(中南工业大学资源环境与建筑工程学院， 长沙 410083)
摘 要: 系统阐述了分形插值的原理, 介绍了分形布朗运动(FBM)的概念及其构造方法，针对自然界实际系统分形特性，提出了实际FBM系统分形特性的判别准则。在此基础之上提出了基于FBM的分形插值方法，阐述了分形插值的基本条件；对于实际的裂隙结构，利用分形插值方法建立的模型进行了渗流计算，并与常规插值所得结果进行了比较。结果表明，对于具有分形特性的实际的复杂、非线性系统，利用基于FBM的分形插值方法从大尺度来构造微观细节，能保持微观与宏观之间的相似性， 更能取得有效的结果。
关键字: 分形 插值 布朗运动
（College of Resources, Environment and Civil Engineering,Central South University of Technology, Changsha 410083, P. R. China）
Abstract:The principle of the fractal interpolation was systematically discussed, the concept and constructing arithmetic of FBM were introduced, and the authors advanced the ruler to identify fractal property and the arithmetic of the fractal interpolation of real FBM system. Based on the fractal FBM interpolation, the authors advanced a fractal model of seepage of real fracture, and gave the comparison between the fractal model and other model. The result proved that the method, that used FBM method to build the small scale date with the big scale date, could keep the similarity between the macrostructure and microstructure and got more useful result.
Key words: fractal interpolation Brownian Motion
