Self-Affine Fractals and the Fractal Dimension of Fractured Rock Profiles

查看全文 作　　者：Shi Xingjue,Xu Heming,Niu Zhiren and Fan ZengjieUniversity of Science and Technology of China,Hefei 230026,China Seismologicai Bureau of Shanxi,Xi’an 710068,China 出　　处：《Earthquake Research in China》索引1994年第8卷第3期,共7页 基　　金：the Joint Earthquake Science Foundation, China 摘　　要：The measured profiles of laboratory fractured rocks should be self-affine fractal.The scaling properties of these profiles are described by two parameters-the fractal dimension D and the crossover length tc The D values of eight profiles are calculated by the ruler method and by the standard deviation method respectively.It is shown that if tc is far greater than the sampling step tc two methods yield the same results,although if it is far smaller than r,the D by the standard method will be about 1.20,while D by the ruler method will very close to 1.0,because two fractal dimensions,local and global,exist on two sides of tc In order to obtain the local fractal dimension which may be close to that of the standard deviation method,the ruler method must be modified.We propose a way to estimate the tc and to modify the ruler method.Finally,a profile having given D is generated in terms of the principle of non-integer order differential,through which the above two methods are verified and lead to the same 关 键 词：SELF-AFFINE FRACTAL RULER METHOD CROSSOVER LENGTH Standard Deviation METHOD