水系结构的分形和分维——Horton水系定律的模型重建及其参数分析

基于标准分形水系等级序列的镜象对称性，重建水系构成定律：从Horton第一，第二定律出发，导出关于河流长度与位序关系的三参数Zipf模型，从Horton第二，第三定律出发，导出广义的Hack定律；从Horton第一，第三定律出发，导出关于河流长度一流域面积关系的异速生长方程，根据上述数学变换结果建立了水系分维方程式，澄清了不同空间，不同类型的各种维数之间的数理关系。     

中国旱涝灾害的分形结构

基于分形理论在中国旱涝灾害研究方面所存在的问题,首先系统地分析了中国华北区、西北区等不同区域和松花江、长江等不同流域旱涝灾害的分形结构,其次以唐山市为例系统分析了同一地点不同等级旱涝灾害分维的时序变化及其关系,进而探讨了以分维为中介参数在旱涝灾害与其影响因素之间建立定量化经验关系的可能。研究结果表明,中国旱涝灾害具有客观的分形结构,分维是表征中国旱涝灾害发生特征的良好参数;在此基础上,系统地计算出了中国旱涝灾害的分维值、分析了唐山市不同等级旱涝灾害分维的时序变化关系,并建立了辽河、长江等流域水系空间维数与流域洪涝分维之间的定量关系式DF=3．6179DR-4．0242(式中DR为流域水系空间维数,DF为流域洪涝分维)。     

西藏伦坡拉盆地丁青湖组油页岩地球化学特征及其地质意义

对伦坡拉盆地丁青湖组油页岩进行了系统采样和地球化学分析,结果显示该地区油页岩SiO₂含量整体较低,K₂O/Na₂O值较高,Al₂O₃+Fe₂O₃为6.43%～10.28%,Al₂O₃/（Na₂O+K₂O）为1.7～4.91,含有一定的铁镁质组分和较多的稳定组分;化学蚀变指数CIA为65～85,Th/U值多集中在0.97～3.38,表明油页岩源区经历了相对中等的风化作用,反映温暖、湿润的气候条件;Sr/Ba值为0.45～0.82,V/（V+Ni）值为0.46～0.68,Th/U平均值为0.59,表明丁青湖组油页岩形成于淡水缺氧的湖泊之中。温暖湿润的气候、丰富的生物来源及淡水缺氧的沉积环境是伦坡拉盆地丁青湖组油页岩形成的重要条件。     

任楼矿井72煤层断层构造分形特征研究

利用分形理论,对安徽皖北任搂煤矿72煤层断层分形特征进行了研究,计算了不同构造分区的维数。研究发现构造复杂性不同及断裂性质的不同其分形维数也有所不同,构造简单,断层分维数小,而构造复杂区,断层分为数相对较大;剪切断裂带具有较低的分维值,张扭性断裂带分维值较高。     

黄河硫同位素组成与青藏高原隆起

黄河水的平均δ^３4ＳＯ₄^{2-值为＋８．４‰，是世界主要大河中硫同位素组成最重的河流；从上游至下游，河水的矿δ３4ＳＯ₄2-值规律性地逐渐增重，在龙门—三门峡河段达最大值。这反映了由于青藏高原隆起而引起的中国西北地区气候干燥趋势及随后出现的沙漠化、古盐湖蒸发岩的形成和黄土堆积环境对黄河水硫同位素组成的控制性影响。}     

长江下荆江段分形学特征与河道演化

采用盒数维法对长江下荆江各不同时期河道岸线的分形学特征进行探讨。研究表明,下荆江河道岸线的盒数维介于1078~123之间,较黄河、海河、滦河等河流的维数要小,相当于黄河下游和长江下游平原区的维数,反映出下荆江河段是高成熟度的河段。这与长江中游地区的其他河段不相称,可能是由江汉-洞庭湖平原长期沉降所造成。河道裁弯之后,河道岸线由复杂变简单,分维数显著减少。裁弯取直事件发生在分维数值为119~123之间,即分维数可作为河道突变事件发生的一个预警参数。     

