区域化探数据处理的几种分形方法   总被引：20，自引：1，他引：20  

韩东昱龚庆杰  向运川 《地质通报》2004,23(7):714-719

地球化学变量兼有随机性、确定性和区域结构性的特征，传统的数学方法难以精确地描述地球化学变量的空间分布规律，而新兴的分形几何是刻画空间不规则形体的一种比较有效的工具，且分维值可以表征空间不规则形体的确定性本质。基于分形原理，提出含量-总量法、空间分形插值法和分形趋势面法3种新的分形技术，应用于区域化探数据处理。在几个典型矿区应用后发现，上述分形方法不仅可以有效地模拟地球化学变量的空间分布特征，而且在保留原始有效异常信息的基础上可以更合理地区分地球化学变量的背景与异常，具有发现和强化弱异常信息的重要功效。  相似文献   

Similarities between strike-slip faults at different scales and a simple age determining method for active faults   总被引：1，自引：0，他引：1  

Young-Seog Kim  David J. Sanderson 《Island Arc》2004,13(1):128-143

Abstract Several differently scaled strike‐slip faults were examined. The faults shared many geometric features, such as secondary fractures and linkage structures (damage zones). Differences in fault style were not related to specific scale ranges. However, it was recognized that differences in style may occur in different tectonic settings (e.g. dilational/contractional relays or wall/linkage/tip zones), different locations along the master fault or different fault evolution stages. Fractal dimensions were compared for two faults (Gozo and San Andreas), which supports the idea of self‐similarity. Fractal dimensions for traces of faults and fractures of damage zones were higher (D ～1.35) than for the main fault traces (D ～1.005) because of increased complexity due to secondary faults and fractures. Based on the statistical analysis of another fault evolution study, single event movements in earthquake faults typically have a maximum earthquake slip : rupture length ratio of approximately 10^?4, although this has only been established for large earthquake faults because of limited data. Most geological faults have a much higher maximum cumulative displacement : fault length ratio; that is, approximately 10^?2 to 10^?1 (e.g. Gozo, ～10^?2; San Andreas, ～10^?1). The final cumulative displacement on a fault is produced by accumulation of slip along ruptures. Hence, using the available information from earthquake faults, such as earthquake slip, recurrence interval, maximum cumulative displacement and fault length, the approximate age of active faults can be estimated. The lower limit of estimated active fault age is expressed with maximum cumulative displacement, earthquake slip and recurrence interval as T ? (d_max /u) · I(M).  相似文献   

基于灰色算子的尾矿坝浸润线混沌研究   总被引：2，自引：0，他引：2  

蒋卫东  李夕兵  贺怀建  胡柳青 《岩土力学》2004,25(2):242-245

对于尾矿坝浸润线时间序列，通过建立一个灰色算子，来弱化坝体高度、库内水位等因素所带来的确定性影响，突出混沌特性，形成新的时间序列，对该序列进行相空间重构后，求取关联维。德兴铜矿2#尾矿坝浸润线观测数据的分析结果表明，灰色算子能较好地处理混沌问题，浸润线时间序列存在着非整数维，是一个混沌系统：对于尾矿坝安全不能进行长期预测，而需要长期监测。  相似文献   

多孔介质非饱和导水率预测的分形模型   总被引：6，自引：0，他引：6       下载免费PDF全文

刘建国  王洪涛  聂永丰 《水科学进展》2004,15(3):269-275

多孔介质非饱和导水率是地下水污染预测与评价的重要参数。根据分形几何的基本原理和方法,推导出了与Campbell经验公式在形式上完全一致的多孔介质非饱和导水率的预测公式。公式中的幂指数为介质孔隙分维和随机行走分维的函数,分别体现了多孔介质的静态性质与动态性质对其中水分运动的影响,但静态性质的影响是主要的,即导水率主要受多孔介质的结构控制。根据文献中报道的大量数据,利用笔者推导的预测公式计算得到的幂指数的统计值与试验测定的幂指数的统计值基本一致,说明推导的理论公式预测多孔介质非饱和导水率是较为可靠的。  相似文献   

A Corrected and Generalized Successive Random Additions Algorithm for Simulating Fractional Levy Motions     

Hui-Hai Liu  Gudmundur S. Bodvarsson  Silong Lu  Fred J. Molz 《Mathematical Geology》2004,36(3):361-378

Simulation of subsurface heterogeneity is important for modeling subsurface flow and transport processes. Previous studies have indicated that subsurface property variations can often be characterized by fractional Brownian motion (fBm) or (truncated) fractional Levy motion (fLm). Because Levy-stable distributions have many novel and often unfamiliar properties, studies on generating fLm distributions are rare in the literature. In this study, we generalize a relatively simple and computationally efficient successive random additions (SRA) algorithm, originally developed for generating Gaussian fractals, to simulate fLm distributions. We also propose an additional important step in response to continued observations that the traditional SRA algorithm often generates fractal distributions having poor scaling and correlation properties. Finally, the generalized and modified SRA algorithm is validated through numerical tests.  相似文献   

基于光谱空间密度分析的边缘提取     

刘楠  舒宁 《武汉大学学报(信息科学版)》2004,29(12):1093-1096

针对传统的边缘提取方法大部分不适应高光谱数据的特点，提出了基于光谱空间密度分析边缘提取的思想。在分组主分量变换提取第一主分量作为特征维的基础上，采用面向对象的二次判别边缘的方法，通过立体判决将光谱空间中低密度超椭球体集群视为真实边缘点集群。试验表明，此方法是合理可行的。  相似文献   

