前震活动特征及其识别的研究（Ⅰ）

分析了近２０年来中国大陆强震（Ｍ≥７．０）和华北地区中强地震前广义前震序列时间和空间分布的多分形特征，计算其广义分维谱Ｄｑ和标度指数谱Ｆ（α），并探讨了它们随时间的变化．结果表明：（１）对广义前震活动，在所研究地区的时、空分布，均呈现多分形结构；（２）大地震发生前半年至一年，地震活动时、空分布的高次分维Ｄ∞呈下降趋势．这种降维特征，亦在实验室含水大样本岩石破坏前，声发射序列Ｄ∞的变化中观测到；（３）与中强地震相比，大地震孕育区地震活动的空间高次分维偏低，表明地壳应力分布的高度不均匀性，是板内大地震孕育环境中的本质因素之一．     

前震活动特征及其识别的研究（Ⅰ）

分析了近２０年来中国大陆强震（Ｍ≥７．０）和华北地区中强地震前广义前震序列时间和空间分布的多分形特征，计算其广义分维谱Ｄ_ｑ和标度指数谱Ｆ（α），并探讨了它们随时间的变化．结果表明：（１）对广义前震活动，在所研究地区的时、空分布，均呈现多分形结构；（２）大地震发生前半年至一年，地震活动时、空分布的高次分维Ｄ_∞呈下降趋势．这种降维特征，亦在实验室含水大样本岩石破坏前，声发射序列Ｄ_∞的变化中观测到；（３）与中强地震相比，大地震孕育区地震活动的空间高次分维偏低，表明地壳应力分布的高度不均匀性，是板内大地震孕育环境中的本质因素之一．     

地震活动多标度分形特征及预报应用

探讨了多标度分形在刻划复杂系统方面的优越性,研究了江苏及邻区1970年以来的5.5级以上地震的多标度分形特征,着重研究了地震前后多标度分形的广义维数谱和奇异性谱.研究结果表明:所有震例的广义维数谱和奇异性谱均经历了远离地震时、异常出现时和异常消失时的三个特征变化阶段;异常出现的时间在震前半年至一年半内;多数震例异常在震前几个月内回返恢复,少数在震后数个月内恢复.上述结果说明利用地震时序的多标度分形特征对于该地区的半年至一年尺度的中强地震预报是有意义的.     

天山地区地貌系统的自仿射分形与多重分形特征研究

利用标准偏差法和固定质量法，研究了新疆天山地区跨越多个不同构造地貌单元的两条地形剖线的自仿射分形和多重分形特征。结果表明：在所研究的标度范围内，两条剖线均表现出了不同特征的多度域分形性质，多重分形谱Dq的形态和值域范围也呈现出不同特征研究认为，地貌形态并不是完全随机的，而是一种确定性随机，不同标度区间的分维值表征了内外营力作用的方式，强度和空间尺度，同时提出地貌宏观与微观作用尺度的分界点在5km左右。这些结果对地貌动力学定量研究具有重要意义。     

岩石剖面线的自仿射分形研究

0 引言 由B.B.Mandelbrot创建发展的分形几何学,已被广泛地应用于众多的领域中。无论在力学、化学、生物学、生理学,还是地学、冶金学、材料学,甚至经济学、书法、艺术等领域中均能看到分形研究成果。自然界中很多现象具有统计自相似特征,人们可以用自相似分形维数研究这些自然现象。有些地质现象用自相似分形描述不大合适,需用另一个分形,即称为自仿射分形的模型来刻划,如地震断层的迹线等。岩石断面的垂直剖面线也具有自仿射分形的特征。     

分形噪声、多维分形滤波及地球物理测井曲线处理应用

白噪声、布郎运动以及其它满足在双对数坐标中呈一直线和信号具分形结构、自相似性或尺度无关性。地球物理信号通常表现为多个这种信号的叠加,表面为多维分形特征,研究、模拟在双对数坐标中成一直线的信号以及如何将多维分形中多个这种信号剖分出来,对于理解相应的地质、地球物理成因机制有重要意义。通过对两口井的地球物理测井曲线处理,可以初步看出,在选定的物理测井曲线中,其具多维分形特征,不同的沉积过程相互叠架在原始测井曲线中,用滤波方法分析分解信号,可以了解不同沉积作用特征并进一步分析可能的环境变化控制机制。开发的图形界面程序使得这一过程极为容易。     

辽宁省地震活动时间分布的分维特征

应用分数维理论与方法，对地震活动时间分布不均匀结构，建立自相似分形集。利用其相似维数Ｄ的变化特征，来研究辽宁省中强地震前后和显著地震活动的时间结构。发现中强地震前Ｄ值随时间系统减小，余震序列的Ｄ值变大，前震序列的Ｄ值明显偏低。对震群活动的研究表明，一般震群活动的Ｄ值均较高，而前兆震群活动的Ｄ值也明显偏低。     

