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地震

地震 ›› 2000, Vol. 20 ›› Issue (3): 1-8.

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离散点集（地震）空间分布多重分形计算的精度估算

朱令人, 龙海英   

  1. 新疆维吾尔自治区地震局,乌鲁木齐 830011
  • 收稿日期:1999-12-06 修回日期:2000-01-12 出版日期:2000-07-31 发布日期:2022-09-30
  • 作者简介:朱令人（1941-）,男,江苏江阴人,研究员,1997年博士生导师,主要从事地震综合预报、非线性科学在地震学中应用及地震统计等研究。
  • 基金资助:
    地震科学联合基金会资助项目(92287）

Precision estimate on multi-fractal calculation of spatial distribution for earthquake dispersion and point sets

ZHU Ling-ren, LONG Hai-ying   

  1. Seismological Bureau of Xinjiang Uigur Autonomous Region, Urumchi 830011, China
  • Received:1999-12-06 Revised:2000-01-12 Online:2000-07-31 Published:2022-09-30

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摘要： 地震是一种非线性现象,因而很多人计算地震分布的分形维数,但具体各种计算方法的误差（或精度）是多少,还没有定量的估计。鉴于地震空间分布具有有限、离散、点集的特点,用双标度Contor 多分形集理论模型数值模拟来估算其精度（误差）,并判定各种方法的优劣。理论模型数值模拟得出如下结论:① 随着样本容量的增大,计算精度会提高;② 固定半径法（RAD） 计算误差偏大,固定质量法（MAS）和最小生成树法（MST）较好;③ 当样本容量达到约200时,MAS法和MST 法计算误差大体可稳定在0.05的范围内。

关键词: 多重分形, 精度, 理论模型, 样本容量

Abstract: Earthquake is a non-line phenomenon, so many seismologists calculate the fractal dimension of seismic distribution. However, the precision of calculation method is uncertain. Because the space-time distribution of earthquakes is characteristics of limitation, dispersion and point sets, we use the digital simulation of theory models of two-dimension double-rule Contor sets to estimate its precision （or error）,and to judge some methods good or not. From the theory models simulated digitally,we obtained some results.① As the samples increasing, the precision of several methods is increasing.② The error of the fixed radius method （RAD） is too big,while ones of the fixed mass method （MAS） and the minimal spanning tree method （MST） is smaller.③ When the numbers of samples are more than 200,the calculation precision of MAS and MST is around 0.05.

Key words: Multi-fractal, Precision, Theory model, Numbers of samples

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