新西兰地区地震活动时空分布的多重分形特征研究

利用多重分形维数谱估计的Hill方法，讨论了新西兰地震活动区地震活动的震源分布、震中分布以及时间间隔分布的多重分形特征．结果表明，该地区浅源地震的震中分布和震源分布在给定不同的起始震级的条件下均具有明显的丛集特征；对于中、深源地震这种特征不甚明显．而地震活动时间间隔分布则无论对于浅源和中、深源地震均呈单重分形的性质，但具有分形性质的尺度范围有较大的差别．这些结果表明，浅源地震与中、深源地震的活动特征显著不同．      

非线性震级频度关系与两类地震活动系统

在假定地震活动系统具有分形特征的前提下,首先推导出了震级频度关系的非线性表达式,进而指出地震活动系统可分为两类:整体地震活动受一个统一的大系统控制的Ⅰ类地震活动系统和整体地震活动受一个以上大系统控制的Ⅱ类地震活动系统．通常情况下,两类地震活动系统可以相互转变. 在华北地区一般强震前地震活动系统将由Ⅰ转变为Ⅱ类系统,这种变化可作为地震趋势判断的一个指标．另外,本文得到的非线性震级频度关系b值和线性震级频度关系b值之差b以及和非线性项系数有关的参数Muj可作为中短期地震预报的一对参数．      

关于地震震级-频度关系式及其非线性项的讨论

研究了震级频度关系式中非线性项产生的原因,指出由于地震孕育过程是非线性的,很多地震现象都服从分形和混沌规律,因此传统的震级频度关系式中应含有非线性项,才能全面描述地震过程的非线性规律．得出了新的含有非线性项的震级频度关系式．讨论了该公式中非线性项的含义．     

震级-频度关系小震端分布特征的一种可能的解释

通过震级-频度关系资料和地震台站分布资料的分析,发现震级-频度关系曲线在震级较小的一端的分布特征反映了地震能量分形和地震台站状况交互作用的结果,从而在地震序列分析中,考虑不同历史时期地震台站的状况及其影响,是一项必不可少的工作.     

广义地震应变能释放的多重分形特征

利用基于小波变换的多重分形谱估计方法，研究了以中国东西部地区为代表的板内地震活动和以新西兰、日本为代表的板缘地震活动广义应变能释放的多重分形特征．结果表明，中国东、西部地震活动广义应变能释放的多重分形特征有明显差别，新西兰与日本的地震活动广义应变能释放的多重分形特征也有明显不同；地震活动的多重分形特征与构造的复杂程度有关．      

地震活动期、幕最大地震M1的估计及中-长期地震趋势预测

提出一种地震活动期、幕最大地震M1的估计方法：利用中低震级累计频度∑N与震级近似的直线关系得到间隔地震频度N与震级的线性关系。用间隔度N与震级的线性关系估计最大地震M1。结果表明，以震级－间隔频率的线性关系估计的M1比震级－累计频度关系得到的M1更接近实际发生的最大地震震级，震级－累计频率关系得到M1通常被高估。基于震级－累计频度关系曲线的特征和震级－间隔频度的线性关系估计的最大地震M1，可为中－长期地震趋势预测提供新的信息。研究表明，中国大陆自1979年开始的地震幕即将结束，而帕米尔东北侧自1915年以来的地震平静期也将结束。     

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。     

地震丛集的分形新方法—物理分形

地震时间丛集的传统分形分析方法把地震事件看作是时间轴上无质量的数学点。这些方法得到的结果主要反映了大量小地震的活动特征。本文发展了一个新的物理分形分析的筛子方法，采用一系列震级筛子来研究不同震级地震的分布特征。对华北和南加洲的研究结果表明，同一地区地震目录中不同震级范围的子集合具有近似相等的分维数，华北Ｄ＝０．３，南加洲Ｄ＝０．４。     

震级——频度的客观分布及计算b值的要点

在前人研究震级—频度关系的基础上,我们分别通过十个具有独立过程和十个非独立过程的地震序列,详细研究了它们实际的震级一频度分布.由十个独立过程的地震序列震级—频度分布证明,低震级端的频度分布特征决非因地震仪漏记所致.无论是独立过程或是非独立过程的地震序列归一化后的震级频度分布是类似的.作为初级近似,它们十分接近对数正态分布.对于这些序列,G-R关系只在特征震级右侧除掉高震级拖尾段后的范围内成立,并不能在整个震级范围内满足.同时,我们也讨论了在计算b值时诸如合理选择下限震级这样一些需注意的问题.     

