地震激发的地球自由振荡研究综述
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摘要
地球自由振荡的研究已成为探查地球内部结构的重要手段之一.影响地球自由振荡的因素有很多,如地球物理学结构横向不均匀性及径向不均匀性、地球自转、地球椭率、地球内部各向异性、非弹性性以及震源机制性质,还有地球外界如引潮力等.本文详细介绍和总结了近几十年来关于地球自由振荡理论研究、实验及观测资料方面的研究,重点是数值模拟方法方面的研究工作.通过观测和理论分析对比,以数值实验的方式推测地球内部更详细的结构分布,如地球内部密度分布以及波速度等特性;并从弹性波理论出发结合高性能并行计算对全球自由振荡过程进行数值模拟研究.
The research of the Earth′s free oscillations has become one of the major means to study the Earth′s internal structure.There are many factors concerning with the Earth′s free oscillations,such as the Earth′s lateral heterogeneity and radial heterogeneity,self-rotation,ellipticity,anisotropy,anelasticity and focal mechanism,together with other factors such as tidal and atmosphere pressure effects.In this paper,we make a brief review of the researches and developments on the Earth′s free oscillation theories and observation results.We focus on the analytical and numerical methods to conduct the detailed research work on these phenomena.Through comparing the experiment and observation results with the theoretical or numerical simulation results,we will be able to image more detailed Earth′s internal structure,such as material density distribution and elastic wave speeds.The combination of the elastic wave theory and high-performance parallel computational technology for the research of the Earth′s free oscillations is also discussed briefly.
The research of the Earth′s free oscillations has become one of the major means to study the Earth′s internal structure.There are many factors concerning with the Earth′s free oscillations,such as the Earth′s lateral heterogeneity and radial heterogeneity,self-rotation,ellipticity,anisotropy,anelasticity and focal mechanism,together with other factors such as tidal and atmosphere pressure effects.In this paper,we make a brief review of the researches and developments on the Earth′s free oscillation theories and observation results.We focus on the analytical and numerical methods to conduct the detailed research work on these phenomena.Through comparing the experiment and observation results with the theoretical or numerical simulation results,we will be able to image more detailed Earth′s internal structure,such as material density distribution and elastic wave speeds.The combination of the elastic wave theory and high-performance parallel computational technology for the research of the Earth′s free oscillations is also discussed briefly.
引文
[1]Benioff H,Press F,Smith S.Excitation of the free oscilla-tions of the earth by earthquake[J].J Geophys Res,1961,66(2):605~619.
[2]Alsop L E,Sutton G H,Ewing M.Free oscillations of theEarth observed on strain and pendulum seismographs[J].J.Geophys.Res.,1961,66:631~641.
[3]Lay T,Wallace T C.Modern global seismology[M].San Die-go:Academic Press,1995,117~173.
[4]Dahlen F A.The normal modes of a rotationg,ellipticalEarth.[J].Geophys.J.R.Astr.,1968,16:329~367.
[5]Alsop L E.Excitation of free oscillations of the Earth by thekurile islands Earthquake of 13 october 1963[J].Bulletin ofthe Seismological Society of America,1964,54(5A):1341~1348.
[6]Alterman Z S,Eyal Y,Merzer A M.On free oscillations ofthe Earth[J].Geophysical Surveys,1974,1:409~428.
[7]Kawakatsu H.Can'pure-path'models explain free oscillationdata?[J].Geophysical Research Letters,1983,10(3):186~189.
[8]Tsuboi S,GellerI R.Partial derivatives of the eigenfrequencesof a laterally heterogeneous Earth model[J].Geophysical Re-search Letters,1985,12(12):817~820.
[9]Tsuboi N.Free oscillations of a laterally heterogeneous andanelastic Earth[J].Pageoph,1995,145:445~457.
[10]Schnidrig R W.Free oscillations illuminate the mantle[J].nature,1999,398:292~293.
[11]Backus G,Gilbert F.The rotational splitting of the free os-cillations of the Earth[J].Proceedings of the National Acade-my of Sciences of the UNited States of America,1961,47:362~371.
[12]Geller R J,Stein S.Split free oscillation amplitudes for the1960 chilean and 1964 alaskan Earthquakes[J].Bulletin ofthe Seismological Society of America,1977,67(3):651~660.
