分形及其在地震研究中的应用
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摘要
本文简要介绍了分形的基本理论,对分形在地震研究中的应用进行了阐述。着重介绍了近年来地震分形在地震预报中应用的一些成果。在此基础上,提出了作者对于开展进一步工作的意见,认为应该对区域和全球的地震分形进行全局性、系统性的研究,逐渐探索地震分形的物理机制和动力学机制,从而在地震研究上取得新进展。
The present paper reported the basic theories of fractal and its application in seismic study.The temporal-space characteristics of seismic fractal and its application in seismic prediction are emphasized.Based on the discussion,several proposals were put forward for the further studies of seismic fractal.These proposals include carrying on a global and systematical study of seismic fractal of local and global earthquakes and exploring the physical and dynamical mechanism of seismic fractal.It is believed that these proposals can help us get breakthroughs on seismic study.
The present paper reported the basic theories of fractal and its application in seismic study.The temporal-space characteristics of seismic fractal and its application in seismic prediction are emphasized.Based on the discussion,several proposals were put forward for the further studies of seismic fractal.These proposals include carrying on a global and systematical study of seismic fractal of local and global earthquakes and exploring the physical and dynamical mechanism of seismic fractal.It is believed that these proposals can help us get breakthroughs on seismic study.
引文
[1]Mandelbrot.B.B.How long is the coast of Britain? Statistical self-similarity and fractal dimension[J].Science,1967,156:636-638
[2]朱令人,龙海英.地震多重分形计算的最小生成树法[J].地震学报,2000,22(4):410-417
[3]李娟.地震的分形特征及R/S标度不变性[J].自然杂志,2001,23(4):206-210
[4]Manderbort B B.The Fractal Geometry of Nature[M].San Fransico:W.H.Freenan and company,1982
[5]燕云鹏.台湾地区地震活动的分形研究[D].北京:中国地震局地质研究所,2002
[6]蔡强,周成虎,裴韬,等.华北地震时空多重分形的时间演化特征研究[J].地震,2002,22(2):74-80
[7]朱令人.地震分形[M].北京:地震出版社,1996
[8]Smalley R F.Chatelain J L,Turcotte D L,et al.A fractal approach to the clustering of earthquakes:applications to the seismicity of the New Hebrides[J].BSSA,1987,77(4):1368-1381
[9]Adam Filip Idziak.A Study of Spatial Distribution of Induced Seismicity in the Upper Silesian Coal Basin[J].Natural Hazards,1999,19:97-105
[10]Avadh Ram,P.N.S.Roy,Fractal Dimensions of Blocks Using a Box-counting Technique for the 2001 Bhuj Earthquake,Gujarat,India[J].Pure and Applied Geophysics,2005,162(3):531-548
[11]Kagan Y.Y,Knopoff L.Spatial distribution of earthquake:the two-point correlation function[J].Geophys.J.R.Astr.Soc.,1980(62):303-320
[12]Sadovskiy M.A.Characteristic dimensions of rock and hierarchical properties of seismicity[J].USSR Phys Solid Earth Engl Trans,1984(20):87-96
