首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 415 毫秒
1.
Fractal trees as a model for drainage systems are described in its generalized non-homogeneous form from the viewpoint of fractal geometry. Box covering techniques are used to show the numerical equivalence between the Hausdorff-Besicovitch dimension and the similarity dimension of the fractally-dominant dust formed by the sources. In this way, the similarity relationD=log (N)/log (1/r) is reinterpreted in terms of bifurcation and length ratio (r B andr L ) asD=log (r B )/log (r L ). We test this relation for non-homogeneous exact fractal trees and two natural drainage systems. The fact thatr B andr L are common parameters in quantitative geomorphology allows a trivial stimation of the fractal dimension of well-known drainage basins.  相似文献   

2.
The perimeter-area fractal model and its application to geology   总被引：14，自引：0，他引：14  
Perimeters and areas of similarly shaped fractal geometries in two-dimensional space are related to one another by power-law relationships. The exponents obtained from these power laws are associated with, but do not necessarily provide, unbiased estimates of the fractal dimensions of the perimeters and areas. The exponent (DAL) obtained from perimeter-area analysis can be used only as a reliable estimate of the dimension of the perimeter (DL) if the dimension of the measured area is DA=2. If DA<2, then the exponent DAL=2DL/DA>DL. Similar relations hold true for area and volumes of three-dimensional fractal geometries. The newly derived results are used for characterizing Au associated alteration zones in porphyry systems in the Mitchell-Sulphurets mineral district, northwestern British Columbia.  相似文献   

3.
Summary Many rock mass classification systems exist to assist the engineer in assessing the rock support requirements for underground design. On-going research in this area is directed at attempting to utilize the fractal dimension and the acoustic emission response of the tuffs at the Nevada Yucca Mountain to further aid in rock mass classification. Acoustic emission response is shown to be correlated with the porosity of the sample. Engineering behaviour of the rock varies dramatically with porosity; events and peak amplitude offer a means to distinguish between fracture porosity and pore porosity and consequently the engineering behaviour of the rock. Fractal dimension is used to characterize the roughness of fracture surfaces. Two fractal dimension calculation methods, one based on the semi-variogram for the surface and the other based on the use of dividers, are applied for this purpose. The divider method is shown to resolve deviation from a straight line; the semi-variogram method is shown to identify statistical similarity to various types of noise.Nomenclature D fractal dimension - AE acoustic emission - b b-value determined from log(frequency) against log(amplitude) plots - (h) semi-variogram function - h lag distance for semi-variogram function - H an exponent term related to fractal dimension asD=2 –H  相似文献   

4.
The aim of the presented study is to assess the fractal dimension (D) and the geometrical characteristics (length and width) of the landslides identified in North of Tehran, Iran. At first, the landslide locations (528 landslides) were identified by interpretation of aerial photographs, satellite images and field surveys, and then to calculate the fractal dimension (D), we used the computer programming named as FRACEK. In the next step, geometrical characteristics of each landslide such as length (L) and width (W) were calculated by ArcGIS software. The landslide polygons were digitized from the mentioned landslide inventory map and rotated based on movement direction. The fractal dimension for all landslides varied between 1.665 and 1.968. Subsequently, the relationship between the length/width ratios and theirs fractal D values for 528 landslides was calculated. The results showed that correlation coefficients (R), which are different regression models such as exponential, linear, logarithmic, polynomial, and power, between D and L/W ratio are relatively high, respectively (0.75, 0.75, 0.76, 0.78, and 0.75). It can be concluded that the fractal dimension values and geometry characteristics of landslides would be useful indices for the management of hazardous areas, susceptible slopes, land use planning, and landslide hazard mitigation.  相似文献   

5.
《Engineering Geology》2002,63(1-2):141-155
Fractal theory is used in the present study to develop a more reliable method for rock mass characterization. Field studies have been carried out in opencast mines of dolomite, limestone, fluorite; sandstone and shale in coalmines. Fractal dimension of blasted fragments (Dfrag) and in situ rock blocks (Din situ) is calculated using size distribution curves according to Schumann's model. Based on the co-relation between Uniaxial Compressive Strength (UCS) and Dfrag, it is observed that change in fractal dimension is nominal beyond the UCS value of 20. From the co-relation between Bieniawaski's Rock Mass Rating (RMR) and Din situ, it is found that there is a sharp increase in fractal dimension for RMR greater than 40. Co-relation between RMR and Dfrag/Din situ shows that as RMR increases, Dfrag/Din situ ratio decreases. Rock mass classification based on fractal geometry is suggested.  相似文献   

