Lakes on fractal surfaces: A null hypothesis for lake-rich landscapes

A class of stochastic processes known as fractional Brownian motion (fBm) provides strikingly realistic simulations of certain types of terrain, particularly those which appear to be unmodified by geomorphological and geological processes. In addition to their less serious applications in video games and science fiction movies, fractal terrain simulations have proven useful in a number of areas of spatial analysis. For example, they can provide sample data sets for testing the efficiency of data structures and algorithms designed for topographic applications. Previous work has shown that stream networks simulated on fBm surfaces show the same deviations from accepted theories of channel network topology as do real stream networks, implying that such deviations originate in the geometrical constraints of packing channels onto surfaces, rather than from geological or other environmental controls. In effect, this work demonstrates the usefulness of fBm as a null hypothesis for terrain. One difficulty, however, stems from the abundant pits which occur in the simulations, because peaks and pits are equally likely. Flooding of pits on fBm surfaces was simulated to obtain lakes. Lake-rich stream networks were extracted and represented with a suitable integer code. The relative frequencies of various network topologies and groups of topologies were compared to known characteristics of channel networks on real lake-rich landscapes. Lake-string topologies are significantly less abundant than in glaciated landscapes. Lake areas show good fits to hyperbolic distributions, but lake in-degrees do not fit the negative binomial model. fBm surfaces are appropriate null hypotheses of scale-free, lake-rich landscapes.This paper was presented at Emerging Concepts, MGUS-87 Conference, Redwood City, California, 13–15 April 1987.     

非线性方法油气平面成像预测的研究

系统论和非线性方法为石油地球物理勘探注入了新的动力。本文试通过分形理论结合人工神经网络方法对测井资料进行解释,对油气分布进行平面成像预测。     

Fractal measures of drainage network to investigate surface deformation from remote sensing data: A paradigm from Hindukush (NE-Afghanistan)

This approach represents the relative susceptibility of the topography of the earth to active deformation by means of geometrical distinctiveness of the river networks. This investigation employs the fractal analysis of drainage system extracted from ASTER Global Digital Elevation Model (GDEM-30m resolution). The objective is to mark active structures and to pinpoint the areas robustly influenced by neotectonics. This approach was examined in the Hindukush, NE-Afghanistan. This region is frequently affected by deadly earthquakes and the modern fault activities and deformation are driven by the collision between the northward-moving Indian subcontinent and Eurasia. This attempt is based on the fact that drainage system is strained to linearize due to neotectonic deformation. Hence, the low fractal dimensions of the Kabul, Panjsher, Laghman, Andarab, Alingar and Kocha Rivers are credited to active tectonics. A comprehensive textural examination is conducted to probe the linearization, heterogeneity and connectivity of the drainage patterns. The aspects for these natural textures are computed by using the fractal dimension (FD), lacunarity (LA) and succolarity (SA) approach. All these methods are naturally interrelated, i.e. objects with similar FD can be further differentiated with LA and/or SA analysis. The maps of FD, LA and SA values are generated by using a sliding window of 50 arc seconds by 50 arc seconds (50" × 50"). Afterwards, the maps are interpreted in terms of regional susceptibility to neotectonics. This method is useful to pinpoint numerous zones where the drainage system is highly controlled by Hindukush active structures. In the North-Northeast of the Kabul block, we recognized active tectonic blocks. The region comprising, Kabul, Panjsher, Andrab, Alingar and Badakhshan is more susceptible to damaging events. This investigation concludes that the fractal analysis of the river networks is a bonus tool to localize areas vulnerable to deadly incidents influencing the Earth’s topography and consequently intimidate human lives.     

应用CT技术研究瘦煤在不同温度下孔隙变化特征

应用µCT225kvFCB型高精度(µm级)CT试验分析系统,对直径1 mm的瘦煤从18 ℃到600 ℃高温下的热破裂过程进行了显微CT观测和分析.发现了瘦煤的热破裂规律:300 ℃煤样中大量小的孔隙贯通成大的孔隙团,因此瘦煤的热破裂阈值在300 ℃附近,从常温到300 ℃煤样的孔隙率增加了0.5倍左右.研究了煤样在100~600 ℃范围内热破裂孔隙分布的分形规律,研究发现:从100 ℃到600 ℃,煤样的分形维数D随温度升高呈现先减小、后增加的趋势.孔隙的演化规律:由初始较规则的小孔隙变形,过渡到大量较规则、小孔隙贯通成不规则的大的孔隙团,之后孔隙团缩合减小趋于规则.分布初值的对数随温度升高呈现先降低后增加的趋势;从18 ℃到600 ℃孔隙数量的演化规律为先减小后增加.     

