Analysis on structure of igneous formation with fractal dimension of logs

Reflecting the structure of igneous formation by calculating fractal dimension of logs, the fractal di- mension of pyroclastic is larger than lava. Structure of pyroclastic is more complicated than that of lava, so reflecting the structure of igneous formation＇s complexity with fractal dimension is feasible. It is feasible to reflect the structure of igneous formation＇s complexity with fractal dimension.     

低渗透碎屑岩储层孔隙结构分形维数计算方法——以川中地区须家河组储层41块岩样为例

为对比基于含水饱和度和汞饱和度2种方法计算低渗透碎屑岩储层孔隙结构分形维数的优劣性,分别采用2种方法对川中地区须家河组41块储集岩的毛细管压力曲线进行分形维数计算.结果表明:采用汞饱和度计算的孔隙结构分形维数与排驱压力、分选因数等表征储层孔隙结构的参数相关性较好.随着岩样分形维数增大,排驱压力增大、分选因数减小,相关性明显.采用含水饱和度计算的孔隙结构分形维数与排驱压力、分选因数等相关性较差.在条件许可时,可利用恒速压汞实验计算储集岩孔隙结构分形维数.     

Heterogenous zircons from Mesozoic igneous rocks in the North China Craton and their tectonic implications

Based on a synthesis of zircon inheritance from Mesozoic igneous rocks in the eastern portion of the North China Craton (NCC) , it is proposed that inherited zircons with Neoproterozoic ages identified from these rocks are of a heterogenous derivation from the Yangtze /South China block, rather than from the NCC itself. The mechanism that introduces these zircons incorporated into the NCC is likely by tectonic underplating during the Triassic continental subduction of the Yangtze block beneath the NCC. Tectonic addition of abundant crustal materials represented by the heterogenous zircons into the NCC, probably along Moho or weak interfaces within the NCC's crust, led to the crustal thickening in the NCC. These heterogenous materials, either as ( partial) source rocks or as contaminants of the magmas generated during an extension environment following the crustal thickening, were reworked and therefore have significant contribution to petrogenesis of the Mesozoic igneous rocks. The crustal thickening resulted from the tectonic underplating, as indicated by the distribution extent of the heterogenous zircons, is spatially similar to that of the lithospheric thinning, with both mainly occurring in the eastern segment of the NCC. This is probably suggestive of an intrinsic relation between the thickening and thinning events during the Mesozoic evolution of the NCC.     

Heterogenous zircons from Mesozoic igneous rocks in the North China Craton and their tectonic implications

Based on a synthesis of zircon inheritance from Mesozoic igneous rocks in the eastern portion of the North China Craton （NCC） , it is proposed that inherited zircons with Neoproterozoie ages identified from these rocks are of a heterogenous derivation from the Yangtze/South China block, rather than from the NCC itself. The mechanism that introduces these zircons incorporated into the NCC is likely by tectonic underplating during the Triassic continental subduction of the Yangtze block beneath the NCC. Tectonic addition of abundant crustal materials represented by the heterogenous zircons into the NCC, probably along Moho or weak interfaces within the NCC＇s crust, led to the crustal thickening in the NCC. These heterogenous materials, either as （partial） source rocks or as contaminants of the magmas generated during an extension environment following the crustal thickening, were reworked and therefore have significant contribution to petrogenesis of the Mesozoic igneous rocks. The crustal thickening resulted from the tectonic underplating, as indicated by the distribution extent of the heterogenous zircons, is spatially similar to that of the lithospheric thinning, with both mainly occurring in the eastern segment of the NCC. This is probably suggestive of an intrinsic relation between the thickening and thinning events during the Mesozoic evolution of the NCC.     

RESEARCH ON FRACTAL CHARACTERISTICS OF URBAN TRAFFIC NETWORK STRUCTURE BASED ON GIS

Traffic network is an importance aspect of researching controllable parameters of an urban spatial morpholo-gy. Based on GIS, traffic network structure complexity can be understood by using fractal geometry in which thelength-radius dimension describes change of network density, and ramification-radius dimension describes complexity andaccessibility of urban network. It is propitious to analyze urban traffic network and to understand dynamic change processof traffic network using expanding fractal-dimension quantification. Meanwhile the length-radius dimension and ramifica-tion-radius dimension could be regard as reference factor of quantitative describing urban traffic network.     