6.
For ABO 4 type ternary oxides, high pressure phase transformations known up to the present are reviewed, and an attempt is made to explain and predict crystal structures of their high pressure phases. When ABO 4 type compounds are plotted based on the two variables, k=r A /r B and t=(r A +r B )/2r O, where r A , r B , and r O are the ionic radii of A and B cations and divalent oxygen, they can be classified into the major structure types. It is found empirically that a compound basically transforms to the structure type isostructural with a compound lying in a classified area with the same k and larger t values in the diagram.  相似文献   

7.
The aim of this short note is to test whether the morphological skeletal network (MSN) of water bodies that resembles a river network follows Horton's laws. A fractal relationship of MSN of a water body is also shown. This investigation shows that the MSN of the Nizamsagar reservoir follows Horton's laws. Furthermore, this reservoir has a fractal dimension (D m) of 1.92 which was computed by using two morphometric quantities and the fractal dimension of the main skeletal length (d). This value tallies exactly with the fractal dimension (D f) of the whole MSN computed through box-counting method.  相似文献   

8.
To investigate inhomogeneous and porous structures in nature, the concept of fractal dimension was established. This paper briefly introduces the definition and measurement methods of fractal dimension. Three different methods including mercury injection capillary pressure (MICP), nuclear magnetic resonance (NMR), and nitrogen adsorption (BET) were applied to determine the fractal dimensions of the pore space of eight carbonate rock samples taken from West Tushka area, Egypt. In the case of fractal behavior, the capillary pressure P c and cumulative fraction V c resulting from MICP are linearly related with a slope of D-3 in a double logarithmic plot with D being the value of fractal dimension. For NMR, the cumulative intensity fraction V c and relaxation time T 2 show a linear relation with a slope of 3-D in a double logarithmic plot. Fractal dimension can also be determined by the specific surface area S por derived from nitrogen adsorption measurements and the effective hydraulic radius. The fractal dimension D shows a linear relation with the logarithm of S por . The fractal dimension is also used in models of permeability prediction. To consider a more comprehensive data set, another 34 carbonate samples taken from the same study area were integrated in the discussion on BET method and permeability prediction. Most of the 42 rock samples show a good agreement between measured permeability and predicted permeability if the mean surface fractal dimension for each facies is used.  相似文献   

9.
The ongoing continent?Ccontinent collision between Indian and Eurasian plates houses a seismic gap in the geologically complex and tectonically active central Himalaya. The seismic gap is characterized by unevenly distributed seismicity. The highly complex geology with equally intricate structural elements of Himalaya offers an almost insurmountable challenge to estimating seismogenic hazard using conventional methods of Physics. Here, we apply integrated unconventional hazard mapping approach of the fractal analysis for the past earthquakes and the box counting fractal dimension of structural elements in order to understand the seismogenesis of the region properly. The study area extends from latitude 28°N?C33°N and longitude 76°E?C81°E has been divided into twenty-five blocks, and the capacity fractal dimension (D 0) of each block has been calculated using the fractal box counting technique. The study of entire blocks reveal that four blocks are having very low value of D 0 (0.536, 0.550, 0.619 and 0.678). Among these four blocks two are characterized by intense clustering of earthquakes indicated by low value of correlation fractal dimension (D c ) (0.245, 0.836 and 0.946). Further, these two blocks are categorized as highly stressed zones and the remaining two are characterized by intense clustering of structural elements in the study area. Based on the above observations, integrated analysis of the D c of earthquakes and D 0 of structural elements has led to the identification of diagnostic seismic hazard pattern for the four blocks.  相似文献   