[13]Dickey J O.Earth Rotation[M]:American Geophysical U-nion,1995,356~368.
[14]Smith M F,Masters G.The effect of coriolis coupling of freeoscillation multiplets on the determination of aspherical Earthstructures[J].Geophysical Research Letters,1989,16(3):263~266.
[15]Dahlen F A.The normal modes of a rotating,ellipticalEarth-II near-resonance multiplet coupling[J].Geophys.J.R.Astr.,1969,18:397~436.
[16]Dahlen F A,Sailor R V.Rotational and elliptical splitting ofthe free oscillations of the Earth[J].Geophys.J.R.Astr.SOC,1979,58:609~623.
[17]Kenneth C,Creager T H J.Aspherical structure of the core-mantle boundary from PKP travel times[J].Geophysical Re-search Letters,1986,13(13):1497~1500.
[18]Luh P C,Dziewonski A M.Theoretical normal-mode spectraof a rotating elliptical Earth[J].Geophys.J.R.astr.SOC,1976,45:617~645.
[19]Rogister Y.Splitting of seismic-free oscillations and of theSlichter triplet using the normal mode theory of a rotating,ellipsoidal Earth[J].Physics of the Earth and Planetary Inte-riors,2003,140:169~182.
[20]Dziewonski A M,Gilbert F.Solidity of the inner core of theEarth inferred from normal mode observations[J].Nature,1971,234:465~466.
[21]Woodhouse J H,Giardini D,Li X D.Evidence for inner coreanisotropy from free oscillations[J].Geophysical ResearchLetters,1986,13(13):1549~1552.
[22]Dorman J,Ewing J,Alsop L E.Oscillations of the Earth:new core-mantle boundary model based on low-order free vi-brations[J].Proceedings of the National Academy of Sci-ences of the United States of America,1965,54:364~368.
[23]Giardini D,Woodhouse J H.Splitting functions of long-peri-od normal modes of the Earth[J].J.Geophys.Res.,1988,93(B11):716~729.
[24]Ishii M,Tromp J,Dziewonski A M.Joint inversion of nor-mal mode and body wave data for inner core anistropy:later-ally homogeneous anisotropy[J].J.Geophys.Res.,2002,107(B12):2379~2395.
[25]Tromp J.Normal-mode splitting due to inner-core anisotropy[J].Geophys.J.int,1995,121:963~968.
[26]Oda H,Isoda S,Inouye Y.Elastic constants and anelasticproperties of an anisotropic periclase sphere as determined bythe resonant sphere technique[J].Journal of Geophysical Re-search,1994,99(B8):15517~15527.
[27]Song X,Helmberger D V.A P wave velocity model of Earth's core[J].Journal of Geophysical Research,1995,100(B7):9817~9830.
[28]Koper K D,Pyle M L,Franks J M.Constraints on aspheri-cal core structure from PKiKP-PcP differential travel times[J].Journal of Geophysical Research,2003,108(B3):1~15.
[29]雷湘鄂,孙和平,许厚泽,石耀霖.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[J].中国科学(D辑:地球科学),2007,37(4):504~511.Lei X E,Sun H P,Xu H Z,Shi Y L.Check of Earth's freeoscillations excited by Sumatra-Andaman Large earthquakeand discussions on the anistropy of inner core[J].Science inChina(series D:earth sciences),2007,50(6):909~917.
[30]Smith M F,Masters G.Aspherical structure constraintsfrom free oscillation frequency and attenuation measurements[J].J Geophys Res,1989,94(B2):1953~1976.
[31]Masters T G,Widmer R.Free oscillations:frequencies andattenuations[M].Americal Geophysical Union,1995,104~125.
[32]Jobert N,Roult G.Periods and damping of free oscillationsobserved in france after sixteen earthquakes[J].Geophys.J.R.astr.SOC,1976,45:155~176.
[33]Davies J H.Seismically“fast”geodynamic mantle models[J].Geophysical Research Letters,2001,28(1):73~76.
[34]Fukao Y,Suda N.Core modes of the earth's free oscillationsand structure of the inner core[J].Geophysical ResearchLetters,1989,16(5):401~404.