丹江口水库库区及周边地区河网形态、地貌特征及构造活动性意义

河流作为构造-气候相互作用最为敏感的地貌单元,记录了丰富的水系演化、构造变形以及气候变化等信息。通过研究河流的形成与演化过程来阐述区域地貌和构造活动特征是构造地貌研究的一个突破点,河流形态的空间变化是阐述河流形成与演化特征最为直观有效的方法。丹江口水库库区地貌特征复杂、地质灾害频发、差异性构造活动较为强烈,是开展构造地貌研究的理想场所。通过对丹江口水库库区及周边地区河流形态特征、地貌特征及构造活动特征等进行综合分析发现,河网分维值空间特征与区域内构造活动性较强的断裂的空间分布高度吻合,构造活动性较强的断裂带及周边地区,河网受到构造活动的影响,发育不成熟,河网分维值出现低值,分维值均小于1.115;构造活动性较弱的断裂带及周边地区,河网发育过程中未受到构造活动的影响,发育较成熟,河网分维值高,分维值均大于1.25;而河网分维值空间变化与地形坡度、平均高程等地貌参数相关性不显著。因此,区域构造活动性特征是河网形态空间变化控制的关键因素。利用河网形态的分维特征量化区域构造活动的强弱及各区域构造活动的差异,对于河流的形成与演化、构造活动性及预测地质灾害的发生等方面的研究都有一定的参考价值。      

天然裂缝空间分布的分维与多分维特征——理论分析和实际应用

本文应用康托集理论对美国纽约州西部阿巴拉契亚平原地区27个野外点上发育的天然裂缝的空间分布特征进行了研究。主要新发现如下:①天然裂缝间距具有多分维的特点。在相对小尺度范围内,平均分维数为0.15,反映出裂缝在小尺度上的不规则性和丛集性;在相对大尺度范围内,平均分维数为0.52,表明裂缝在大尺度上倾向于规则性和均匀性;②分维数随裂缝优势方向的变化而发生变化,这一现象可解释为是先存裂缝与后期裂缝相互作用的结果,也可解释为裂缝形成时由应力强度不同所致;③本项研究提出的裂缝多分维分析方法可有效地开展构造复杂区(尤其是对野外观察不到多期裂缝交     

陕甘宁接壤区气候暖干化及其生态环境意义

应用陕甘宁接壤区1951-2000年气温、降水及1956-2000年陕甘宁接壤区 7条主要河流径流量实测记录,在实地调研的基础上对气象数据和水文数据分析后得出结论,陕甘宁接壤区近年来气候呈现暖干化趋势,全区增温线性倾向值为 0．194℃／10 a,高于全球近百年的趋势（0．05℃／10 a）,区内增温趋势强弱差异显著。陕甘宁接壤区气候变干表现在 2个方面：①年降水量减少;②地表径流量减少。降水线性倾向值平均为－1．0759 mm／a,地表径流总量1956-2000年减少速率为 0．4844 m³／a。陕甘宁接壤区生态环境在暖干化的气候背景下继续恶化,生态贫水化严重,水土流失加剧,沙漠扩大。     

水化学和钙华碳氧稳定同位素在古环境重建中的应用--以贵州荔波小七孔景区响水河为例

文章报道了响水河河水的现场监测结果,得到响水河河水的Ca²+和HCO^-₃非常低,这明显与河床中大规模钙华的存在和景区内发育的茂密植被不匹配;并仔细观察发现,钙华表面有被侵蚀的痕迹,如溶蚀槽和溶蚀坑等,这说明目前所见钙华可能是过去环境条件下的产物。根据钙华碳氧稳定同位素组成特征的分析得出:近4000年来,该地区总的气候环境变化趋势是4000～3400aB.P.为相对温暖湿润期,植被生长好,为良性生态期;3400～2000aB.P.前期仍比较温暖但干燥,后期到2000aB.P.左右变得比较凉爽,从这一冷期到大致900aB.P.前后,气候有些波动,但幅度较小,夹有冷暖干湿的交替;而900aB.P.至今,钙华碳氧稳定同位素值的急剧增加,反映出气候的冷干和源区人类活动加剧造成的水土流失增加,岩溶石漠化加重,生态朝恶化方向发展     

An assessment of seismicity parameters in northwest Himalaya and adjoining regions

