地震时间序列多重分形计算精度估计  

The Precision Estimate of Multi-fractal Methods of Time Sequence of Earthquakes

作　　者：朱令人[1] 周仕勇[1] 杨马陵[2] 洪时中 龚宇清[4] 王海涛[1] 

机构地区：[1]新疆维吾尔自治区地震局,中国乌鲁木齐830011 [2]广东省地震局,中国广州510070 [3]成都市地震局,中国成都610015 [4]新疆电子计算中心,中国乌鲁木齐830011

出　　处：《中国地震》2000年第2期166-175,共10页Earthquake Research in China

基　　金：地震科学联合基金资助!(92 2 87)

摘　　要：目前计算地震时间分形的方法很多 ,但具体各种计算方法的误差 (或精度 )是多少 ,还没有一个定量的结果。本文针对这一问题 ,利用Cantor多分形集理论模型数值模拟来估算其精度 (误差 ) ,进而解决有限、离散、点集的多重分形维数谱的计算精度 (误差 )估计问题。通过一维 (时间 )理论模型数值模拟得出如下结论 :(1)存在尺度问题、样本容量问题、基准点选取问题、不同计算方法差异等 ;(2 )固定质量 (MAS)法和最小生成树 (MST)法能较好地反映出不同 q值时的结构特性 ,而数盒子法较差。固定半径法 (RAD)在负q区误差较大 ;(3)多重分形也有尺度问题 ,这是无标度区的客观存在的反映 ;(4 )边界影响对MST法不存在 ,对MAS和RAD法存在 ;(5)随着样本容量的增加 ,分维值的精度将会提高。At the present,there are many methods of calculating seismic time\|fractal.However,there isn′t a fix quantify result about the precision of every method.So,in this paper,we use the theory models imitated digitally for Cantor set to solve precision estimate problems of calculating multi\|fractal spectrums about seismic distribution with limit,dispersion and point sets.By calculating the precision of one dimension distribution of theory models,we obtained some results as follows:(1)There exist many problems such as rules,numbers of samples,basic point selection,different methods and so on.(2)The fixed mass method(MAS) and the minimal spanning tree mthod (MST) can give good structure characteristics in different value q ,while the counting boxes method can′t.And the error of the fixed radius method in range of q is too big.(3)There are problems of rules for multi\|fractal,it is objective reflection for non\|rule.(4)MST has the boundary problem,while MAS and RAD don′t.(5)With increasing numbers of samples,the precision of all fractal\|dimension values becomes higher.

关 键 词：多重分形 精度 理论模型 样本容量 地震时间序列 

分 类 号：P315.5[天文地球—地震学]