基于分层结构参数变化的地球自由振荡简正模研究
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摘要
大地震激发导致的地球自由振荡可为获得地球深部结构提供重要手段,通过理论计算自由振荡简正模的本征周期,并与实测结果进行比较,可为地球深内部结构和新地球模型的研究提供有效约束.采用微分方程数值积分技术和G-D1066A地球模型,本文计算了0～48阶的187个球型自由振荡简正模的本征周期,将计算结果与Gilbertt和Dziewonski等3组模型理论结果及Ness等4组观测结果进行比较,相对偏差在0.3%以内.分析说明由于考虑了地幔、外核和内核等不同分层密度和拉梅参数变化的影响,获得了较高精度的地球自由振荡简正模周期.本文提供的理论计算结果可为修正真实地球内部参数提供有效参考.
The research of Earth's free oscillations generated by large earthquakes gives important support to the study of Earth's deep internal structure.By comparing calculated normal mode eigenperiods with observations can offer an efficient constraint in the research of Earth's internal structure and new earth model.Using numerical integration method and Earth model G-D1066A, we obtain 187 eigenperiods between angular order 0 and 48.The relative errors between our results and previous three theoretical or four observed results are under 0.3%.The analysis shows that because the effects of density and Lame's parameters in different layers of Earth's interior are considered, the eigenperiods we obtained have good precision.The theoretical results given in this paper can give effective reference for revising the parameters of real Earth's interior.
The research of Earth's free oscillations generated by large earthquakes gives important support to the study of Earth's deep internal structure.By comparing calculated normal mode eigenperiods with observations can offer an efficient constraint in the research of Earth's internal structure and new earth model.Using numerical integration method and Earth model G-D1066A, we obtain 187 eigenperiods between angular order 0 and 48.The relative errors between our results and previous three theoretical or four observed results are under 0.3%.The analysis shows that because the effects of density and Lame's parameters in different layers of Earth's interior are considered, the eigenperiods we obtained have good precision.The theoretical results given in this paper can give effective reference for revising the parameters of real Earth's interior.
引文
[1] 严珍珍,张怀,杨长春等.地震激发的地球自由振荡研究综述.地球物理学进展,2008,23(3) :686～693 Yan Z Z,Zhang H,Yang C H,et al.A review of the Earth's free oscillations excited by earthquakes.Progress in Geophysics(in Chinese),2008,23(3) :686～689
[2] 方俊.地球自由振荡(续).测量与地球物理集刊,1986,8:53～69 Fang J.Earth free oscillation(continued).Geodesy and Geophysics Colloquium(in Chinese),1986,g : 53～69
[3] Takeuchi H,Saito M.Seismic surface waves.In Bolt B A ed.Seismology:Surface Waves and Free Oscillations,Methods in Computational Physics.New York: Academic Press,1972,11:217～295
[4] 方明.地球自由振荡--正演、反演理论中若干问题的研究[博士论文].武汉:中国科学院测量与地球物理研究所, 1991 Fang M.Earth free oscillation-studies on some problems of forward,inversion theory[Ph.D.thesis](in Chinese). Wuhan: Institute of Geodesy and Geophysics,Chinese Academy of Sciences,1991
[5] 严珍珍,张怀,杨长春等.地震激发地球自由振荡过程的数值模拟初步探索.地球科学进展,2008,23(10) :1020～1026 Yan Z Z,Zhang H,Yang C H,et al.An initial study of the numerical simulation of the Earth's free oscillations process excited by earthquake.Advance in Earth Sciences(in Chinese),2008,23(10) :1020～1026
[6] 雷湘鄂,许厚泽,孙和平.利用超导重力观测资料检测地球自由振荡.科学通报,2002,47(18) :1432～1436 Lei X E,Xu H Z,Sun H P.Check of free oscillation signal with SG data.Chinese Science Bulletin,2002,47(18) :1573～1578
[7] 孙和平,雷湘鄂.重力技术在地球自由振荡检测研究中的应用.地球物理学进展,2005,20(4) :974～979 Sun H P,Lei X E.Application of the gravity technique on detection of the Earth's free oscillations.Progress in Geophysics(in Chinese),2005,20(4) :974～979
[8] 宋秀青,于海英.印度洋9.0级大地震激发的基频地球球型振荡.地震地磁观测与研究,2005,26(4) :13～17 Song X Q,Yu H Y.Fundamental spheroidal mode excited by the earthquake of 9.0 in the Indian Ocean on Dec.26th 2004.Seismological and Geomagnetic Observation and Research(in Chinese),2005,26(4) :13～17