In this study, an assessment of seismicity parameters in the northwest Himalaya and adjoining regions using an earthquake catalog from India Meteorological Department covering a period from June 1, 1998 to June 30, 2011 has been carried out. The spatial distributions of seismicity parameters, namely magnitude of completeness, M _C, a value, b value, and correlation fractal dimension, D _C, are estimated for the studied region. The M _C, a, and b values are found to be 2.5, 4.601, and 0.83, respectively. Despite significant gaps, the spatial distributions of a and b values are seen to follow similar trend and are found scattering in between Main Boundary Thrust (MBT) and South Tibet Detachment, adjoining areas of Mahendragarh-Dehradun Fault (MDF), Delhi-Haridwar Ridge (DHR) and Moradabad Fault (MF), and the southern flank of Karakoram Fault and Indus-Tsangpo Suture Zone. The estimated spatial distribution of b and a values is within 90 % of confidence level, thereby indicating non-uniform stress accumulation or higher rock fracturing density in the studied region caused by strong tectonization following several earthquakes. Negative correlation between low b value and high D _C is observed predominantly in the region between the MBT and Munsiari Thrust or Main Central Thrust-I of Garhwal and Kumaon Himalaya, adjoining zones of MDF, DHR, and MF of Indo-Gangetic plain, and the eastern flank of the studied region, suggesting the presence of asperities in the zone. At the same time, active creeping process can be inferred in between the MBT and Main Central Thrust of Garhwal Himalaya and the surrounding areas of Shimla region of the Himalayan arc to the northwestern part of the studied region from the positive correlation between b value and D _C. The results indicate that the structural heterogeneity caused by different stress accumulation and rock fracturing densities exists due to continuous tectonic adjustments between different geomorphic features of the studied region. An attempt has also been made to classify the studied region into smaller seismic zones by observing the spatial patterns of b value and D _C that are fractal properties of the observed seismicity, along with the prevalent fault networks.     

地质统计学及其在第四纪研究中的应用

地质统计学是数学地质领域最为活跃而实用的分支,它是以区域化变量理论为基础,以变异函数为基本工具,研究那些在空间分布上既具有随机性又具有结构性的自然现象的科学。在第四纪研究中的很多特征(变量)均可看成区域化变量进行地质统计学分析。作者在讨论了经典概率论及数理统计方法简单地应用于第四纪研究可能出现的问题后,着重介绍了用于第四纪研究中的若干地质统计学方法及基本理论,同时,对地质统计学方法应用于第四纪研究中的前景进行了分析。     

非等轴颗粒付林图解

非等轴颗粒付林图解由直线a=1、b=1、a=b和曲线a2b=1、ab2=1分割成10个微区,并对应于不同的e_x、e_y、e_z组合和应变类型。这些直线和曲线分别对应于特殊的e_x、e_y、e_z组合和岩石应变类型。岩石的应变类型有18种。函数a.b的表征方程有4种类型,并分别表征直线a=1/k₁和b=1/k₂所分割的4个区间。a,b表征方程的确定取决于岩石总的变形行为。此图解可用于非等轴颗粒标志体应变测量和应变类型的确定和图示,文章给出了应用实例.      

The use of the fractal dimension to quantify the morphology of irregular-shaped particles

For several decades, sedimentologists have had difficulty in obtaining an efficient index of particle form that can be used to specify adequately irregular morphology of sedimentary particles. Mandelbrot has suggested the use of the fractal dimension as a single value estimate of form, in order to characterize morphologically closed loops of an irregular nature. The concept of fractal dimension derives from Richardson's unpublished suggestion that a stable linear relationship appears when the logarithm of the perimeter estimate of an irregular outline is plotted against the logarithm of the unit of measurement (step length). Decreases in step length result in an increase in perimeter by a constant weight (b) for particles whose morphological variations are the same at all measurement scales (self-similarity). The fractal dimension (D) equals 1.0-(b), where b is the slope coefficient of the best-fitting linear regression of the plot. The value of D lies between 1.0 and 2.0, with increasing values of D correlating with increasing irregularity of the outline. In practice, particle outline morphology is not always self-similar, such that two or possibly more fractal elements can occur for many outlines. Two fractal elements reflect the morphological difference between micro-scale edge textural effects (D₁) and macro-scale particle structural effects (D₂) generated by the presence of crenellate-edge morphology (re-entrants). Fractal calibration on a range of regular/irregular particle outline morphologies, plus examination of carbonate beach, pyroclastic and weathered quartz particles indicates that this type of analysis is best suited for morphological characterization of irregular and crenellate particles. In this respect, fractal analysis appears as the complementary analytical technique to harmonic form analysis in order to achieve an adequate specification of all types of particles on a continuum of irregular to regular morphology.     