[13]Hiarte D.Dimension estimates of earthquake epicenters and hypocenters[J].Norlinear Sci.,1998,8:581-618
[14]Hiarte D.Document for the Statistical Seismology Library,Research Report,School of Mathematics and Computing Sciences[M].Wellington:Victoria University of Wellington Press,2000
[15]Hiarte D.Multifractals:Theory and Application[M].New York:Chapman&Hall/CRC Press,2001
[16]Hirata T,Imoto M.Multifracal analysis of spatial distribution of microearthquakes in the Kanto Region[J].Geophys Int,1991(107):155-162
[17]Hirabayashi T.Multifractal analysis of earthquakes[J].Pageopy,1992(138):591-610
[18]Jeen-Hwa Wang.Fractal Characterization of seismic networks in Taiwan TAO[J].Geophys,1993(6):116-120
[19]Wang,J H and Lee,C W,Fractal Characterization of an Earthquake Sequence[J].Physica A,1995,221:162-158
[20]王琳瑛,朱传镇,黄容良.地震时空分布结构的多重分形特征的研究[J].地震,1994,16(5):1-18
[21]陈时军,Harte D,马丽,等.新西兰地区地震活动时空分布的多重分形特征研究[J].地震学报,2003,25(3):298-307
[22]刁守中,蒋海昆,华爱军,等.华北地区地震时间结构的多分形特征[J].内陆地震,1996,10(2):103-111
[23]平建军,张清荣.1989年大同6.1级地震前山西带小震活动时间分布结构多重分形维数的变化特征[J].华北地震科学,1996,14(2):42-46
[24]Legrand D,Cisternas A,Dorbath L.Multifractal analysis of the 1992 Erzincan aftershock sequence[J].Geophysical Research Letters,1996,23(9):933-936
[25]Dimitriu P P,Scordilis E M.Multifractal Analysis of the Arnea,Greece Seismicity with Potential Implications for Earthquake Prediction[J].Natural Hazards,2000,21:277-295
[26]Kossobokov V G,Keilis-Borok V I.Implications of a Statistical Physics Approach for Earthquake Hazard Assessment and Forecasting[J].Pure and Applied Geophysics,2000,157(11-12):2323-2349
[27]Olivia Bazacliu,Mircea Radulian.Seismicity variations in depth and time in the Vrancea(Romania)subcrustal region[J].Natural Hazards,1999,19(2-3):165-177
[28]Bogdan Enescu,Kiyoshi Ito.Some premonitory phenomena of the 1995 Hyogo-Ken Nanbu(Kobe)earthquake:seismicity,b-value and fuactal dimension[J].Tectonophysics,2001(338):297-314
[29]Kiyashchenko D,Smirnova N.Seismic hazard precursory evolution:fractal and multifractal aspects[J].Physics and Chemistry of the Earth,2004(29):367-378
[30]朱令人,周仕勇,杨马陵,等.强震前多重分形谱的异常及其物理解释以乌什研究区为例[J].内陆地震,1995,7(2):97-103
[31]安镇文,杨翠华,王琳瑛,等.地震时空丛集的多重分形研究[J].地球物理学报,2000,43(1):74-80
[32]石绍先,范杨,邓志辉,等.云南10次大震前地震活动分形研究[J].中国地震,1996,12(4):367-377
[33]彭克银,高伟.分形方法在地震序列类型早期判别中的应用[J].地震,1996,16(1):68-73
[34]李强.江苏及邻区地震时序的多重分形特征及其预报意义[J].地震研究,2002,25(3):257-261
[35]刘长海,刘义高.中强地震前后地震时间序列的自仿射分形特征[J].地震学报,1994,16(3):352-360
[36]汪秉宏,郑兆钧,李东升,等.地震分布多重分形特征的中期预报意义探讨[J].地震学刊,1998:19-18
[37]King,G.The accommodation of large stains in the upper lithosphere of the earth and other solids by self-similar faultsystems:the geometrical origin of b value[J],Puer Appl.Geophys.1983,121:761-815