[35]Pollitz F F,Park J,Dahlen F A.Observations of free oscilla-tion amplitude anomalies[J].Geophysical Research Letters,1987,14(9):895~898.
[36]Stein S,Okal E A.Speed and size of the sumatra earthquake[J].Nature,2005,434:581~582.
[37]Suda N,Nawa K,Fukao Y.Earth′s background free oscilla-tions[J].Science,1998,279(27):2089~2092.
[38]Nishida K.Statistical features of Earth's continuous free os-cillations[J].Journal of Geophysical Research,1999,104(B12):28741~28750.
[39]Tanimoto T,Um J.Cause of continuous oscillations of theEarth[J].Journal of Geophysical Research,1999,104(B12):28723~28739.
[40]Kurbasova G S,Rykhlova L V.Free oscillations of parame-ters of the Earth′s motion in the Earth~Moon system[J].Astronomy Reports,2001,45(11):922~928.
[41]Fukao Y,Nishida K,Suda N.A theory of the Earth′s back-ground free oscillations[J].Journal of Geophysical Research,2002,107(B9):1~11.
[42]胡小刚,柳林涛,柯小平,许厚泽,孙和平等.利用小波方法处理2004年苏门答腊大地震后的超导重力数据检测低于1.5 mHz自由振荡信号的耦合和分裂术[J].中国科学(D辑:地球科学),2006,36(10):925~935.Hu X G,Liu L T,Ke X P.Wavelet filter analysis of split-ting and coupling of seismic normal modes below 1.5 mHzwith superconducting gra-vimeter records after the December26,2004 Sumatra earthquake[J].Science in China(seriesD:earth sciences),2006,49(12):1259~1269.
[43]雷湘鄂,孙和平,许厚泽.利用超导重力观测资料检测地球自由振荡[J].科学通报,2002,47(18):1132~1136.Lei X E,Sun H P,Xu H Z.Check of free oscillation signalwith SG data[J].Chinese Science Bulletin,2002,47(8):1573~1578.
[44]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[J].地球物理学进展,2005,20(4):974~979.Sun H P,Lei X E,Hsu H Z.Application of the gravity tech-nique on detection of the Earth s free oscillations[J].Pro-gress in Geophysics(in Chinese),2005,20(4):974~979.
[45]Camp M V.Measuring seismic normal modes with the GWRC021 superconducting gravimeter[J].Physics of the Earthand Planetary Interiors,1999,116:81~92.
[46]于海英,朱元清,寿海涛.印度洋9.0级大地震激发的地球球型振荡和环型振荡[J].地球物理学进展,2006,21(3):706~716.Yu H Y,Zhu Y Q,Shou H T.Toroidal and spheroidal modeof the earth's free oscilation excited by the Indian ocean earth-quake[J].Progress in Geophysics(in Chinese),2006,21(3):706~716.
[47]邱泽华,马瑾,池顺良.钻孔差应变仪观测的苏门达腊大地震激发的地球环型自由振荡[J].地球物理学报,2007,50(3):797~805.Qiu Z H,Ma J,Chi S L,Liu H M.Earth's free torsional oscil-lations of the great Sumatra earthquake observed with bore-hole shear strainmeter.Chinese J.Geophys.(in Chinese),2007,50(3):797~805.
[48]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[J].地震地磁观测与研究,2005,26(4):13~17.Song X Q,Yu H Y.Fundamental spheroidal mode excited bythe earthquake of 9.0 in the Indian Ocean on Dec.26th 2004[J].Seismological and Geomagnetic Observation and Re-search,(in Chinese),2005,26(4):13~17.
[49]Braitenberg C,Zadro M.Comparative analysis of the free os-cillations generated by the sumatra-andaman islands 2004 andthe Chile 1960 Earthquakes[J].Bulletin of the SeismologicalSociety of America,2007,97(1A):S6~S17.
[50]Boyd J P.Chebyshev and Fourier Spectral Methods[M].New York:DOVER Publications,Inc.,2000.
[51]Komatitsch D,Tromp J.Spectral-element simulations ofglobal seismic wave propagation—II.Three-dimensional mod-els,oceans,rotation and self-gravitation[J].Geophys.J.Int,2002,150:303~318.
