053 (for the north section) andD ₁(K _S)=0.7758 (for the south section). The north section and the south section belong to two self-similar systems with different information dimensions respectively. The extent of the self-organization of seismic activity in the south section is higher than that in the north section. This is helpful for us to judge the major dangerous section in the key region of the seismic monitoring. The research about the information dimension of the temporal and the spatial distributions of earthquakes is significant for the exploration of active fault zones and seismic prediction.     

A study on the characteristics of the information dimension D 1 of the temporal and spatial distributions of earthquakes in an active fault zone

The research of the information dimension (D ₁) in an active fault zone considers the contribution of each seismic event to information and reflects the characteristics of the temporal and spatial distributions of earthquakes from a new point of view, avoiding some short-comings of the research about the capacity dimension (D ₀). The results of calculation show that the information dimension of the temporal distribution in Xianshuihe active fault zone before Luhuo large earthquake isD ₁=0.1051. It is a consult creterion of large earthquakes in future in the fault zone. The information dimensions of the temporal distribution of the earthquakes in Anninghe active fault zone are respectivelyD ₁(t _N)=0.1363 (for the north section) andD ₁(t _S)=0.06710 (for the south section). The information dimensions of the spatial distribution are respectivelyD ₁(K _N)=1.053 (for the north section) andD ₁(K _S)=0.7758 (for the south section). The north section and the south section belong to two self-similar systems with different information dimensions respectively. The extent of the self-organization of seismic activity in the south section is higher than that in the north section. This is helpful for us to judge the major dangerous section in the key region of the seismic monitoring. The research about the information dimension of the temporal and the spatial distributions of earthquakes is significant for the exploration of active fault zones and seismic prediction. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 372–379, 1991. This paper is sponsored by the Chinese Joint Seismological Science Foundation. The English version is improved by Zhenwen An.     

台湾地区地震的空间关联维特征与构造环境研究

采用关联维方法对台湾地区地震活动的空间特征进行了研究。先利用 10 0a来台湾的地震目录计算各个地震区、带的关联维数 ,将地震空间分布的分形特征定量表达出来 ,然后综合分析地震空间分布的关联维数和孕震构造环境之间的关系 ,得出了以下结论 :1)台湾东、西部地震区由于地震属于不同的大地构造单元 ,因此关联维数有较大的差异 ;2 )在各地震区内部的各个地震带由于板块构造、地壳结构、活断层分布上的差异 ,而具有与其构造特征相对应的关联维数 ;3)各地震带内部的各个不同的部位又由于不同的构造应力场 ,而导致地震分布上出现不同的丛集性 ,表现为不同的关联维数。这些结论充分说明通过关联维分析所得到的地震活动的空间图像与地震活动所代表的不同地质构造背景有着良好的对应关系     

Attractor reconstruction from the time series of information entropy of seismic kinetics process

The attractor is reconstructed from the time series of the information entropy of the seismic kinetics process. It is shown that the seismic kinetics process is governed by three order parameters and is characterized by a strange attractor in the three-dimensional phase space. The D_q-spectrum of the multifractal measure induced by the attractor, which describes the topological structure of the latter, is obtained. The monofractal dimension of the attractor is D_q(0) = 2.31…, and the correlation dimension is D_q(2) = 2.16…. The estimate of the largest Lyapunov exponent of the attractor λ1 = 0.331…. The positive signature of the largest Lyapunov exponent suggests that the attractor is chaotic and the behavior of the phase trajectory is unpredictable.     

地震时空丛集的多重分形研究

为探索大地震发生的可预测性,应用分形理论并根据标准数盒子的数值计算方法,研究了华北地区历史地震和唐山地区地震活动的空间分布特征,估算了地震活动能量的分维值并研究了其多重分形谱的几何结构．初步结果显示出大地震发生前,广义维值有明显的下降过程,分形谱ｆ（α）结构有右偏现象．在低于上述时空层次的唐山地区,孕震系统也有类似特征出现．这些异常现象揭示出孕震动力系统的物理机理和激变前的某些不稳定性．