新疆天山地区地貌分形与多重分形特征研究

利用投影覆盖法和投影覆盖概率对新疆天山地区不同构造地貌类型进行了分形与多重分形特征的研究。结果表明：在所研究的标度范围内，不同地貌区均表现出明显的多度域分形，分维值总体上呈现出高山区＞中低山区＞盆地区特点，多重分形谱Dq的形态和值域范围也表现出不同特征。研究认为，地貌表面的分维值与地貌形成的内外力地质作用方式和强度密切相关，并提出5-6km的尺度可作为地貌学研究中宏观与微观作用的分界点。     

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。     

1976年黑山,砣矶二次震群多分形特征研究

依据“固定半径法”的定义及原理,对１９７６年黑山、砣矶震群的时间结构的广义维数Ｄｑ－１和标度指数谱ｆ（ａ）－ａ曲线的特征进行了初步研究。结果表明二次前兆震群表现出各自的特征,即砣矶震群地震时间多分形结果出现剧变型异常、其表征为ｑ为负值时Ｄｑ值大,ｑ为正值时Ｄｑ减小且变化幅度大。与此同时,ｆ（ａ）两端下降,ａ跨度也较大,而黑山震群地震时间多分形结构没有出现明显异常,Ｄｑ－ｑ曲线平缓,ｆ（ａ）－ａ谱曲     

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。     

用去趋势涨落分析研究北京气候的长程变化特征

无标度性广泛存在于自然界系统包括气候系统中,其特征之一是可观测量存在幂函数关系,它揭示了气候系统的复杂性.为探索气候可预测性的客观基础,运用去趋势涨落分析(DFA)方法对北京1870～2003 年平均气温和1725～2003年降水序列进行了分析.结果表明,北京年平均气温和降水量均可划分为多个标度不变区域.在特定的标度域内,它们都表现出正长程相关的性质,为制作年际与年代际气候预测提供了理论基础.     

Fractal analysis of rainfall observed in two different climatic regions

Abstract

The importance of high-resolution rainfall data to understand the intricacies of the dynamics of hydrological processes and describe them in a sophisticated and accurate way has been increasingly realized. The present study investigates the general suitability of fractal (or scaling) theory for understanding the rainfall behaviour and transforming rainfall data from one time scale to another. The study, employing a multi-fractal approach, follows the research undertaken earlier by the author (Sivakumar, 2000) employing a mono-fractal approach in which some preliminary indication as to the possibility of existence of (multi-) fractals was obtained. Rainfall data of three different resolutions, six-hourly, daily, and weekly, observed over a period of 25 years in two different climatic regions: a subtropical climatic region (Leaf River basin, Mississippi, USA); and an equatorial climatic region (Singapore) are analysed. The existence of multi-fractal behaviour in the rainfall data is investigated using (a) the power spectrum method; (b) the empirical probability distribution function (PDF) method; (c) the statistical moment scaling method; and (d) the probability distribution multiple scaling (PDMS) method. The results achieved from all these methods for the six different rainfall data sets considered indicate the existence of multi-fractal behaviour of rainfall observed in Leaf River basin and Singapore, providing further support to the results obtained using the mono-fractal approach (Sivakumar, 2000). The suitability of a multi-fractal framework to characterize the behaviour of rainfall observed in the above two significantly different climatic regions, subtropical and equatorial, seems to suggest the general suitability of the fractal theory for transforming rainfall from one time scale to another. Investigations with rainfall data from several other climatic regions are underway with a view to strengthening the above conclusions.     

京津唐地区地震灾害区域宏观脆弱性变化的初步研究——空间变化

在讨论和明确地震灾害区域宏观脆弱性的含义、分析层次和描述角度的基础上,以京津唐地区和2000年为例,构建了一个由25个指标组成的描述该地区地震灾害区域宏观脆弱性的指标体系;基于该指标体系,以主成分分析作为定量分析方法中的主线,对该地区该类脆弱性空间变化的特点和规律进行了初步的定量概括和综合。结果表明:研究区地震灾害区域宏观脆弱性的空间变化主要表现为6种脆弱性模式,各模式反映的脆弱性空间差异在形式、幅度和主要驱动因素上各异;北京、天津、唐山和秦皇岛等大中城市的市区是研究区脆弱性最大的部位,大大高于全区脆弱性的平均状况,而较全区脆弱性平均状况明显小的地区则集中在京、津两地诸郊县,研究区其他地区的脆弱性状况大体围绕全区平均水平小幅波动     

华北地震时空多重分形的时间演化特征研究

应用分形理论,采用扩充数盒子方法EBA对华北地区1960~ 1982年发生的地震时间分布进行了多重分形谱计算。结果表明,在这期间该地区的几次较强地震在分形谱上都有明显的反映,强震年份的分形谱发生较大幅度变化,正q区D_q 值下降,负q区D_q 值上升,具有一定的预报意义。文中进而计算了几次较强地震的地震序列(1966年邢台、1969年渤海、1975年海城、1976年唐山)的空间多重分形谱,研究其随时间的演化现象,表明强震前后分形谱变动幅度较大,震群型地震序列和主震型地震序列的分形谱呈现出不同的变化趋势。     