Log evaluation of fractured igneous reservoirs in Songliao Basin

The petrophysical parameters are bad in most igneous reservoirs of Songliao Basin because of the very low porosity and permeability. The evaluation of igneous reservoirs has not been fully studied so far. The current technique of formation evaluation and interpretation used in sedimentary formations face a series of problems and difficulties. In this study, The PCA was used to identify lithology, a multi-mineral model "QAPM" was proposed. "Surface effect" must be considered when evaluating saturation. A software "SIMPLE" was developed and was used to deal with the logging data in over 70 wells with good results were achieved.     

Log evaluation of fractured igneous reservoirs in Songliao Basin

The petrophysical parameters are bad in most igneous reservoirs of Songliao Basin because of the very low porosity and permeability. The evaluation of igneous reservoirs has not been fully studied so far. The current technique of formation evaluation and interpretation used in sedimentary formations face a series of prob- lems and difficulties. In this study, The PCA was used to identify lithology, a multi-mineral model “QAPM” was proposed. “Surface effect” must be considered when evaluating saturation. A software “SIMPLE” was developed and was used to deal with the logging data in over 70 wells with good results were achieved.     

ON FRACTAL MECHANISM OF COASTLINE —A Case Study of China

MANDELBROT enunciated the uncertainty of the length of a coastline in his paper“How long is the coast-line of Britain?“ published in “Science“in 1967.The fractal concept was presented for the first time in that paper and has been applied to many fields ever since.According to the fractal theory and conditions of fractal research of coastline,the controls of faults and biologic function on the fractal character of coastline are preliminarily discussed on the basis of GIS in this paper.Finally,some significant conclusions are drawn:1)the faults control the basic trends of coastlines of two study areas;2)the fractal dimension of coastline of Taiwan is smaller than that of Changle-Lufent,because the faults of Taiwan more intensely control the trend and fractal dimension of the coastline;3)the larger the fractal dimension of the faults or the major faults ,the more the controlling effect of them on the trend and fractal dimension of coastline;4)the larger fractal dimension of the coastline of Changle-Lufeng indicates that the biologic function intensely shapes the coastline .In a word ,the controls of faults and biologic function on the fractal character of coastline are discussed with a case study of China in this paper,it can be seen that faults and biologic function both have influence over the trend and fractal dimension of coastline,the fractal mechanism of coastline of two study areas may be so.     

A FRACTAL STUDY ON URBAN SYSTEM IN NORTHEAST CHINA

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INFLUENCE OF SERIES OF SQUARE GRIDS ON FRACTAL DIMENSIONS—A Case Study of Mountains of China＇s Mainland

MANDELBROT enunciated the uncertainty of the length of a coastline in his paper “How long is the coastline of Britain?” published in Science in 1967. The fractal concept was presented for the first time in that paper and has been applied to many fields ever since. Although fractal dimensions of lots of phenomena were calculated by the box-counting method, the quantitative influence of series of square grids on them is ignored. The issue is systematically discussed as a case study of the mountains of China‘s Mainland in this paper. And some significant conclusions are drawn as follows: 1) Although the fractal character objectively exists in the mountains of China‘s Mainland, and it does not vary with the changes of series of square grids, the fractal dimensions of the mountains of China‘s Mainland are different with these changes. 2) The fractal dimensions of the mountains of China‘s Mainlandvary with the average lengths of sides of series of square grids. The fractal dimension of the mountains of China‘s Mainland is the function of the average length of side of square grid. They conform to the formula D=f(r) (where D is the fractal dimension, and r is the average length of side of square grid). 3) Different dots of data collection can affect the fractal dimension of the mountains of China‘s Mainland. 4) The same range of length of side of square grid and dots of data collection can ensure the comparison of fractal dimensions of the mountains of China‘ s Mainland. The research is helpful to get the more understanding of fractal and fractal dimension, and ensure that the fractal studies would be scientific.     