[9] 邱泽华,马瑾,池顺良等.钻孔差应变仪观测的苏门答腊大地震激发的地球环型自由振荡.地球物理学报,2007,50(3) :797～805 Qiu Z H,Ma J,Chi S L,et al.Earth' s free torsional oscillations of the great Sumatra earthquake observed with borehole shear strainmeter.Chinese J.Geophys.(in Chinese),2007,50(3) :797～805
[10] 万永革,盛书中,周公威等.中国数字地震台网记录的苏门答腊-安达曼地震激发的地球球型自由振荡的检测.地震学报,2007,29(4) :369～381 Wan Y G,Sheng S Z,Zhou G W,et al.Spheroidal oscillations of the earth stimulated by the Sumatra-Andaman earthquake with CDSN data.Acta Seismologica Sinica(in Chinese),2007,29(4) :369～381
[11] 任佳,陈华静,王松等.汶川大地震激发的地球球型自由振荡.中国地震,2009,25(3) :73～80 Ren J,Chen H J,Wang S,et al.The Earth's spheroidal oscillations induced by the Wenchuan earthquake.Earthquake Research in China(in Chinese),2009,25(3) :73～80
[12] 雷湘鄂,许厚泽,孙和平.由5个国际超导重力仪台站资料检测到的秘鲁8.2级大地震所激发的球型自由振荡现象.中国科学(D辑),2004,34(5) :483～491 Lei X E,Xu H Z,Sun H P.Detection of spheroidal free oscillation excited by Peru 8.2 M_s earthquake with five international superconducting gravimeter data.Science in China(Ser.D),2005,48(1) :123～133
[13] 徐华君,柳林涛,罗孝文.标准Morlet小波变换检测地球自由振荡.测绘学报,2009,38(1) :16～21 Xu H J,Liu L T,Luo X W.Normal Morlet wavelet transform and its application to detection of the Earth's free oscillations.Acta Geodaetica et Cartographica Sinica(in Chinese),2009,38(1) :16～21
[14] Gilbert F,Dziewonski A M.An application of Normal Mode theory to the retrieval of structural parameters and source mechanisms from seismic spectra.Philosophical Transactions of the Royal Society of London.Series A,Mathematical and Physical Sciences,1975,278:178～269
[15] 郭俊义.地球物理学基础.北京:测绘出版社,2001.197～208 Guo J Y.Fundamentals of Geophysics(in Chinese).Beijing: The Surveying and Mapping Press,2001.197～208
[16] Alterman Z S,Jarosh H,Pekeris C L.Oscillation of the earth.Proceedings of the Royal Society of London.Series A,Mathematical and Physical Sciences,1959,252:80～95
[17] 杨兆,孙和平,雷湘鄂.环型自由振荡简正模的计算.大地测量与地球动力学,2007,27(4) :38～43 Yang Z,Sun H P,Lei X E.Computation of normal modes of toroidal oscillation.Journal of Geodesy and Geod ynamics(in Chinese),2007,27(4) :38～43
[18] Derr J S.Internal structure of the earth inferred from free oscillations.J.Geophys.Res.,1969,74(22) :5202～5220
[19] Jordan T H,Anderson D L.Earth structure from free oscillations and travel times.Geophys.JR astr.Soc.,1974,36:411～459
[20] Ness N R,Harrison C T,Slichter L B.Observation of the free oscillation of the earth.J.Geophys.Res.,1961,66(2) :621～629
[21] Dziewonski A M,Gilbert F.Observations of normal modes from 84 recordings of the Alaskan earthquake of 1964 March 28.Geophys.J R astr.Soc.,1972,27:293～446
[22] 雷湘鄂,许厚泽,孙和平.苏门达腊大地震激发的地球自由振荡及其谱线分裂的检测与讨论.中国科学(D辑),2007, 37(4) :504～511 Lei X E,Xu H Z,Sun H P.Check of Earth's free oscillations excited by Sumatra-Andaman large earthquake and discussions on the anisotropy of inner core.Science in China(Ser.D),2007,50(6) :909～917
[23] Masters T G,Widmer R.Free oscillations: frequencies and attenuations.Global Earth Physics..a Handbook of Physical Constants,1995
[2] 方俊.地球自由振荡(续).测量与地球物理集刊,1986,8:53～69 Fang J.Earth free oscillation(continued).Geodesy and Geophysics Colloquium(in Chinese),1986,g : 53～69
[3] Takeuchi H,Saito M.Seismic surface waves.In Bolt B A ed.Seismology:Surface Waves and Free Oscillations,Methods in Computational Physics.New York: Academic Press,1972,11:217～295
[4] 方明.地球自由振荡--正演、反演理论中若干问题的研究[博士论文].武汉:中国科学院测量与地球物理研究所, 1991 Fang M.Earth free oscillation-studies on some problems of forward,inversion theory[Ph.D.thesis](in Chinese). Wuhan: Institute of Geodesy and Geophysics,Chinese Academy of Sciences,1991
[5] 严珍珍,张怀,杨长春等.地震激发地球自由振荡过程的数值模拟初步探索.地球科学进展,2008,23(10) :1020～1026 Yan Z Z,Zhang H,Yang C H,et al.An initial study of the numerical simulation of the Earth's free oscillations process excited by earthquake.Advance in Earth Sciences(in Chinese),2008,23(10) :1020～1026