黔北地区牛蹄塘组海相页岩孔隙结构及其非均质性特征

马查拉煤系地层是昌都赋煤带主要煤系地层之一。为明确风化对西藏马查拉煤系地层孔隙结构特征的影响,本文以西藏早石炭世马查拉组剖面不同类型风化岩石为研究对象,利用氮气吸附试验及分形理论对微观孔隙结构及其复杂程度进行研究。试验结果表明：岩石的吸脱附等温线都呈现反“S”型,孔隙结构呈现同质化发展趋势。相对压力(P/P₀)可以根据岩样吸脱附曲线的上升趋势分为小于0.1、0.1~0.45及大于0.45 3个阶段。岩样孔径结构集中分布在1~5 nm范围内,其中泥质碎屑灰岩、粉矿质泥岩、粉砂岩、泥岩和灰岩在1~2 nm范围内孔隙体积较大,煤层的比表面积和孔体积与相邻岩层相比较低。风化煤岩大孔分形维数明显高于小孔,孔隙结构复杂程度更高,煤层及碳质泥岩的孔隙分形维数相较其他类型岩石更低。研究结果可服务于昌都地区开发和灾害防治。     

土壤湿度对不规则起伏地表雷电垂直电场传播影响的研究

本文采用二维fractional Brown motion(f Bm)随机分形界面模拟不规则起伏地表,基于Longmire-Scott提出的土壤电参数等效模型(L-S模型),分析研究不规则起伏地表的土壤湿度对地闪回击垂直电场传播的影响。结果表明:(1)地表的不规则起伏程度主要会引起垂直电场峰值的衰减和上升沿时间的滞后。随着地表不规则起伏程度的增大,垂直电场峰值衰减越明显,且波形上升沿时间增长。(2)无论地表不规则程度如何,随着土壤湿度的增大,垂直电场的衰减反而减小。(3)总的来说,地表的不规则程度越大,土壤湿度越小,垂直电场的峰值衰减越大,波头上升沿时间越长。     

分形理论在成矿预测中的应用

分形理论是人类进行思维和探索复杂性而定量描述的一种新方法，是研究大自然界中不规则现象的有力数学工具，在地质领域中的应用非常广泛。介绍Ｒ／Ｓ分析法原则，并结合实例来研究地质体和地质现象的分形特征，确定地质异常，建立地质异常分形模型。     

Elastic-wave velocities for porous media with power-law distribution of pore sizes

 A system consisting of an elastic matrix with randomly distributed pores of uniform shapes but with sizes governed by a power-law distribution is investigated in a theoretical way. The velocities of elastic waves propagating through such a system are calculated. The obtained results are that the velocities decrease with increasing total porosity and for a given porosity velocities moderately decrease with increasing absolute value of the exponent D in a power-law distribution of pore sizes. Received: 3 July 1995 / Accepted: 2 August 1996     

岩石单颗粒压缩破碎的数值模拟分析

岩石颗粒破碎是影响粒状材料剪切强度和变形的最主要因素, 岩石颗粒破碎并不是想象的那么难, 像花岗岩颗粒有时在很小的压应力作用下就可以破碎。岩石单颗粒破碎的物理试验结果常常很离散, 完成大量单颗粒破碎的物理试验费时费力不现实, 采用离散单元法(Discrete element method, DEM)PFC软件模拟单颗粒压缩破碎试验, 既能克服单颗粒破碎物理试验的缺陷, 又能解决单颗粒破碎物理试验工作量大的难题, 是研究单颗粒破碎的理想选择。基于DEM的软件PFC2D, 将粒径为0.075～0.1245mm的基本粒子捆绑成不同粒径的单颗粒, 模拟岩石单颗粒压缩破碎试验, 观察颗粒破碎演化过程, 统计单颗粒破碎强度。计算单颗粒压缩破碎后颗粒分布的分维, 验证单颗粒破碎强度的分形模型和单颗粒破碎强度的尺寸效应。文中引用玄武岩单颗粒破碎试验结果, 与单颗粒破碎的离散单元模拟结果进行比较, 验证单颗粒破碎强度的尺寸效应和修正的Weibull理论的离散单元模拟结果。