Silicon and oxygen isotopic composition of igneous rocks from the eastern Manus Basin

This paper reports silicon and oxygen isotopes of 20 kinds of igneous rocks and their major elements from the eastern Manus Basin. Combining silicon and oxygen isotopic data from other studies, we suppose that both δ30Si and δ18O values increase with the increasing of SiO2 content. It means that the fractionation of silicon and oxygen isotopes are affected by the silica content. The positive correlation between CaO/Al2O3 ratios and MgO and that between Si/Al and SiO2 content indicate that clinopyroxene is the predominant mineral phase in our samples. We suppose that the fractionation of silicon and oxygen isotopes are influenced by mineral fractional crystallization. Probably, it is due to their different silicon and oxygen bridges. In this study, the δ30Simean value=-0.17‰±0.17‰ and δ18Omean value= +6.07‰±0.57‰ are higher than normal δ30Si and δ18O values of mantle, and we propose that these igneous rocks in the eastern Manus Basin are affected by hydrothermal alteration.     

一种基于分块的分形图像压缩方法

分形编码具有高压缩比的特点,但在编码过程中其匹配搜索时间开销巨大.提出一种基于分块的分形图像压缩方法:依据人眼视觉特性在PSNR变化不大的情况下,图像主观质量感受不明显的特点,将图像在空域分割为若干相对较小的块,对感兴趣区可采取一分为四的方法进一步减小块的大小,然后对每个块分别进行分形编码,并重构.结果表明,在PSNR略有降低的情况下,编码的匹配搜索时间大幅减少,同时重构图像的主观质量并没有明显降低.     

Development and application of geochemical data processing system based on fractal theory

GC-GIS system is a geochemical data processing system based on fractal theory. The system realized quantity statistics function by calling Surfer and MapInfo software, and it is compiled with Visual Ba...     

Study on the fractal character of magnetic anomaly fields and the delineation of tectonic elements in the South China Sea

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基于CT扫描红层砂岩孔隙多标度分形维数的确定方法

岩石作为一种典型的多孔介质,其内部孔隙结构、形态特征极为复杂,运用常规线性系统内参数描述较为困难,因而采用非线性系统内分形维数这一参数来定量表征孔隙结构的非线性分布特征较为合适。岩石内部孔隙结构分布具有统计意义上的分形特征,因此分形维数的确定对于定量表征孔隙结构分布规律,以及揭示岩石各种力学行为与物理力学指标有着重要意义。将图像处理与阈值分割、分形理论和数理统计相结合,针对CT扫描切片图像,三维重建孔隙结构空间分布模型,计算Hausdorff测度空间下孔隙结构分布盒维数与集束维数。同时,针对孔隙结构空间分布复杂程度的定量表征,提出体素盒维数与圆柱体空间集束维数假想,并通过多种数理统计方法进行假设检验。最后,指出孔隙结构分布是一种多标度分形模型,仅仅单个维数无法描述其全部细节特征,需采用多重分形谱来更为全面表征孔隙分布的细观特征。研究结果表明,Hausdorff测度空间下的平面盒维数可较为全面表征平面孔隙分布特征,但对于针对灰度CT图像构建的体素盒维数可替代传统意义下定义的盒维数,在细观尺度下能更可靠、准确、全面地定量表征孔隙体积分布规律; 集束维数实质是用来定量表征孔隙位置分布规律,若等于欧氏维数,则表明孔隙位置分布具有随机性。      

Long-term trend and fractal of annual runoff process in mainstream of Tarim River

Based on the time series data from the Aral hydrological station for the period of 1958-2005, the paper reveals the long-term trend and fractal of the annual runoff process in the mainstream of the Tarim River by using the wavelet analysis method and the fractal theory. The main conclusions are as follows： 1） From a large time scale point of view, i.e. the time scale of 16 （24） years, the annual runoff basically shows a slightly decreasing trend as a whole from 1958 to 2005. If the time scale is reduced to 8 （23） or 4 （22） years, the annual runoff still displays the basic trend as the large time scale, but it has fluctuated more obviously during the period. 2） The correlation dimension for the annual runoff process is 3.4307, non-integral, which indicates that the process has both fractal and chaotic characteristics. The correlation dimension is above 3, which means that at least four independent variables are needed to describe the dynamics of the annual runoff process. 3） The Hurst exponent for the first period （1958-1973） is 0.5036, which equals 0.5 approximately and indicates that the annual runoff process is in chaos. The Hurst exponents for the second （1974-1989） and third （1990-2005） periods are both greater than 0.50, which indicate that the annual runoff process showed a long-enduring characteristic in the two periods. The Hurst exponent for the period from 1990 to 2005 indicates that the annual runoff will show a slightly increasing trend in the 16 years after 2005.     

