最小能量准则用于1995年河北沙城M_L 4.1地震序列破裂性质的探讨
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摘要
运用变分原理,我们得到了最小地震波辐射能量约束准则并用于研究震源的物理过程.通过研究1995年ML4.1河北沙城地震序列主震和余震的动力学过程,可知主震和余震震源的动态破裂过程明显不同;ML4.1主震的破裂速度与瑞利波速相近,约为剪切波速度的0.89倍;而28个余震的破裂速度远远小于剪切波速度,大约是剪切波速度的0.05到0.55倍.根据裂纹扩展模型,计算得到其余震的地震波辐射效率多在10%以下,这也说明了余震的地震效率较低.我们认为余震震源的动态破裂过程应与断层内部新生裂纹的扩展有关,而非简单的岩体间的相对滑动.余震震源的动态破裂传播与破裂能占主导地位的小地震有关.这些小震所带来的破裂能也导致了断层的进一步扩展.在对该地震序列的研究中,我们发现主震与余震的震源破裂过程在能量分配上有着本质的区别.因此当地震断层尺度相当小时,破裂能的贡献不能忽略,它的大小将显著地影响地震波辐射能的大小.
From variational principle,we have derived the minimum radiation energy criterion(MREC),and use it in the earthquake source dynamics study.For the 1995 ML 4.1 Shacheng Heibei earthquake sequence,we come to the conclusion that the dynamic rupture processes of main shock and aftershocks are totally different: the rupture speed of the ML 4.1 main shock is about 0.89 of shear wave speed,closing to the Rayleigh wave speed,while the rupture speeds of the remained 28 aftershocks range from 0.05 to 0.55 of shear wave speed,which is much smaller than shear wave speed.In addition,based on the circular crack extending model,we also calculate the seismic radiation efficiencies for this earthquake sequence,and the results indicate that,for most aftershocks,the radiation efficiencies are less than 10%,inferring a low seismic efficiency.In our study,we suggest that the dynamic rupture processes of these aftershocks could be related to the crack(sub-fault) extension inside the main fault,rather than the simple momentum of the moving block,which has been commonly assumed in the fault frictional motion if an overshoot occurs during earthquake rupture.The local stress concentrations inside the fault after main shock may play an important role in sustaining the crack extension.Therefore,the fracturing process associated with the crack extension for the aftershock becomes a main energy dissipation mechanism.Compared with the ML 4.1 main shock,we also find that there exists an essential difference in the earthquake energy partition for the aftershock source dynamics.In other words,the fracture energy dissipation could not be ignored in the source parameter estimation for the earthquake faulting,especially for small earthquakes.Otherwise,the radiated seismic energy could be overestimated or underestimated.
From variational principle,we have derived the minimum radiation energy criterion(MREC),and use it in the earthquake source dynamics study.For the 1995 ML 4.1 Shacheng Heibei earthquake sequence,we come to the conclusion that the dynamic rupture processes of main shock and aftershocks are totally different: the rupture speed of the ML 4.1 main shock is about 0.89 of shear wave speed,closing to the Rayleigh wave speed,while the rupture speeds of the remained 28 aftershocks range from 0.05 to 0.55 of shear wave speed,which is much smaller than shear wave speed.In addition,based on the circular crack extending model,we also calculate the seismic radiation efficiencies for this earthquake sequence,and the results indicate that,for most aftershocks,the radiation efficiencies are less than 10%,inferring a low seismic efficiency.In our study,we suggest that the dynamic rupture processes of these aftershocks could be related to the crack(sub-fault) extension inside the main fault,rather than the simple momentum of the moving block,which has been commonly assumed in the fault frictional motion if an overshoot occurs during earthquake rupture.The local stress concentrations inside the fault after main shock may play an important role in sustaining the crack extension.Therefore,the fracturing process associated with the crack extension for the aftershock becomes a main energy dissipation mechanism.Compared with the ML 4.1 main shock,we also find that there exists an essential difference in the earthquake energy partition for the aftershock source dynamics.In other words,the fracture energy dissipation could not be ignored in the source parameter estimation for the earthquake faulting,especially for small earthquakes.Otherwise,the radiated seismic energy could be overestimated or underestimated.