[52]Komatitsch D,Tromp J.Spectral-element simulations ofglobal seismic wave propagation—I.Validation[J].Geo-phys.J.Int,2002,149:390~412.
[53]Komatitsch D,Vilotte J P,Vai R.The spectral elementmethod for elastic wave equations-application to 2-D and 3-Dseismic problems[J].Int.J.Numer.Meth.Engng.,1999,45:1139~1164.
[54]Komatitsch D,Ritsema J,Tromp J.The spectral-elementmethod,beowulf computing,and global seismology[J].Sci-ence,2002,298:1737~1742.
[55]Komatitsch D,Tromp J.Introduction to the spectral elementmethod for three-dimensional seismic wave propagation[J].Geophys.J.Int,1999,139:806~822.
[56]Tsuboi S,Komatitsch D,Chen J.Modeling of global seismicwave propagation on the Earth Simulator[J].Journal of theEarth Simulator,2004,1:57~66.
[57]Komatitsch D,Liu Q Y,Tromp J.Simulations of GroundMotion in the Los Angeles Basin Based upon the Spectral-El-ement Method[J].Bulletin of the Seismological Society of A-merica,2004,94(1):187~206.
[2]Alsop L E,Sutton G H,Ewing M.Free oscillations of theEarth observed on strain and pendulum seismographs[J].J.Geophys.Res.,1961,66:631~641.
[3]Lay T,Wallace T C.Modern global seismology[M].San Die-go:Academic Press,1995,117~173.
[4]Dahlen F A.The normal modes of a rotationg,ellipticalEarth.[J].Geophys.J.R.Astr.,1968,16:329~367.
[5]Alsop L E.Excitation of free oscillations of the Earth by thekurile islands Earthquake of 13 october 1963[J].Bulletin ofthe Seismological Society of America,1964,54(5A):1341~1348.
[6]Alterman Z S,Eyal Y,Merzer A M.On free oscillations ofthe Earth[J].Geophysical Surveys,1974,1:409~428.
[7]Kawakatsu H.Can'pure-path'models explain free oscillationdata?[J].Geophysical Research Letters,1983,10(3):186~189.
[8]Tsuboi S,GellerI R.Partial derivatives of the eigenfrequencesof a laterally heterogeneous Earth model[J].Geophysical Re-search Letters,1985,12(12):817~820.
[9]Tsuboi N.Free oscillations of a laterally heterogeneous andanelastic Earth[J].Pageoph,1995,145:445~457.
[10]Schnidrig R W.Free oscillations illuminate the mantle[J].nature,1999,398:292~293.
[11]Backus G,Gilbert F.The rotational splitting of the free os-cillations of the Earth[J].Proceedings of the National Acade-my of Sciences of the UNited States of America,1961,47:362~371.
[12]Geller R J,Stein S.Split free oscillation amplitudes for the1960 chilean and 1964 alaskan Earthquakes[J].Bulletin ofthe Seismological Society of America,1977,67(3):651~660.
[13]Dickey J O.Earth Rotation[M]:American Geophysical U-nion,1995,356~368.
[14]Smith M F,Masters G.The effect of coriolis coupling of freeoscillation multiplets on the determination of aspherical Earthstructures[J].Geophysical Research Letters,1989,16(3):263~266.
[15]Dahlen F A.The normal modes of a rotating,ellipticalEarth-II near-resonance multiplet coupling[J].Geophys.J.R.Astr.,1969,18:397~436.
[16]Dahlen F A,Sailor R V.Rotational and elliptical splitting ofthe free oscillations of the Earth[J].Geophys.J.R.Astr.SOC,1979,58:609~623.
[17]Kenneth C,Creager T H J.Aspherical structure of the core-mantle boundary from PKP travel times[J].Geophysical Re-search Letters,1986,13(13):1497~1500.
[18]Luh P C,Dziewonski A M.Theoretical normal-mode spectraof a rotating elliptical Earth[J].Geophys.J.R.astr.SOC,1976,45:617~645.
[19]Rogister Y.Splitting of seismic-free oscillations and of theSlichter triplet using the normal mode theory of a rotating,ellipsoidal Earth[J].Physics of the Earth and Planetary Inte-riors,2003,140:169~182.