10.
The particle size distribution in small watershed changes under different land uses and affects soil erodibility. The aims of this study were (1) to investigate the volume fractal dimension of particle size distribution under different land uses in a typical small watershed of purple soil, (2) to estimate soil erodibilities of various land uses utilizing the Erosion-Productivity Impact Calculator (EPIC) model and the nomogram (NOMO) model, and (3) to relate volume fractal dimension with the soil erodibility used in the Universal Soil Loss Equation (USLE) in purple soil areas. Laser diffractions and double-logarithmic model were used to measure and calculate volume fractal dimension values. The results show that soil volume fractal dimensions were well linearly fitted to the double-logarithmic model with high correlation coefficients of 0.902–0.936 under six land uses in the small watershed. The averaged volume fractal dimension values under different land uses, from high to low were in the order of Zea mays L, Ipomoea batatas, Citrus reticulata Blanco, Setaria viridis, Robinia pseudoacacia L, Pinus massoniana Lamb. The volume fractal dimension was positively correlated to clay particle fraction (R = 0.933). The average soil erodibility values under different land uses from high to low were in the order of Setaria viridis, Citrus reticulata Blanco, Pinus massoniana Lamb, Zea mays L, Ipomoea batatas, Robinia pseudoacacia L while average soil erodibilities from high to low values were in the order of Setaria viridis, Citrus reticulata Blanco, Zea mays L, Ipomoea batatas, Pinus massoniana Lamb, Robinia pseudoacacia L. The soil erodibilities calculated by the two models were similar, and positively correlated (R = 0.630–0.877). The volume fractal dimension values of six land uses were negatively correlated to both soil erodibility estimated by EPIC and by NOMO models. Moreover, the correlations of the volume fractal dimension values of Zea mays L, Ipomoea batatas and Citrus reticulata Blanco estimated by EPIC or NOMO were lower than those of Pinus massoniana Lamb, Robinia pseudoacacia L and Setaria viridis. Further research is needed to determine the influence of volume fractal dimension on the soil erodibility under different land use and managements.  相似文献   

11.
Developing useful biological isoscapes for areas of the world is a priority. This is the case for Mexico that hosts a large percentage of North America's Neotropical migrant birds. Here we investigated the use of House Sparrow (Passer domesticus) feathers to create a spatially explicit feather deuterium isoscape for that country using samples (n = 461) that were collected across Mexico. Considerable and useful spatial hydrogen isotopic structure was observed, suggesting that isotopes may be a potential forensic tool for evaluating origins of Mexican derived fauna and flora. The most positive feather δD values occurred in the northeast and most negative in the south-central part of the country, roughly matching δD patterns observed in groundwater. A weak negative isotopic relationship was found with altitude in both the Pacific and Atlantic drainage systems. The most parsimonious model describing isotopic spatial variation in feathers between 300 and 3000 m a.s.l. included groundwater δD (δDgw; precipitation proxy), sex, amount of precipitation, and the coefficient of variation in amount of precipitation. Overall, δDgw was a poor predictor of sparrow δDf values for all of Mexico. However, this relationship was considerably strengthened when we considered sex separately, removed the Baja peninsula from our sample, and considered the Atlantic and Pacific drainage basins separately. The strongest relationship between δDgw and δDf was found for female sparrows in the Atlantic drainage basin (r2 = 0.464). We recommend that researchers interested in inferring origins of migratory birds and other animals in Mexico create species specific isotopic basemaps that may be guided by the isotopic patterns we have observed for House Sparrows and groundwater.  相似文献   

12.
《Applied Geochemistry》2000,15(8):1203-1218
Ca6[Al(OH)6]2(CrO4)3·26H2O, the chromate analog of the sulfate mineral ettringite, was synthesized and characterized by X-ray diffraction, Fourier transform infra-red spectroscopy, thermogravimetric analyses, energy dispersive X-ray spectrometry, and bulk chemical analyses. The solubility of the synthesized solid was measured in a series of dissolution and precipitation experiments conducted at 5–75°C and at initial pH values between 10.5 and 12.5. The ion activity product (IAP) for the reaction Ca6[Al(OH)6]2(CrO4)3·26H2O⇌6Ca2++2Al(OH)−4+3CrO2−4+4OH−+26H2O varies with pH unless a CaCrO4(aq) complex is included in the speciation model. The log K for the formation of this complex by the reaction Ca2++CrO2−4=CaCrO4(aq) was obtained by minimizing the variance in the IAP for Ca6[Al(OH)6]2(CrO4)3·26H2O. There is no significant trend in the formation constant with temperature and the average log K is 2.77±0.16 over the temperature range 5–75°C. The log solubility product (log KSP) of Ca6[Al(OH)6]2(CrO4)3·26H2O at 25°C is −41.46±0.30. The temperature dependence of the log KSP is log KSP=A−B/T+D log(T) where A=498.94±48.99, B=27,499±2257, and D=−181.11±16.74. The values of ΔG0r,298 and ΔH0r,298 for the dissolution reaction are 236.6±3.9 and 77.5±2.4 kJ mol−1. the values of ΔC0P,r,298 and ΔS0r,298 are −1506±140 and −534±83 J mol−1 K−1. Using these values and published standard state partial molal quantities for constituent ions, ΔG0f,298=−15,131±19 kJ mol−1, ΔH0f,298=−17,330±8.6 kJ mol−1, ΔS0298=2.19±0.10 kJ mol−1 K−1, and ΔC0Pf,298=2.12±0.53 kJ mol−1 K−1, were calculated.  相似文献   