[38]沈小七,陈宇卫,刘东旺,等.华东及安徽地区断裂构造及分形分析[J].灾害学,2005,20(3):53-56
[39]武孔春.地震序列性质与断层分形关系的探讨[J].地震研究,1995,18(2):174-182
[40]陈时军,David H.,王丽凤,等.广义地震应变能释放的多重分形特征[J].地震学报,2003,25(2):182-190
[41]吴云,龚凯虹,周硕愚,等.地震能量时空分布的自仿射分形特征[J].地壳形变与地震,1997,17(2):20-26
[42]蒋维强.地震主压力轴分布的分形特征研究[J].中国地震,1994,10(2):129-135
[43]Lasocki S,De Luca L.Monte Carlo Studies of Relationsbetween Fractal Dimensions in Monofractal Data Sets[J].Pure Appl.Geophys.,1998,152:213-220
[44]韩渭宾,徐叶邦,王维恩.容量维、信息维随时间变化特征与地震预报[J].地球物理学报,1993(36):195-202
[45]洪时中,洪时明.分维与地震科学[J].科学,1990,21(2):34-40
[46]朱令人,龙海英.离散点集(地震)空间分布多重分形计算的精度估算[J].地震,2000,20(3):1-8
[47]朱令人,周仕勇,杨马陵,等.地震时间序列多重分形计算精度估计[J].中国地震,2000,16(2):166-175
[48]张晓东.地震分布非点集分形理论探讨[J].地震,2000,20:70-74
[49]陈颙,陈凌.分形几何学[M].北京:地震出版社,2005
[2]朱令人,龙海英.地震多重分形计算的最小生成树法[J].地震学报,2000,22(4):410-417
[3]李娟.地震的分形特征及R/S标度不变性[J].自然杂志,2001,23(4):206-210
[4]Manderbort B B.The Fractal Geometry of Nature[M].San Fransico:W.H.Freenan and company,1982
[5]燕云鹏.台湾地区地震活动的分形研究[D].北京:中国地震局地质研究所,2002
[6]蔡强,周成虎,裴韬,等.华北地震时空多重分形的时间演化特征研究[J].地震,2002,22(2):74-80
[7]朱令人.地震分形[M].北京:地震出版社,1996
[8]Smalley R F.Chatelain J L,Turcotte D L,et al.A fractal approach to the clustering of earthquakes:applications to the seismicity of the New Hebrides[J].BSSA,1987,77(4):1368-1381
[9]Adam Filip Idziak.A Study of Spatial Distribution of Induced Seismicity in the Upper Silesian Coal Basin[J].Natural Hazards,1999,19:97-105
[10]Avadh Ram,P.N.S.Roy,Fractal Dimensions of Blocks Using a Box-counting Technique for the 2001 Bhuj Earthquake,Gujarat,India[J].Pure and Applied Geophysics,2005,162(3):531-548
[11]Kagan Y.Y,Knopoff L.Spatial distribution of earthquake:the two-point correlation function[J].Geophys.J.R.Astr.Soc.,1980(62):303-320
[12]Sadovskiy M.A.Characteristic dimensions of rock and hierarchical properties of seismicity[J].USSR Phys Solid Earth Engl Trans,1984(20):87-96
[13]Hiarte D.Dimension estimates of earthquake epicenters and hypocenters[J].Norlinear Sci.,1998,8:581-618
[14]Hiarte D.Document for the Statistical Seismology Library,Research Report,School of Mathematics and Computing Sciences[M].Wellington:Victoria University of Wellington Press,2000
[15]Hiarte D.Multifractals:Theory and Application[M].New York:Chapman&Hall/CRC Press,2001
[16]Hirata T,Imoto M.Multifracal analysis of spatial distribution of microearthquakes in the Kanto Region[J].Geophys Int,1991(107):155-162
[17]Hirabayashi T.Multifractal analysis of earthquakes[J].Pageopy,1992(138):591-610
[18]Jeen-Hwa Wang.Fractal Characterization of seismic networks in Taiwan TAO[J].Geophys,1993(6):116-120
[19]Wang,J H and Lee,C W,Fractal Characterization of an Earthquake Sequence[J].Physica A,1995,221:162-158