GIS-based landslide susceptibility mapping using hybrid integration approaches of fractal dimension with index of entropy and support vector machine

The loess area in the northern part of Baoji City, Shaanxi Province, China is a region with frequently landslide occurrences. The main aim of this study is to quantitatively predict the extent of landslides using the index of entropy model(IOE), the support vector machine model(SVM) and two hybrid models namely the F-IOE model and the F-SVM model constructed by fractal dimension. First, a total of 179 landslides were identified and landslide inventory map was produced, with 70%(125) of the landslides which was optimized by 10-fold crossvalidation being used for training purpose and the remaining 30%(54) of landslides being used for validation purpose. Subsequently, slope angle, slope aspect, altitude, rainfall, plan curvature, distance to rivers, land use, distance to roads, distance to faults, normalized difference vegetation index(NDVI), lithology, and profile curvature were considered as landslide conditioning factors and all factor layers were resampled to a uniform resolution. Then the information gain ratio of each conditioning factors was evaluated. Next, the fractal dimension for each conditioning factors was calculated and the training dataset was used to build four landslide susceptibility models. In the end, the receiver operating characteristic(ROC) curves and three statistical indexes involving positive predictive rate(PPR), negative predictive rate(NPR) and accuracy(ACC) were applied to validate and compare the performance of these four models. The results showed that the F-SVM model had the highest PPR, NPR, ACC and AUC values for training and validation datasets, respectively, followed by the F-IOE model.Finally, it is concluded that the F-SVM model performed best in all models, the hybrid model built by fractal dimension has advantages than original model, and can provide reference for local landslide prevention and decision making.     

FRACTAL ANALYSIS APPLIED TO SPATIAL STRUCTURE OF CHINA＇S VEGETATION

Based on the fractal theory, the spatial structure of China＇s vegetation has been analyzed quantitatively in this paper. Some conclusions are drawn as the following. 1） The relationships between size and frequency of patch area and patch shape index exist objectively for China＇s vegetation. 2） The relationships between perimeter and area exist objectively for China＇s vegetation. 3） The fractal dimension of evergreen needleleaf forests on mountains in subtropical and tropical zones is the largest, while the smallest for deciduous broadleafand evergreen needleleaf mixed forests in temperate zone, reflecting the most complex spatial structure for evergreen needleleaf forests on mountains in subtropical and tropical zones and the simplest for deciduous broadleaf and evergreen needleleaf mixed forests in temperate zone. 4） The fractal dimensions of China＇s vegetation types tend to decrease from thc subtropics to both sides. 5） The stability of spatial structure of deciduous broadleaf and evergreen needleleaf mixed forests in temperate zone is the largest, while the smallest for double-cropping rice, or double-cropping rice and temperate-like grain, and tropical evergreen economic tree plantations and orchards, reflecting the steadiest for deciduous broadleaf and evergreen needleleaf mixed forests in temperate zone and the most unstable for double-cropping rice, or double-cropping rice and temperate-like grain, and tropical evergreen economic tree plantations and orchards in spatial structure. 6） The stability of spatial structure of China＇s vegetation tends to decrease from the temperate zone to both sides, it is significantly pertinent to understand the formation, evolution, dynamics and complexity rule of ecosystem of vegetation.     

The application of fractal study in forecasting flood calamities in Wuzhou, Guangxi

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基于原子力显微镜表征的含油储层微观孔隙结构分析及应用

为研究岩心微观孔隙结构在强碱三元复合驱替过程中的变化特征,以大庆油田南5-4-检725井855.0m处岩心为对象,通过原子力显微镜观察岩心形貌特征,定量分析孔喉宽度和深度;分析驱替过程中岩心样品的面孔率、孔喉宽度和深度、分形维数等参数变化反映的微观孔隙结构变化规律.结果表明:原子力显微镜获得的图像可以真实反映储层岩石微观形貌特征,储层微观孔隙结构具有二段式分形特点.微观孔隙结构变化特征在驱替初期,主要表现为岩石粒间颗粒运移;在驱替中后期,主要表现为强碱三元驱替剂与岩石相互作用,生成驱替剂残留或其他产物.该研究结果对分析强碱三元复合驱替后剩余油分布规律、制定后续开发方案具有指导意义.