13.
Himalayan seismicity is related to continuing northward convergence of Indian plate against Eurasian plate. Earthquakes in this region are mainly caused due to release of elastic strain energy. The Himalayan region can be attributed to highly complex geodynamic process and therefore is best suited for multifractal seismicity analysis. Fractal analysis of earthquakes (mb ?? 3.5) occurred during 1973?C2008 led to the detection of a clustering pattern in the narrow time span. This clustering was identified in three windows of 50 events each having low spatial correlation fractal dimension (D C ) value 0.836, 0.946 and 0.285 which were mainly during the span of 1998 to 2005. This clustering may be considered as an indication of a highly stressed region. The Guttenberg Richter b-value was determined for the same subsets considered for the D C estimation. Based on the fractal clustering pattern of events, we conclude that the clustered events are indicative of a highly stressed region of weak zone from where the rupture propagation eventually may nucleate as a strong earthquake. Multifractal analysis gave some understanding of the heterogeneity of fractal structure of the seismicity and existence of complex interconnected structure of the Himalayan thrust systems. The present analysis indicates an impending strong earthquake, which might help in better hazard mitigation for the Kumaun Himalaya and its surrounding region.  相似文献   

14.
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.  相似文献   

15.
Lower limits for the percentages of stars with various luminosities in the cores of six globular clusters are derived using stellar spatial density distributions f(r) to deep limiting B magnitudes obtained earlier. For NGC 6535 and NGC 5466, the logarithmic density range and Kholopov parameters Df and Dr are also determined. These two parameters are correlated with the mean masses of stars of various subsystems and the total mass (number) of stars in the cluster.  相似文献   

16.
Non-Darcian flow to a well in a leaky aquifer was investigated using a finite difference method. Flow in the leaky aquifer is assumed to be non-Darcian and horizontal, while flow in the aquitard is assumed to be Darcian and vertical. The Forchheimer equation was employed to describe the non-Darcian flow in the aquifer. The finite difference solution was compared with the solution of Birpinar and Sen (2004). The latter overestimates the drawdown at early times and underestimates the drawdown at late times; also, the impact of β D on the drawdown depends on the value of B D, where β D is a dimensionless turbulent factor in the Forchheimer equation and B D is the dimensionless leakage parameter. The impact of leakage on drawdown is similar to that of Darcian flow. A sensitivity analysis indicated that the drawdown is very sensitive to the change in the dimensionless well radius r cD when B D is relatively large, while it is sensitive to the change in B D when B D is relatively small. The numerical solution has been applied to analyze the pumping test data in Chaj-Doab area of Pakistan. Birpinar ME, Sen Z (2004) Forchheimer groundwater flow law type curves for leaky aquifers. J Hydrol Eng 9(1):51??9  相似文献   

17.
Ali. O. Oncel  Tom Wilson   《Tectonophysics》2006,418(3-4):205-218
Seismotectonic parameters including the Gutenberg-Richter b-value and multifractal dimensions D2 and D15 of seismicity patterns (both spatial and temporal) were compared to GPS-derived maximum shear and dilatation strains measured in the Marmara Sea region of western Turkey along the Northern Anatolian Fault Zone (NAFZ). Comparisons of seismotectonic parameters and GPS-derived maximum shear and dilatation strain along the NAFZ in the vicinity of the 1999 M7.4 Izmit earthquake reveal a positive correlation (r = 0.5, p = 0.05) between average dilatation and the Gutenberg-Richter b-value. Significant negative correlation (r = − 0.56, p = 0.03 and r = − 0.56, p = 0.02) was also observed between the spatial fractal dimension D2 and GPS-derived maximum geodetic and shear strain. This relationship suggests that, as maximum geodetic and shear strains increase, seismicity becomes increasingly clustered.Anomalous interrelationships are observed in the Marmara Sea region prior to the Izmit event along a bend in the NAFZ near the eastern end of the Marmara Sea known as the Northern Boundary Fault (NBF). An asperity is located near the northwest end of the NBF. Along the 50-km length of the NBF, GPS strains become slightly compressive. The correlation between b-value and GPS-derived dilatation suggests that regions in compression have increased probability of larger magnitude rupture. The NBF appears to serve as an impediment to the transfer of strain from east to west along the NAFZ. Recurrence times for large earthquakes along the NBF are larger than in surrounding areas. Temporal clustering of seismicity in the vicinity of the NBF may represent foreshocks of an impending rupture.  相似文献   