[20]Dziewonski A M,Gilbert F.Solidity of the inner core of theEarth inferred from normal mode observations[J].Nature,1971,234:465~466.
[21]Woodhouse J H,Giardini D,Li X D.Evidence for inner coreanisotropy from free oscillations[J].Geophysical ResearchLetters,1986,13(13):1549~1552.
[22]Dorman J,Ewing J,Alsop L E.Oscillations of the Earth:new core-mantle boundary model based on low-order free vi-brations[J].Proceedings of the National Academy of Sci-ences of the United States of America,1965,54:364~368.
[23]Giardini D,Woodhouse J H.Splitting functions of long-peri-od normal modes of the Earth[J].J.Geophys.Res.,1988,93(B11):716~729.
[24]Ishii M,Tromp J,Dziewonski A M.Joint inversion of nor-mal mode and body wave data for inner core anistropy:later-ally homogeneous anisotropy[J].J.Geophys.Res.,2002,107(B12):2379~2395.
[25]Tromp J.Normal-mode splitting due to inner-core anisotropy[J].Geophys.J.int,1995,121:963~968.
[26]Oda H,Isoda S,Inouye Y.Elastic constants and anelasticproperties of an anisotropic periclase sphere as determined bythe resonant sphere technique[J].Journal of Geophysical Re-search,1994,99(B8):15517~15527.
[27]Song X,Helmberger D V.A P wave velocity model of Earth's core[J].Journal of Geophysical Research,1995,100(B7):9817~9830.
[28]Koper K D,Pyle M L,Franks J M.Constraints on aspheri-cal core structure from PKiKP-PcP differential travel times[J].Journal of Geophysical Research,2003,108(B3):1~15.
[29]雷湘鄂,孙和平,许厚泽,石耀霖.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[J].中国科学(D辑:地球科学),2007,37(4):504~511.Lei X E,Sun H P,Xu H Z,Shi Y L.Check of Earth's freeoscillations excited by Sumatra-Andaman Large earthquakeand discussions on the anistropy of inner core[J].Science inChina(series D:earth sciences),2007,50(6):909~917.
[30]Smith M F,Masters G.Aspherical structure constraintsfrom free oscillation frequency and attenuation measurements[J].J Geophys Res,1989,94(B2):1953~1976.
[31]Masters T G,Widmer R.Free oscillations:frequencies andattenuations[M].Americal Geophysical Union,1995,104~125.
[32]Jobert N,Roult G.Periods and damping of free oscillationsobserved in france after sixteen earthquakes[J].Geophys.J.R.astr.SOC,1976,45:155~176.
[33]Davies J H.Seismically“fast”geodynamic mantle models[J].Geophysical Research Letters,2001,28(1):73~76.
[34]Fukao Y,Suda N.Core modes of the earth's free oscillationsand structure of the inner core[J].Geophysical ResearchLetters,1989,16(5):401~404.
[35]Pollitz F F,Park J,Dahlen F A.Observations of free oscilla-tion amplitude anomalies[J].Geophysical Research Letters,1987,14(9):895~898.
[36]Stein S,Okal E A.Speed and size of the sumatra earthquake[J].Nature,2005,434:581~582.
[37]Suda N,Nawa K,Fukao Y.Earth′s background free oscilla-tions[J].Science,1998,279(27):2089~2092.
[38]Nishida K.Statistical features of Earth's continuous free os-cillations[J].Journal of Geophysical Research,1999,104(B12):28741~28750.
[39]Tanimoto T,Um J.Cause of continuous oscillations of theEarth[J].Journal of Geophysical Research,1999,104(B12):28723~28739.
[40]Kurbasova G S,Rykhlova L V.Free oscillations of parame-ters of the Earth′s motion in the Earth~Moon system[J].Astronomy Reports,2001,45(11):922~928.
[41]Fukao Y,Nishida K,Suda N.A theory of the Earth′s back-ground free oscillations[J].Journal of Geophysical Research,2002,107(B9):1~11.