利用非均匀细胞自动机模拟震级与应力降关系

为解释实际观测资料震源破裂过程与自相似(分形)模型的不一致性, 本文基于观测结果, 构建了由81×81个细胞单元组成二维非均匀断层模型, 并通过设计的细胞自动机模拟程序进行了模拟试验。 研究结果表明: 断层结构非均匀性是影响孕震过程特征的重要因素, 而且地震强度分布并非简单的自相似。 随着断层非匀质性增加, 破裂过程出现由相对的脆性破坏向塑性破坏特征变化的趋势。 利用细胞自动机不仅能较好地解释震级-频度关系中的大、 小震级段低头现象, 而且也可解释大震级事件具有相对恒定的应力降, 得到了与实际观测研究相一致的结果。     

Discrimination of earthquakes and explosions using multi-fractal singularity spectrums properties

A new method of discrimination of seismic records from earthquakes and explosions is proposed which is based on using properties of their multi-fractal singularity spectrums. The efficiency of the method is illustrated by analysing seismic records from the region of Aswan Dam in Egypt. Current pattern of seismicity in the Upper Egypt is composed by three types of records: tectonic earthquakes, reservoir-induced earthquakes and seismic events generated by quarry blasts. To discriminate quarry blasts from earthquakes of both natures, multi-fractal analysis of records were used. Singularity spectrum support width and multi-fractal generalised Hurst exponents were calculated for all seismic events in the selected data set from a given area. The linear Bayesian discriminator using these characteristics of seismic records provides correct classification for 93 % of earthquakes records and for 99 % of quarry blasts records.     

3D multi-fractal analysis of porous media using 3D digital images: considerations for heterogeneity evaluation

Pore structure heterogeneity is a critical parameter controlling mechanical, electrical and flow transport behaviour of rock. Multi-fractal analysis method was used for a heterogeneity comparison of three-dimensional rock samples with different lithology. Six real digital samples, containing three sandstones and three carbonates, were used. Based on the mercury injection capillary pressure test on these samples, we found that the carbonate samples are more heterogeneous than sandstones, but primary results of multi-fractal behaviours for all samples were similar. We show that if multi-fractal is used to evaluate and compare heterogeneity of different samples, one needs to follow some considerations such as (1) all samples must have the same size in pixel, (2) samples volume must be bigger than representative volume element, (3) multi-fractal dimensions should be firstly normalized to a determined porosity value and (4) multi-fractal results should be interpreted based on resolution of the imaging tool (effects of fine scale sub-resolution pores are missed). Results revealed that using normalized fractal dimensions, the real samples were divided to less and high heterogeneous groups. Moreover, the study of scale effect also showed that porous structures of these samples are scale invariant in a wide range of scales (from one to eight times bigger).     

The Precision Estimate of Multi-Fractal Methods of Time Sequence of Earthquakes

At present,there are many methods of calculating seismic time-fractal.However,there isn’t aquantitative result about the precision of every method.So,in this Paper,we use the digitalimitation of theoretic model to solve precision estimate problems of calculating the precision ofone dimension distribution of theoretic models with Cantor multi-fractal set,we obtained someresults as follows:(1)There exists many problems such as rules,numbers of samples,basicpoint selection,the diffence resulted from different methods and so on.(2)The fixed-massmethod(MAS)and the minimal spanning tree method(MST)can give good structure charac-teristics with different q value,while the counting-boxes method can’t.And the error of thefixed-radius method(RAD)in the range of-q is too big.(3)There are scale problems of rulesfor multi-fractal,it is objective reflection for non-rule area.(4)MST has the boundary prob-lem,while MAS and RAD don’t.(5)With increasing sample number,the precision of allfractal-dimension values becomes     

Impacts of meteorological variations on urban lake water quality: a sensitivity analysis for 12 urban lakes with different trophic states

Response of 12 urban lakes with different trophic states in Beijing to variations of meteorological factors was studied in this research. Monthly water quality parameters, including total nitrogen (TN), total phosphorus (TP), chlorophyll a, chemical oxygen demand (COD), biological oxygen demand (BOD), dissolved oxygen, and water temperature, were analyzed from 2009 to 2011. Results indicated that TN in the urban lakes did not exhibit significant response to meteorological variations owing to relatively lower TN concentration in the urban soil. For the highly eutrophic lakes, TP, chlorophyll a, COD, and BOD were positively correlated with precipitation, and negatively correlated with wind speed (p < 0.05). Chlorophyll a showed significant positive correlation with TP and temperature. Moreover, the abrupt increase of TP occurred in spring, which was associated with higher temperature induced internal phosphorus loading. On average, temperature/precipitation and wind speed/sunshine duration contributed to 10.7–43.8 and 8.3–19.2 % of the variations in water quality. In contrast, lakes with mesotrophication/light eutrophication did not show significant sensitivity to meteorological variations owing to their better buffer capacity and regulation effect of algae growth. Beijing is undergoing increased temperature and heavy rainfall frequency as well as decreased wind speed during the past five decades; the above results infer that water quality of most urban lakes of Beijing is becoming worse under this climate change trend. This study suggested that urban lakes with different trophic states will respond differently to global climate change, and highly eutrophic lakes might face big challenges of water quality deterioration and algae bloom.