引文
[1]Kanamori H,Hauksson E,Hutton L K,et al.Determination of earthquake energy release andMLusingterrascope.Bull.Seism.Soc.Am.,1993,83:330~346
[2]Mayeda K,Walter W R.Moment,energy,stress drop,andsource spectra of western United States earthquakes fromregional coda envelopes.J.Geophys.Res.,1996,101:11195~11208
[3]Abercrombie R.Earthquake source scaling relationships from-1 to 5MLusing seismograms recorded at 2.5km depth.J.Geophys.Res.,1995,100:24015~24036
[4]Hanks T,Thatcher W.Graphical representation of seismicsource parameters.J.Geophys.Res.,1972,77:4393~4405
[5]Brune J N.Tectonic stress and the spectra of seismic shearwaves from earthquakes.J.Geophys.Res.,1970,75:4997~5009
[6]Ide S,Beroza G C.Does apparent stress vary withearthquake size?Geophys.Res.Lett.,2001,28:3349~3352
[7]Ide S.Estimation of radiated energy of finite source models.Bull.Seism.Soc.Am.,2002,92:2994~3005
[8]王培德,王鸣,任道容等.中国—欧共体地震科学合作项目“北京西北延庆—怀来盆地地震学研究”进展.地震地磁观测与研究,1995,16(3):8~14Wang P D,Wang M,Ren D R,et al.Progress of the China-European communities seismology cooperative project‘seismological study of the Yanqing-Huailai basin,NW ofBeijing’.Seismological and Geomagnetic Observation andResearch(in Chinese),1995,16(3):8~14
[9]Chen Y T.Seismological study of the Yanqing-Huailai basin,NW of Beijing.In:Department of International Scientific andTechnological Cooperation SSTC,China(ed.),SuccessfulSino-European Science and Technology Cooperation,1981~1995.Beijing:Tsinghua University Press,134~139
[10]许向彤.小孔径数字地震台网在中小地震震源参数反演中的应用研究[博士论文].北京:中国地震局地球物理研究所,2003Xu X T.The application research of HDSN in the sourceparameters invertion of middle and small earthquakes[Ph.D.thesis].Beijing:Institute of Geophysics,China EarthquakeAdministration,2003
[11]许向彤,陈运泰,王培德.怀来盆地构造应力场.地震地磁观测与研究,1997,18(1):1~8Xu X T,Chen Y T,Wang P D.Tectonic stress field inHuailai basin.Seismological and Geomagnetic Observationand Research(in Chinese),1997,18(1):1~8
[12]许向彤,陈运泰,王培德.1995年7月20日怀来盆地ML4.1地震的破裂过程.地震学报,1999,21(6):570~582Xu X T,Chen Y T,Wang P D.Rupture process of theML=4.1 earthquake in Huailai basin on July 20,1995.ActaSeismologica Sinica,1999,12(6):618~631
[13]许向彤,陈运泰,王培德.1995年7月20日怀来盆地ML4.1地震序列震源参数的精确测定.地震学报,2001,23(3):225~238Xu X T,Chen Y T,Wang P D.Precies determination offocal parameters for July 20,1995ML=4.1 earthquakesequence in the Huailai Basin.Acta Seismologica Sinica(inChinese),2001,23(3):225~238
[14]ZU′N~IGA F R.Fractional overshoot and partial stress drop.Which one?Bull.Seism.Soc.Am.,1993,83(3):939~944
[15]陈学忠,许向彤,翟文杰.1995年7月20日河北沙城ML4.1地震序列破裂过程中应力变化的研究.地震学报,2005,27(3):276~281Chen X Z,Xu X T,Zhai W J.Variation of stress duaring therupture process of the 1995ML=4.1 Shacheng,Heibei,China,Earthquake Sequence.Acta Seismologica Sinica(inChinese),2005,27(3):276~281
[16]Brune J N.The physics of earthquake strong motion.In:Lomnitz C,Rosenblueth E eds.Seismic Risk and EngineeringDecisions.Elasevier,New York,1976,141~177
[17]Savage J C,Wood M D.The relation between apparent stressand stress drop.Bull.Seism.Soc.Am.,1971,61:1381~1338
[18]Aki K,Richards P G.Quantitative Seismology Theory andMethods.San Francisco:Freeman,1980,1 and 2:932
[19]Anderson J G.Seismic energy and stress-drop parameters fora composite source model.Bull.Seism.Soc.Am.,1997,87(1):85~96
[20]Haskell N.Total energy and energy spectral density of elasticwave radiation from propagating faults.Bull.Seism.Soc.Am.,1964,56:1811~1842
[21]Kanamori H,Rivera L.Static and dynamic scaling relationsfor earthquakes and their implications for rupture speed andstress drop.Bull.Seism.Soc.Am.,2004,94(1):314~319
[22]Kanamori H,Brodsky E E.The Physics of Earthquakes.Rep.Prog.Phys.,2004,67:1429~1496
[23]中国地震局监制预报司.地震参数——数字地震学在地震预测中的应用.北京:地震出版社,2003Chinese Earthquake Administration Monitoring andPrediction Bureau.The Use of Digital Seismology in theEarthquake Prediction.Beijing:Seismological Press,2003
