地震地磁效应的分形布朗运动的性质及应用
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摘要
重标极差分析法(R/S,rescaled range analysis method),是研究分数布朗运动及自然现象的自仿射分形的有力工具之一,对于所有时间序列分析都有着广泛的用途.通过对天水台绝对地磁观测Z分量数据序列R/S分析,计算分段数据序列的Hurst指数H发现,昆仑山口西MS8.1地震和汶川MS8.0地震震前2—3个月,H值减小,分维数D增大,相关系数C为负值.这一动态变化表明,地震前数据序列由持久性序列发展为反持久性序列,观测数据的成分发生了改变.这与地壳内部应力变化和岩石破裂实验结果相符.所以,这一动态变化过程可以看作是强震前的一种前兆信号.
Rescaled range analysis (R/S) method is one of the good tools for studying fractal Brownian motion of time-series data and natural phenomena self-affine fractal,being applied widely for all time-series.In this paper,this method is used to analyze absolute geomagnetic Z component observations at Tianshui Observatory.The Hurst exponent H was calculated for each sub-sequence of data in specific time intervals.Our analysis result indicates that,2--3 months before Kunlun MS8.1 earthquake and Wenchuan MS8.0 earthquake,H value decreased and fractal dimension value D increased.Such dynamic variations manifest that the observations varied from persistent behaviour to antipersistent time-series before the earthquakes and the composition of the observed data changed.This variation is consistent with internal crustal stress change and rock failure experiment results.So we may view this dynamic variation as a premonitory symptom of the strong earthquakes.
Rescaled range analysis (R/S) method is one of the good tools for studying fractal Brownian motion of time-series data and natural phenomena self-affine fractal,being applied widely for all time-series.In this paper,this method is used to analyze absolute geomagnetic Z component observations at Tianshui Observatory.The Hurst exponent H was calculated for each sub-sequence of data in specific time intervals.Our analysis result indicates that,2--3 months before Kunlun MS8.1 earthquake and Wenchuan MS8.0 earthquake,H value decreased and fractal dimension value D increased.Such dynamic variations manifest that the observations varied from persistent behaviour to antipersistent time-series before the earthquakes and the composition of the observed data changed.This variation is consistent with internal crustal stress change and rock failure experiment results.So we may view this dynamic variation as a premonitory symptom of the strong earthquakes.
引文
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陈棋福,郑大林,车时,黄蔚北.2008.中国震例[M].北京:地震出版社:426--429.
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张学民,李美,关华平.2009.汶川8.0级地震前的地电阻率异常分析[J].地震,29(1):108--115.
郑勇.2008.5.12汶川地震余震序列震源机制解[EB/OL].[2009-03-20].http:∥www.cea-igp.ac.cn/共享资源/中国大陆部分5级以上地震震源机制解.ht m.
Gotoh K,Hayakawa M,Smirnova N.2003.Fractal analysis of the ULF geomagnetic data obtained at Izu Peninsula,Ja-panin relation to the nearby earthquake swarmof June--August2000[J].Natural Hazards and Earth System Sci-ences,3:229--236.
Hayakawa M,Ito T,Smirnova N.1999.Fractal analysis of ULF geomagnetic data associated withthe Guamearthquakeon August8,1993[J].Geophys Res Lett,26(18):2797--2800.
Kiyashchenko D,Smirnova N,Troyan V,Vallianatos F.2003.Multifractal analysis of the regional seismicity dynamicsbefore the large earthquakes,Precursory evolution of spatial and temporal inhomogeneity of the seismicity distribu-tion[J].Natural Hazards and Earth System Sciences,3:220--228.
Mandelbrot B B.1977.Fractals,Form,Chance and Di mension[M].San Francisco:W HFreeman&Co:365.
Smirnova N,Hayakawa M,Gotoh1K,Volobuev D.2001.Scaling characteristics of ULFgeomagnetic fields at the Guamseismoactive area andtheir dynamicsin relationto the earthquake[J].Natural Hazards and Earth SystemSciences,1:119--126.