地震震级—频度关系中小震端“掉头”现象解释

以辽宁省及其邻近地区的地震记录为例，在考虑台站空间分形的基础上，通过震源深义校正，确认了震级－频度关系中小震端频度的“掉头”现象是由于台站监测能力不足所致 小震端出现的截止震级现象做了出解释。     

Argument on the magnitude-frequency relation

IntroductionSince the magnitude-frequency relation (1)being proposed and applied to the research of global seismicity by Gutenberg and Richter (1944, 1954), it has been widely used in the practice of seismic hazard prediction and of the research of seismic activity in different tectonic regions of the world ((1) is normally known as the G-R law).While with the increase of observational data of events, much researches show that though (1) can fit data well for events with middle value of magn…     

Wavelet-based multifractal analysis of earthquakes temporal distribution in Mammoth Mountain volcano,Mono County,Eastern California

This paper presents a wavelet-based multifractal approach to characterize the statistical properties of temporal distribution of the 1982–2012 seismic activity in Mammoth Mountain volcano. The fractal analysis of time-occurrence series of seismicity has been carried out in relation to seismic swarm in association with magmatic intrusion happening beneath the volcano on 4 May 1989. We used the wavelet transform modulus maxima based multifractal formalism to get the multifractal characteristics of seismicity before, during, and after the unrest. The results revealed that the earthquake sequences across the study area show time-scaling features. It is clearly perceived that the multifractal characteristics are not constant in different periods and there are differences among the seismicity sequences. The attributes of singularity spectrum have been utilized to determine the complexity of seismicity for each period. Findings show that the temporal distribution of earthquakes for swarm period was simpler with respect to pre- and post-swarm periods.     

Nonlinear extensions of a fractal–multifractal approach for environmental modeling

We present the extension of a deterministic fractal geometric procedure aimed at representing the complexity of patterns encountered in environmental applications. The procedure, which is based on transformations of multifractal distributions via fractal functions, is extended through the introduction of nonlinear perturbations in the generating iterated linear maps. We demonstrate, by means of various simulations based on changes in parameters, that the nonlinear perturbations generate yet a richer collection of interesting patterns, as reflected by their overall shapes and their statistical and multifractal properties. It is shown that the nonlinear extensions yield structures that closely resemble complex hydrologic spatio-temporal datasets, such as rainfall and runoff time series, and width-functions of river networks. The implications of this nonlinear approach for environmental modeling and prediction are discussed.     

强震前后广义地震应变释放过程的丛集特征

利用基于小波变换的多重分形奇异谱估计方法,研究了部分强震前后地震活动广义应变.释放过程的多重分形特征。结果表明,晨中区附近- -定范围内地展活动广义应变释放过程具有多重分形特征,但多重分形维数谱随7变化复杂,在强震发生前多重分形维数谱没有明显的变化。广义地震应变释放过程的多重分形奇异谱形态和Hausdorff奇异指数范围能提供更多关于地屣活动过程的信息,特别当η取较大值时Hausdorff奇异指数范围在强晨前明显变窄。研究还表明深源地展和浅源地晨发生前广义应变释放过程多重分形特征存在明显不同。     

Research on the multifractal characteristics of the temporal—spatial distribution of earthquakes over New Zealand area

Using the Hill estimator,general multifractal characteristics of events in the New Zealand area have been dis-cussed.Results show that the spatial distribution of shallow events has apparent clustering characteristics,inde-pendent of the threshold magnitude;but for deep events these characteristics are not clear.While the time interval distribution has obvious clustering characteristics both for deep and shallow events,although with a different scal-ing range,the Hill estimates tend to indicate that the time interval distribution has a unifractal rather than a multi-fractal nature.All above reveal that the seismicity nature for shallow and deepevents is apparently different.     