[6] 雷湘鄂,许厚泽,孙和平.利用超导重力观测资料检测地球自由振荡.科学通报,2002,47(18) :1432～1436 Lei X E,Xu H Z,Sun H P.Check of free oscillation signal with SG data.Chinese Science Bulletin,2002,47(18) :1573～1578
[7] 孙和平,雷湘鄂.重力技术在地球自由振荡检测研究中的应用.地球物理学进展,2005,20(4) :974～979 Sun H P,Lei X E.Application of the gravity technique on detection of the Earth's free oscillations.Progress in Geophysics(in Chinese),2005,20(4) :974～979
[8] 宋秀青,于海英.印度洋9.0级大地震激发的基频地球球型振荡.地震地磁观测与研究,2005,26(4) :13～17 Song X Q,Yu H Y.Fundamental spheroidal mode excited by the earthquake of 9.0 in the Indian Ocean on Dec.26th 2004.Seismological and Geomagnetic Observation and Research(in Chinese),2005,26(4) :13～17
[9] 邱泽华,马瑾,池顺良等.钻孔差应变仪观测的苏门答腊大地震激发的地球环型自由振荡.地球物理学报,2007,50(3) :797～805 Qiu Z H,Ma J,Chi S L,et al.Earth' s free torsional oscillations of the great Sumatra earthquake observed with borehole shear strainmeter.Chinese J.Geophys.(in Chinese),2007,50(3) :797～805
[10] 万永革,盛书中,周公威等.中国数字地震台网记录的苏门答腊-安达曼地震激发的地球球型自由振荡的检测.地震学报,2007,29(4) :369～381 Wan Y G,Sheng S Z,Zhou G W,et al.Spheroidal oscillations of the earth stimulated by the Sumatra-Andaman earthquake with CDSN data.Acta Seismologica Sinica(in Chinese),2007,29(4) :369～381
[11] 任佳,陈华静,王松等.汶川大地震激发的地球球型自由振荡.中国地震,2009,25(3) :73～80 Ren J,Chen H J,Wang S,et al.The Earth's spheroidal oscillations induced by the Wenchuan earthquake.Earthquake Research in China(in Chinese),2009,25(3) :73～80
[12] 雷湘鄂,许厚泽,孙和平.由5个国际超导重力仪台站资料检测到的秘鲁8.2级大地震所激发的球型自由振荡现象.中国科学(D辑),2004,34(5) :483～491 Lei X E,Xu H Z,Sun H P.Detection of spheroidal free oscillation excited by Peru 8.2 M_s earthquake with five international superconducting gravimeter data.Science in China(Ser.D),2005,48(1) :123～133
[13] 徐华君,柳林涛,罗孝文.标准Morlet小波变换检测地球自由振荡.测绘学报,2009,38(1) :16～21 Xu H J,Liu L T,Luo X W.Normal Morlet wavelet transform and its application to detection of the Earth's free oscillations.Acta Geodaetica et Cartographica Sinica(in Chinese),2009,38(1) :16～21
[14] Gilbert F,Dziewonski A M.An application of Normal Mode theory to the retrieval of structural parameters and source mechanisms from seismic spectra.Philosophical Transactions of the Royal Society of London.Series A,Mathematical and Physical Sciences,1975,278:178～269
[15] 郭俊义.地球物理学基础.北京:测绘出版社,2001.197～208 Guo J Y.Fundamentals of Geophysics(in Chinese).Beijing: The Surveying and Mapping Press,2001.197～208
[16] Alterman Z S,Jarosh H,Pekeris C L.Oscillation of the earth.Proceedings of the Royal Society of London.Series A,Mathematical and Physical Sciences,1959,252:80～95
[17] 杨兆,孙和平,雷湘鄂.环型自由振荡简正模的计算.大地测量与地球动力学,2007,27(4) :38～43 Yang Z,Sun H P,Lei X E.Computation of normal modes of toroidal oscillation.Journal of Geodesy and Geod ynamics(in Chinese),2007,27(4) :38～43
[18] Derr J S.Internal structure of the earth inferred from free oscillations.J.Geophys.Res.,1969,74(22) :5202～5220
[19] Jordan T H,Anderson D L.Earth structure from free oscillations and travel times.Geophys.JR astr.Soc.,1974,36:411～459
[20] Ness N R,Harrison C T,Slichter L B.Observation of the free oscillation of the earth.J.Geophys.Res.,1961,66(2) :621～629
[21] Dziewonski A M,Gilbert F.Observations of normal modes from 84 recordings of the Alaskan earthquake of 1964 March 28.Geophys.J R astr.Soc.,1972,27:293～446
[22] 雷湘鄂,许厚泽,孙和平.苏门达腊大地震激发的地球自由振荡及其谱线分裂的检测与讨论.中国科学(D辑),2007, 37(4) :504～511 Lei X E,Xu H Z,Sun H P.Check of Earth's free oscillations excited by Sumatra-Andaman large earthquake and discussions on the anisotropy of inner core.Science in China(Ser.D),2007,50(6) :909～917
[23] Masters T G,Widmer R.Free oscillations: frequencies and attenuations.Global Earth Physics..a Handbook of Physical Constants,1995
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