Tzanis A,Vallianatos F.2002.Aphysical model of electric earthquake precursors due to crack propagation and the mo-tion of charged edge dislocatios[G]∥Hayakawa M,Molchanov O Aeds.Seismo-Electromagnetics:Lithosphere-At-mosphere-Ionosphere Coupling.Tokyo:Terra Sci Pub Co:117--130.
Vallianatos F,Tzanis A.1999.A model for the generation of precursory electric and magnetic fields associated with thedeformation rate of the earthquake focus[G]∥Hayakawa Med.At mospheric and Ionospheric Electromagnetic Phe-nomena Associated with Earthquakes.Tokyo:Terra Sci Publ Co:287--306.
Vallianatos F,Makris J P,Saltas V.2004.Monofractal and multifractal analysisin short-termti me dynamics of ULFge-omagnetic field measuredin Crete,Greece[C]∥Bull Geol Soc Greece,Vol.XXXVI:1298--1307.
陈棋福,郑大林,车时,黄蔚北.2008.中国震例[M].北京:地震出版社:426--429.
丁鉴海,卢振业,黄雪香.1994.地震地磁学[M].北京:地震出版社:1.
高红兵,潘瑾,陈宏民.2001.我国证券市场波动的Hurst指数[J].东华大学学报(自然科学版),27(4):22--25.
许力生,陈运泰.2004.从全球长期波形资料反演2001年11月14日昆仑山口地震时空破裂过程[J].中国科学:D辑,34(3):256--264.
尤明庆.2000.岩石试样的强度及变形破坏过程[M].北京:地质出版社:156.
张继红.1997.分数维在地磁方法中的应用[J].地震研究,20(4):398--401.
张学民,李美,关华平.2009.汶川8.0级地震前的地电阻率异常分析[J].地震,29(1):108--115.
郑勇.2008.5.12汶川地震余震序列震源机制解[EB/OL].[2009-03-20].http:∥www.cea-igp.ac.cn/共享资源/中国大陆部分5级以上地震震源机制解.ht m.
Gotoh K,Hayakawa M,Smirnova N.2003.Fractal analysis of the ULF geomagnetic data obtained at Izu Peninsula,Ja-panin relation to the nearby earthquake swarmof June--August2000[J].Natural Hazards and Earth System Sci-ences,3:229--236.
Hayakawa M,Ito T,Smirnova N.1999.Fractal analysis of ULF geomagnetic data associated withthe Guamearthquakeon August8,1993[J].Geophys Res Lett,26(18):2797--2800.
Kiyashchenko D,Smirnova N,Troyan V,Vallianatos F.2003.Multifractal analysis of the regional seismicity dynamicsbefore the large earthquakes,Precursory evolution of spatial and temporal inhomogeneity of the seismicity distribu-tion[J].Natural Hazards and Earth System Sciences,3:220--228.
Mandelbrot B B.1977.Fractals,Form,Chance and Di mension[M].San Francisco:W HFreeman&Co:365.
Smirnova N,Hayakawa M,Gotoh1K,Volobuev D.2001.Scaling characteristics of ULFgeomagnetic fields at the Guamseismoactive area andtheir dynamicsin relationto the earthquake[J].Natural Hazards and Earth SystemSciences,1:119--126.
Tzanis A,Vallianatos F.2002.Aphysical model of electric earthquake precursors due to crack propagation and the mo-tion of charged edge dislocatios[G]∥Hayakawa M,Molchanov O Aeds.Seismo-Electromagnetics:Lithosphere-At-mosphere-Ionosphere Coupling.Tokyo:Terra Sci Pub Co:117--130.
Vallianatos F,Tzanis A.1999.A model for the generation of precursory electric and magnetic fields associated with thedeformation rate of the earthquake focus[G]∥Hayakawa Med.At mospheric and Ionospheric Electromagnetic Phe-nomena Associated with Earthquakes.Tokyo:Terra Sci Publ Co:287--306.
Vallianatos F,Makris J P,Saltas V.2004.Monofractal and multifractal analysisin short-termti me dynamics of ULFge-omagnetic field measuredin Crete,Greece[C]∥Bull Geol Soc Greece,Vol.XXXVI:1298--1307.
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