[2]Mayeda K,Walter W R.Moment,energy,stress drop,andsource spectra of western United States earthquakes fromregional coda envelopes.J.Geophys.Res.,1996,101:11195~11208
[3]Abercrombie R.Earthquake source scaling relationships from-1 to 5MLusing seismograms recorded at 2.5km depth.J.Geophys.Res.,1995,100:24015~24036
[4]Hanks T,Thatcher W.Graphical representation of seismicsource parameters.J.Geophys.Res.,1972,77:4393~4405
[5]Brune J N.Tectonic stress and the spectra of seismic shearwaves from earthquakes.J.Geophys.Res.,1970,75:4997~5009
[6]Ide S,Beroza G C.Does apparent stress vary withearthquake size?Geophys.Res.Lett.,2001,28:3349~3352
[7]Ide S.Estimation of radiated energy of finite source models.Bull.Seism.Soc.Am.,2002,92:2994~3005
[8]王培德,王鸣,任道容等.中国—欧共体地震科学合作项目“北京西北延庆—怀来盆地地震学研究”进展.地震地磁观测与研究,1995,16(3):8~14Wang P D,Wang M,Ren D R,et al.Progress of the China-European communities seismology cooperative project‘seismological study of the Yanqing-Huailai basin,NW ofBeijing’.Seismological and Geomagnetic Observation andResearch(in Chinese),1995,16(3):8~14
[9]Chen Y T.Seismological study of the Yanqing-Huailai basin,NW of Beijing.In:Department of International Scientific andTechnological Cooperation SSTC,China(ed.),SuccessfulSino-European Science and Technology Cooperation,1981~1995.Beijing:Tsinghua University Press,134~139
[10]许向彤.小孔径数字地震台网在中小地震震源参数反演中的应用研究[博士论文].北京:中国地震局地球物理研究所,2003Xu X T.The application research of HDSN in the sourceparameters invertion of middle and small earthquakes[Ph.D.thesis].Beijing:Institute of Geophysics,China EarthquakeAdministration,2003
[11]许向彤,陈运泰,王培德.怀来盆地构造应力场.地震地磁观测与研究,1997,18(1):1~8Xu X T,Chen Y T,Wang P D.Tectonic stress field inHuailai basin.Seismological and Geomagnetic Observationand Research(in Chinese),1997,18(1):1~8
[12]许向彤,陈运泰,王培德.1995年7月20日怀来盆地ML4.1地震的破裂过程.地震学报,1999,21(6):570~582Xu X T,Chen Y T,Wang P D.Rupture process of theML=4.1 earthquake in Huailai basin on July 20,1995.ActaSeismologica Sinica,1999,12(6):618~631
[13]许向彤,陈运泰,王培德.1995年7月20日怀来盆地ML4.1地震序列震源参数的精确测定.地震学报,2001,23(3):225~238Xu X T,Chen Y T,Wang P D.Precies determination offocal parameters for July 20,1995ML=4.1 earthquakesequence in the Huailai Basin.Acta Seismologica Sinica(inChinese),2001,23(3):225~238
[14]ZU′N~IGA F R.Fractional overshoot and partial stress drop.Which one?Bull.Seism.Soc.Am.,1993,83(3):939~944
[15]陈学忠,许向彤,翟文杰.1995年7月20日河北沙城ML4.1地震序列破裂过程中应力变化的研究.地震学报,2005,27(3):276~281Chen X Z,Xu X T,Zhai W J.Variation of stress duaring therupture process of the 1995ML=4.1 Shacheng,Heibei,China,Earthquake Sequence.Acta Seismologica Sinica(inChinese),2005,27(3):276~281
[16]Brune J N.The physics of earthquake strong motion.In:Lomnitz C,Rosenblueth E eds.Seismic Risk and EngineeringDecisions.Elasevier,New York,1976,141~177
[17]Savage J C,Wood M D.The relation between apparent stressand stress drop.Bull.Seism.Soc.Am.,1971,61:1381~1338
[18]Aki K,Richards P G.Quantitative Seismology Theory andMethods.San Francisco:Freeman,1980,1 and 2:932
[19]Anderson J G.Seismic energy and stress-drop parameters fora composite source model.Bull.Seism.Soc.Am.,1997,87(1):85~96
[20]Haskell N.Total energy and energy spectral density of elasticwave radiation from propagating faults.Bull.Seism.Soc.Am.,1964,56:1811~1842
[21]Kanamori H,Rivera L.Static and dynamic scaling relationsfor earthquakes and their implications for rupture speed andstress drop.Bull.Seism.Soc.Am.,2004,94(1):314~319
[22]Kanamori H,Brodsky E E.The Physics of Earthquakes.Rep.Prog.Phys.,2004,67:1429~1496
[23]中国地震局监制预报司.地震参数——数字地震学在地震预测中的应用.北京:地震出版社,2003Chinese Earthquake Administration Monitoring andPrediction Bureau.The Use of Digital Seismology in theEarthquake Prediction.Beijing:Seismological Press,2003
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