18.
德兴铜矿是中国东部重要的大型斑岩铜矿,由朱砂红、铜厂和富家坞等3个矿床组成。在详细的野外脉体填图基础上,文章把德兴铜厂斑岩铜矿的成矿脉体划分为A脉、B脉、D脉和H脉等4种类型。研究发现,A脉的形成与钾化蚀变有关,脉体不规则且不连续,以粒状石英±钾长石±黑云母±磁铁矿±少量黄铁矿±少量黄铜矿的矿物组合为特征;B脉的形成与钾质硅酸盐水解有关,脉体较规则且连续,以石英±辉钼矿±黄铜矿±黄铁矿的矿物组合为特征,石英颗粒呈典型的梳状或长柱状对称于脉壁生长;D脉的形成与石英-绢云母化蚀变有关,以黄铁矿±石英±黄铜矿的矿物组合为特征,脉壁发育绢云母晕;H脉的形成与碳酸盐化有关,以方解石±赤铁矿±黄铁矿±黄铜矿的矿物组合为特征。这4种脉体分别记录了成矿流体演化至不同阶段,热液蚀变作用的特点及其与Cu-Mo硫化物沉淀的关系。脉体的宽度-间距定量统计分析表明,脉体宽度(T)服从于幂次分布定律;脉体间距(S)服从于负指数分布或介于对数正态分布与负指数分布之间。脉体宽度分维值D值(0.91~1.35)普遍>1,反映脉体系统的连通性较差,矿化程度较弱。脉体间距变差系数Cν值(0.49~0.92)均<1,说明脉体簇生聚集程度较低,矿化程度较弱;处于脉体聚集中心的脉体,代表着热液流体运移的通道,制约着其他脉体的展布。  相似文献   

19.
黑龙江省逊克县高松山金矿床地质分形特征及成矿预测   总被引：1，自引：0，他引：1  
高松山金矿床是中国人民武装警察部队黄金第一支队在小兴安岭-张广才岭成矿带北段发现的大型浅成低温热液矿床,随着研究的深入,发现其具有优越的成矿地质条件和良好的找矿前景。在总结前人成果的基础上,文章利用分形学理论对金矿资源量和品位进行了分析,结果显示资源量在大于250 kg标度区间时,分维数D值为1.69,表明资源量在该区段内的普查存在较好的前景,同时,品位分维数D值为1.10~1.40时,其成矿仅与细脉状烟灰色石英-细粒黄铁矿成矿阶段紧密相关。利用钻孔资料分析品位在垂向上的分形特征发现,分维数D值介于1~1.5时,表现为垂向不圈闭延伸,反映其深部可能存在隐伏矿体。在资源评价方面,通过对断裂构造似等距控矿规律的研究,结合帕累托定律（Pareto law）和阻尼曲线模型,对深部可能存在的矿体规模和部位进行了预测,资源量大于4960 kg的矿体仍有2处未发现,中等资源量规模的矿体存在巨大空间,同时,预测隐伏矿体可能在已有地表矿体相间部位的深部。  相似文献   

20.
The aim of this short note is to test whether the morphological skeletal network (MSN) of water bodies that resembles a river network follows Horton's laws. A fractal relationship of MSN of a water body is also shown. This investigation shows that the MSN of the Nizamsagar reservoir follows Horton's laws. Furthermore, this reservoir has a fractal dimension (D m) of 1.92 which was computed by using two morphometric quantities and the fractal dimension of the main skeletal length (d). This value tallies exactly with the fractal dimension (D f) of the whole MSN computed through box-counting method.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号