Multifractal versus monofractal analysis of wetland topography

The land surface elevation distribution will serve as fundamental input data to any wetland flow model. As an alternative to the traditional smooth function approach to represent or interpolate elevation data, we explore the use of Levy monofractals and universal multifractals as a means for defining a statistically equivalent topography. The motivation behind this effort is that fractals, like natural topography, are irregular, they offer a way to relate elevation variations measured at different scales, and the relationships are of a statistical nature. The study site was a riparian wetland near Savannah, GA, that contained beavers, and a total of four elevation transects were examined. The elevation increments showed definite non-Gaussian behavior, with parameter values, such as the Hurst coefficient and Lévy index (α), depending on the question of presence of beaver activity. It was obvious that the data were highly irregular, especially the transects influenced by beavers. Significantly different α values were obtained depending on whether the entire data set or just the tails were examined, which demonstrated inability of the monofractal model to reflect fully the irregularity of wetland data. Further analysis confirmed definite multifractal scaling, and it is concluded that the multifractal model is superior for this data set. Universal multifractal parameters are calculated and compared to those obtained previously for more typical terrain. Although it is difficult to consider a unique universal multifractal parameter α for the entire wetland, multifractal-like scaling was evident in each transect as reflected by the nonlinear behaviors of the scaling functions. We demonstrate a good agreement between theory and measurements up to a critical order of statistical moments, q _D , close to 3.5 and obtain realistic unconditioned simulations of multifractal wetland topography based on our parameter estimates. Future work should be devoted to conditioning multifractal realizations to data and to obtaining larger data sets so that the question of anisotropy may be studied.     

Nuclear magnetic resonance <Emphasis Type="Italic">T</Emphasis><Subscript>2</Subscript> spectrum: multifractal characteristics and pore structure evaluation

Pore structure characteristics are important to oil and gas exploration in complex low-permeability reservoirs. Using multifractal theory and nuclear magnetic resonance (NMR), we studied the pore structure of low-permeability sandstone rocks from the 4th Member (E_S4) of the Shahejie Formation in the south slope of the Dongying Sag. We used the existing pore structure data from petrophysics, core slices, and mercury injection tests to classify the pore structure into three categories and five subcategories. Then, the T₂ spectra of samples with different pore structures were interpolated, and the one- and three-dimensional fractal dimensions and the multifractal spectrum were obtained. Parameters α (intensity of singularity) and f (α) (density of distribution) were extracted from the multifractal spectra. The differences in the three fractal dimensions suggest that the pore structure types correlate with α and f (α). The results calculated based on the multifractal spectrum is consistent with that of the core slices and mercury injection. Finally, the proposed method was applied to an actual logging profile to evaluate the pore structure of low-permeability sandstone reservoirs.     

板内与板间地震活动时空分布的多重分形特征研究

利用多重分形分析方法,考察了中国大陆和台湾地区以及新西兰的地震活动广义应变释放时间和空间分布的多重分形特征. 结果表明,地震活动时空分布的多重分形特征与不同地球动力学环境关系密切. 强震活动时间分布在板间地区具有比板内地区更明显的丛集性, 对中小地震这种丛集性差异较小;强震活动空间分布在板内地区具有比板间地区更强的丛集性,但对中小地震则相反.      

基于Prager硬化的钢管混凝土非线性梁单元

根据三类钢管混凝土构件的荷载位移曲线论述了Prager硬化规则应用于钢管混凝土材料非线性分析的合理性,由随动硬化材料屈服面方程的全微分出发,采用塑性势理论推导了钢管混凝土梁单元的非线性刚度矩阵。建立了钢管混凝土梁单元的初始屈服面方程,由Prager硬化规则建立了后继屈服面方程,并推导了屈服面移动量的计算公式。根据钢管混凝土的特点,探讨了确定硬化参数的方法。算例的结果有良好的精度。