Study on simulating strong ground motion by fractal stochastic method     

GUO Meng-qiu  WANG Bin  XU Zhao-yong 《地震学报(英文版)》2005,18(4):490-495

The time history of strong ground motion can be synthesized by empirical Green's function (EGF) method.Firstly a large seismic event is discretized into a series of subevents; secondly recordings of earthquakes with proper size and spatial distribution are chosen as time history (EGF) of those subevents; finally the EGFs are summated to get the time history of ground motion caused by the large event.  相似文献   

Correlation Fractal and Multifractal Characteristics of Seismic Activity in the Taiwan Area, China   总被引：2，自引：0，他引：2  

XU Jiandong  HUANG Jianf  WEI Fuquan  YAN Yunpeng  LI Yaping  LIN Chien-te Institute of Geology  China Earthquake Administration  Beijing  Chin  Earthquake Administration of Fujian Province  Fuzhou  Fujian  China China Aero Geophysical Survey  Remote Sensing for Land  Resources  Beijing  China Leader University  Tainan  Taiwan  China 《《地质学报》英文版》2005,79(2):225-232

Based on the analysis of newly collected data of plate tectonics, distribution of active faults and crustal deformation, the Taiwan area is divided into two seismic regions and six seismic belts. Then, correlation fractal dimensions of all the regions and belts are calculated, and the fractal characteristics of hypocenteral distribution can be quantitatively analyzed. Finally, multifractal dimensions Dq and f(α) are calculated by using the earthquake catalog of the past 11 years in the Taiwan area. This study indicates that (1) there exists a favorable corresponding relationship between spatial images of seismic activity described with correlation fractal dimension analysis and tectonic settings; (2) the temporal structure of earthquakes is not single but multifractal fractal, and the pattern of Dq variation with time is a good indicator for predicting strong earthquake events.  相似文献   

Fractally Invariant Distributions and an Application in Geochemical Exploration     

Wei Shen  D. R. Cohen 《Mathematical Geology》2005,37(8):895-913

Fractal modelling has been applied extensively as a means of characterizing the spatial distribution of geological phenomena that display self-similarity at differing scales of measurement. A fractal distribution exists where the number of objects exhibiting values larger than a specified magnitude displays a power-law dependence on that magnitude, and where this relationship is scale-invariant. This paper shows that a number of distributions, including power-function, Pareto, log-normal and Zipf, display fractal properties under certain conditions and that this may be used as the mathematical basis for developing fractal models for data exhibiting such distributions. Population limits, derived from fractal modelling using a summation method, are compared with those derived from more conventional probability plot modelling of stream sediment geochemical data from north-eastern New South Wales. Despite some degree of subjectivity in determining the number of populations to use in the models, both the fractal and probability plot modelling have assisted in isolating anomalous observations in the geochemical data related to the occurrence of mineralisation or lithological differences between sub-catchments. Thresholds for the main background populations determined by the fractal model are similar to those established using probability plot modelling, however the summation method displays less capacity to separate out anomalous populations, especially where such populations display extensive overlap. This suggests, in the geochemical data example provided, that subtle differences in the population parameters may not significantly alter the fractal dimension.  相似文献   

三峡库区巴东县城附近主要滑坡边界轨迹分形分维特征与滑坡稳定性关系   总被引：4，自引：1，他引：4       下载免费PDF全文

吴树仁  韩金良  石菊松  张永双  何锋  董诚 《地球学报》2005,26(5):455-460

为了探索复杂滑坡轨迹结构演化及其稳定性定量分析计算的新途径，本文利用分形分维理论，分析三峡库区巴东县城附近滑坡边界轨迹的几何分形结构，并采用盒维数法分别求得巴东县城附近11个滑坡边界轨迹的分维值，计算结果表明：每个滑坡的轨迹结构具有其特征性的分维值，轨迹结构越复杂，结构层次越清楚，分维值越高；其中，榨房坪滑坡和黄腊石滑坡的分维值最高，分别为1.50和1.483，西壤口和谭家湾滑坡的分维值最低，分别为0.925和0.732；而黄土坡和赵树岭滑坡的分维值介于二者之间，分别为1.111和1.091。结合典型滑坡边界轨迹结构演化与滑坡稳定性关系的定性分析及前期滑坡稳定性定量计算和模拟分析，初步揭示：滑坡边界轨迹结构与稳定性是密切相关的，滑坡边界轨迹宏观扩展增值越明显，轨迹结构越复杂，分维值越高，其稳定性条件也越差，因此，分数维可作为衡量滑坡轨迹结构复杂性和稳定性的重要标志；滑坡边界轨迹宏观扩展变形存在一个极限，超过这个极限滑坡的局部失稳就转化为整体滑动；而滑坡边界轨迹则记录了滑坡变形扩展现象和信息，因此，相对应地滑坡轨迹分形结构的分维值也应存在一个极值，在极值点滑坡体处于临滑状态；滑坡边界轨迹结构的极限分维值大致为1.4～1.5，此时滑坡接近于整体极限失稳状态，而分维值在1.1～1.3之间则表示滑坡处于整体稳定，局部存在潜在失稳状态，分维值小于1则表示滑坡处于相对稳定状态。  相似文献