[42]胡小刚,柳林涛,柯小平,许厚泽,孙和平等.利用小波方法处理2004年苏门答腊大地震后的超导重力数据检测低于1.5 mHz自由振荡信号的耦合和分裂术[J].中国科学(D辑:地球科学),2006,36(10):925~935.Hu X G,Liu L T,Ke X P.Wavelet filter analysis of split-ting and coupling of seismic normal modes below 1.5 mHzwith superconducting gra-vimeter records after the December26,2004 Sumatra earthquake[J].Science in China(seriesD:earth sciences),2006,49(12):1259~1269.
[43]雷湘鄂,孙和平,许厚泽.利用超导重力观测资料检测地球自由振荡[J].科学通报,2002,47(18):1132~1136.Lei X E,Sun H P,Xu H Z.Check of free oscillation signalwith SG data[J].Chinese Science Bulletin,2002,47(8):1573~1578.
[44]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[J].地球物理学进展,2005,20(4):974~979.Sun H P,Lei X E,Hsu H Z.Application of the gravity tech-nique on detection of the Earth s free oscillations[J].Pro-gress in Geophysics(in Chinese),2005,20(4):974~979.
[45]Camp M V.Measuring seismic normal modes with the GWRC021 superconducting gravimeter[J].Physics of the Earthand Planetary Interiors,1999,116:81~92.
[46]于海英,朱元清,寿海涛.印度洋9.0级大地震激发的地球球型振荡和环型振荡[J].地球物理学进展,2006,21(3):706~716.Yu H Y,Zhu Y Q,Shou H T.Toroidal and spheroidal modeof the earth's free oscilation excited by the Indian ocean earth-quake[J].Progress in Geophysics(in Chinese),2006,21(3):706~716.
[47]邱泽华,马瑾,池顺良.钻孔差应变仪观测的苏门达腊大地震激发的地球环型自由振荡[J].地球物理学报,2007,50(3):797~805.Qiu Z H,Ma J,Chi S L,Liu H M.Earth's free torsional oscil-lations of the great Sumatra earthquake observed with bore-hole shear strainmeter.Chinese J.Geophys.(in Chinese),2007,50(3):797~805.
[48]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[J].地震地磁观测与研究,2005,26(4):13~17.Song X Q,Yu H Y.Fundamental spheroidal mode excited bythe earthquake of 9.0 in the Indian Ocean on Dec.26th 2004[J].Seismological and Geomagnetic Observation and Re-search,(in Chinese),2005,26(4):13~17.
[49]Braitenberg C,Zadro M.Comparative analysis of the free os-cillations generated by the sumatra-andaman islands 2004 andthe Chile 1960 Earthquakes[J].Bulletin of the SeismologicalSociety of America,2007,97(1A):S6~S17.
[50]Boyd J P.Chebyshev and Fourier Spectral Methods[M].New York:DOVER Publications,Inc.,2000.
[51]Komatitsch D,Tromp J.Spectral-element simulations ofglobal seismic wave propagation—II.Three-dimensional mod-els,oceans,rotation and self-gravitation[J].Geophys.J.Int,2002,150:303~318.
[52]Komatitsch D,Tromp J.Spectral-element simulations ofglobal seismic wave propagation—I.Validation[J].Geo-phys.J.Int,2002,149:390~412.
[53]Komatitsch D,Vilotte J P,Vai R.The spectral elementmethod for elastic wave equations-application to 2-D and 3-Dseismic problems[J].Int.J.Numer.Meth.Engng.,1999,45:1139~1164.
[54]Komatitsch D,Ritsema J,Tromp J.The spectral-elementmethod,beowulf computing,and global seismology[J].Sci-ence,2002,298:1737~1742.
[55]Komatitsch D,Tromp J.Introduction to the spectral elementmethod for three-dimensional seismic wave propagation[J].Geophys.J.Int,1999,139:806~822.
[56]Tsuboi S,Komatitsch D,Chen J.Modeling of global seismicwave propagation on the Earth Simulator[J].Journal of theEarth Simulator,2004,1:57~66.
[57]Komatitsch D,Liu Q Y,Tromp J.Simulations of GroundMotion in the Los Angeles Basin Based upon the Spectral-El-ement Method[J].Bulletin of the Seismological Society of A-merica,2004,94(1):187~206.
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