辽河科尔康油田断裂分形特征与油气关系

本文运用分形理论对张强凹陷科尔康油田沙海组下段顶(T₁)、九佛堂组顶(T₂)和义县组顶(T₃)3个反射层断裂系统的分布特征进行了研究,发现在标尺范围(8-0.5cm)内断裂系统具有良好的统计自相似性,不同的研究对象具有不同的分维值(D),而分维值的大小体现了断裂系展布的复杂性。断裂的规模、数目及在相同标尺下的面密度直接影响数盒子数法计算的分维值,不同子区域断裂系统的分维值D与其断裂所占断裂总数的百分比呈良好的正相关关系。不同储集类型的子区域对比表明,东区沙海组下段顶(T₁)分维值高于西区,而西区义县组顶(T₃)分维值高于东区。与油田已知油气分布特征对比后,发现并证实油田内子区域分维值大,油田丰度(含油面积或流体产能)就大。含油气盆地这种内在对应关系,为研究油气聚集和分布规律、评价和预测油气田提供了一种新思路.      

Quantification of Aperture and Relations Between Aperture,Normal Stress and Fluid Flow for Natural Single Rock Fractures

Accurate quantification of rock fracture aperture is important in investigating hydro-mechanical properties of rock fractures. Liquefied wood’s metal was used successfully to determine the spatial distribution of aperture with normal stress for natural single rock fractures. A modified 3D box counting method is developed and applied to quantify the spatial variation of rock fracture aperture with normal stress. New functional relations are developed for the following list: (a) Aperture fractal dimension versus effective normal stress; (b) Aperture fractal dimension versus mean aperture; (c) Fluid flow rate per unit hydraulic gradient per unit width versus mean aperture; (d) Fluid flow rate per unit hydraulic gradient per unit width versus aperture fractal dimension. The aperture fractal dimension was found to be a better parameter than mean aperture to correlate to fluid flow rate of natural single rock fractures. A highly refined variogram technique is used to investigate possible existence of aperture anisotropy. It was observed that the scale dependent fractal parameter, K _v, plays a more prominent role than the fractal dimension, D _a1d, on determining the anisotropy pattern of aperture data. A combined factor that represents both D _a1d and K _v, D _a1d × K _v, is suggested to capture the aperture anisotropy.     

Fractal analysis of major faults in India on a regional scale

The seismicity of a region is implicit of the causal faulting mechanisms and geodynamic diversity of the subsurface regime nucleating earthquakes of different magnitudes, several of which may be as devastating as ones historically reported in global perspective of tectonic complexity as in the case of India. Fractal analysis using box-counting method for the major fault networks across the country estimates fractal dimension, D_f, values to be varying between 0.88 and 1.36. The fault segments in parts of northwest Himalayas, northeast India and Indo-Gangetic plains, are observed to be associated with higher D_f values implicating high seismicity rates. On the other hand, low D_f values in the peninsular India indicate isolated pattern of the underlying faults. The fractal dimension is observed to be indicative of predominant faulting types — higher values conforming to thrust faulting mechanism while lower to strike slip tectonism.     

Das Verhalten des Olivins als Gefügekorn in einigen Olivingesteinen

Zusammenfassung Cebänderte Olivingesteine aus Bursa bei Topuk (Kleinasien) und alpine Olivintektonite aus dem Nonsberg und Ultental (südöstliche Ortleralpen) werden hinsichtlich ihres Olivingefüges untersucht. Eine an Ultentaler und Nonsberger Olivintektoniten bisher nicht beschriebene B-Achsenregelung wird mit der bisher ebenfalls nicht beschriebenen und von der ersteren abweichenden Olivinregelung an den Olivingesteinen aus Bursa konfrontiert.Nach der im Innsbrucker Institut üblichen Bezeichnungsweise werden die kristallographischen Achsen mit dem Index des betreffenden Minerals also z. B. o=Olivin bezeichnet, also a₀, b₀, c₀ Koordinaten, welche sich beispielsweise auf zwei sich kreuzende b-Achsen b₁ und b₂ beziehen, erhalten die Indizes, a₁, b₁, c₁, a₂, b₂, c₂. Wo es sich um Koordinaten des Gefüges handelt, ist dies ausdrücklich betont.Mit 12 Gefügediagrammen im Text.