[20]王琳瑛,朱传镇,黄容良.地震时空分布结构的多重分形特征的研究[J].地震,1994,16(5):1-18
[21]陈时军,Harte D,马丽,等.新西兰地区地震活动时空分布的多重分形特征研究[J].地震学报,2003,25(3):298-307
[22]刁守中,蒋海昆,华爱军,等.华北地区地震时间结构的多分形特征[J].内陆地震,1996,10(2):103-111
[23]平建军,张清荣.1989年大同6.1级地震前山西带小震活动时间分布结构多重分形维数的变化特征[J].华北地震科学,1996,14(2):42-46
[24]Legrand D,Cisternas A,Dorbath L.Multifractal analysis of the 1992 Erzincan aftershock sequence[J].Geophysical Research Letters,1996,23(9):933-936
[25]Dimitriu P P,Scordilis E M.Multifractal Analysis of the Arnea,Greece Seismicity with Potential Implications for Earthquake Prediction[J].Natural Hazards,2000,21:277-295
[26]Kossobokov V G,Keilis-Borok V I.Implications of a Statistical Physics Approach for Earthquake Hazard Assessment and Forecasting[J].Pure and Applied Geophysics,2000,157(11-12):2323-2349
[27]Olivia Bazacliu,Mircea Radulian.Seismicity variations in depth and time in the Vrancea(Romania)subcrustal region[J].Natural Hazards,1999,19(2-3):165-177
[28]Bogdan Enescu,Kiyoshi Ito.Some premonitory phenomena of the 1995 Hyogo-Ken Nanbu(Kobe)earthquake:seismicity,b-value and fuactal dimension[J].Tectonophysics,2001(338):297-314
[29]Kiyashchenko D,Smirnova N.Seismic hazard precursory evolution:fractal and multifractal aspects[J].Physics and Chemistry of the Earth,2004(29):367-378
[30]朱令人,周仕勇,杨马陵,等.强震前多重分形谱的异常及其物理解释以乌什研究区为例[J].内陆地震,1995,7(2):97-103
[31]安镇文,杨翠华,王琳瑛,等.地震时空丛集的多重分形研究[J].地球物理学报,2000,43(1):74-80
[32]石绍先,范杨,邓志辉,等.云南10次大震前地震活动分形研究[J].中国地震,1996,12(4):367-377
[33]彭克银,高伟.分形方法在地震序列类型早期判别中的应用[J].地震,1996,16(1):68-73
[34]李强.江苏及邻区地震时序的多重分形特征及其预报意义[J].地震研究,2002,25(3):257-261
[35]刘长海,刘义高.中强地震前后地震时间序列的自仿射分形特征[J].地震学报,1994,16(3):352-360
[36]汪秉宏,郑兆钧,李东升,等.地震分布多重分形特征的中期预报意义探讨[J].地震学刊,1998:19-18
[37]King,G.The accommodation of large stains in the upper lithosphere of the earth and other solids by self-similar faultsystems:the geometrical origin of b value[J],Puer Appl.Geophys.1983,121:761-815
[38]沈小七,陈宇卫,刘东旺,等.华东及安徽地区断裂构造及分形分析[J].灾害学,2005,20(3):53-56
[39]武孔春.地震序列性质与断层分形关系的探讨[J].地震研究,1995,18(2):174-182
[40]陈时军,David H.,王丽凤,等.广义地震应变能释放的多重分形特征[J].地震学报,2003,25(2):182-190
[41]吴云,龚凯虹,周硕愚,等.地震能量时空分布的自仿射分形特征[J].地壳形变与地震,1997,17(2):20-26
[42]蒋维强.地震主压力轴分布的分形特征研究[J].中国地震,1994,10(2):129-135
[43]Lasocki S,De Luca L.Monte Carlo Studies of Relationsbetween Fractal Dimensions in Monofractal Data Sets[J].Pure Appl.Geophys.,1998,152:213-220
[44]韩渭宾,徐叶邦,王维恩.容量维、信息维随时间变化特征与地震预报[J].地球物理学报,1993(36):195-202
[45]洪时中,洪时明.分维与地震科学[J].科学,1990,21(2):34-40
[46]朱令人,龙海英.离散点集(地震)空间分布多重分形计算的精度估算[J].地震,2000,20(3):1-8
[47]朱令人,周仕勇,杨马陵,等.地震时间序列多重分形计算精度估计[J].中国地震,2000,16(2):166-175
[48]张晓东.地震分布非点集分形理论探讨[J].地震,2000,20:70-74
[49]陈颙,陈凌.分形几何学[M].北京:地震出版社,2005
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