地球内核平动振荡的地震激发
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摘要
本文利用球对称、非自转、弹性和各向同性地球模型(SNREI)理论模拟计算了地球内核平动振荡的地震激发.以2004年12月26日苏门答腊大地震为例,讨论震源机制解(标量地震矩、走向、倾角、滑动角和深度)对内核平动振荡振幅激发的影响;基于全球21个Mw8.0级以上的大地震,分别计算10个数据资料较好的超导重力台站理论上可以接收到的内核平动振荡信号的频率域振幅.结果表明标量地震矩对内核平动振荡振幅的影响最大,走向、倾角、滑动角和深度对内核平动振荡振幅也有一定影响,但是影响相对较小;不同区域获得的由大地震引起的内核平动振荡信号的幅度存在显著差异,此结果为频率域多台站加权迭积提供了计算基础.另外,只有武汉台站接收到的2011年日本Tohoku Mw9.1地震激发的内核平动振荡的振幅值达到了地球表面高精度、高灵敏度的超导重力仪检测水平,振幅值为0.0103nm·s-2.结果说明地震激发的内核平动振荡的信号极其微弱,信号几乎淹没在背景噪声中,必须利用多台站迭积法才有可能将信号提取出来.
The translational oscillation of the solid inner core,which is also called Slichter mode(SM),has an eigenperiod of several hours that is closely related to the Earth′s interior structure,and is one of the fundamental normal modes of the Earth.The SM may be excited by large deep earthquakes,asymmetric crystallization of the fluid material in the outer core,or other unknown excitation sources.The excitation mechanism of them is still unclear.It is supposed that a large earthquake can excite the translational oscillation of the inner core,and amplitudes excited by large earthquakes and received by different stations are calculated in order to verify whether the superconducting gravimeter(SG)can detect such weak signal.Based on the spherical,non-rotating,elastic and isotropic(SNREI)Earth model,the earthquake excitation of translational oscillation in the Earth′s inner core was calculated.Taking the 2004-12-26 Sumatra earthquake as an example,the influence of inner core translational oscillation′s earthquake excitation caused by the focal mechanism solution(scalar seismic moment,strike,dip,slip and depth)was analyzed.Based on 21 earthquakes the magnitude of which were larger than Mw8.0since 1980,10 superconducting gravimeters stations with high-quality observations were chosen,and amplitudes of the inner core translational oscillation received by those stations were calculated theoretically.In the reference focal mechanism solutions,the hypocenter was equivalent to a double couple point source in the focal mechanism model.Six independent seismic moment tensors were determined based on the theory of double couple centroid moment tensors.Based on the Preliminary Reference Earth Model(PREM)combined with the focal mechanism solution,moment tensors of the Green′s function were determined by the weighted sum,and free oscillation displacements were obtained that simulate measured free oscillation signals.It is found that the scalar seismic moment M0 has a major influence on the amplitudes of inner core translational oscillation;additionally,the strike,dip,rake and depth of the hypocenter have minor influences.When one of the M0,strike,dip,rake and depth changes while other keep constant,the difference of amplitudes is 0.223,0.095,0.081,0.139 and 0.187nm·s-2·Hz-1,respectively.And it is indicated that the amplitudes of the inner core translational oscillation in different areas excited by great earthquakes have significant differences,and the results are the basis of weighting stacking the SGs′observation in the frequency domain to detect the signal.In addition,only the Wuhan station received the amplitude excited by 2010 Tohoku Mw9.1earthquake that reached the observational level of the high accuracy and sensitivity superconducting gravimeter with maximum amplitude 0.0103nm·s-2.It implies that the signal is extremely weak and it may be buried in the background noise.It is a good choice that increases the weight of the observations with larger amplitudes after large earthquakes.Weighting stack of the observations to suppress the noise and enlarging the signal should be used to detect the signal.In fact,owing to the ellipticity and rotation of the Earth,the SM splits to form a triplet,including the movement at the Earth′s rotation axis and the equatorial prograde and retrograde translational movements.The earthquake excitation of the triplet based on a rotating,slightly elliptical Earth model would be calculated during the following work.According to the calculation results in this paper,the amplitudes excited by earthquakes are very small,and other possible excitation mechanisms will be researched in the future.
The translational oscillation of the solid inner core,which is also called Slichter mode(SM),has an eigenperiod of several hours that is closely related to the Earth′s interior structure,and is one of the fundamental normal modes of the Earth.The SM may be excited by large deep earthquakes,asymmetric crystallization of the fluid material in the outer core,or other unknown excitation sources.The excitation mechanism of them is still unclear.It is supposed that a large earthquake can excite the translational oscillation of the inner core,and amplitudes excited by large earthquakes and received by different stations are calculated in order to verify whether the superconducting gravimeter(SG)can detect such weak signal.Based on the spherical,non-rotating,elastic and isotropic(SNREI)Earth model,the earthquake excitation of translational oscillation in the Earth′s inner core was calculated.Taking the 2004-12-26 Sumatra earthquake as an example,the influence of inner core translational oscillation′s earthquake excitation caused by the focal mechanism solution(scalar seismic moment,strike,dip,slip and depth)was analyzed.Based on 21 earthquakes the magnitude of which were larger than Mw8.0since 1980,10 superconducting gravimeters stations with high-quality observations were chosen,and amplitudes of the inner core translational oscillation received by those stations were calculated theoretically.In the reference focal mechanism solutions,the hypocenter was equivalent to a double couple point source in the focal mechanism model.Six independent seismic moment tensors were determined based on the theory of double couple centroid moment tensors.Based on the Preliminary Reference Earth Model(PREM)combined with the focal mechanism solution,moment tensors of the Green′s function were determined by the weighted sum,and free oscillation displacements were obtained that simulate measured free oscillation signals.It is found that the scalar seismic moment M0 has a major influence on the amplitudes of inner core translational oscillation;additionally,the strike,dip,rake and depth of the hypocenter have minor influences.When one of the M0,strike,dip,rake and depth changes while other keep constant,the difference of amplitudes is 0.223,0.095,0.081,0.139 and 0.187nm·s-2·Hz-1,respectively.And it is indicated that the amplitudes of the inner core translational oscillation in different areas excited by great earthquakes have significant differences,and the results are the basis of weighting stacking the SGs′observation in the frequency domain to detect the signal.In addition,only the Wuhan station received the amplitude excited by 2010 Tohoku Mw9.1earthquake that reached the observational level of the high accuracy and sensitivity superconducting gravimeter with maximum amplitude 0.0103nm·s-2.It implies that the signal is extremely weak and it may be buried in the background noise.It is a good choice that increases the weight of the observations with larger amplitudes after large earthquakes.Weighting stack of the observations to suppress the noise and enlarging the signal should be used to detect the signal.In fact,owing to the ellipticity and rotation of the Earth,the SM splits to form a triplet,including the movement at the Earth′s rotation axis and the equatorial prograde and retrograde translational movements.The earthquake excitation of the triplet based on a rotating,slightly elliptical Earth model would be calculated during the following work.According to the calculation results in this paper,the amplitudes excited by earthquakes are very small,and other possible excitation mechanisms will be researched in the future.
引文
Aid K,Richards P G.1980.Quantitative Seismology:Theory andMethods.San Francisco:University Science Books.
Courtier N,Ducarme B,Goodkind J,et al.2000.Globalsuperconducting gravimeter observations and the search for thetranslational modes of the inner core.Phys.Earth Planet.Inter.,117(1-4):3-20,doi:10.1016/S0031-9201(99)00083-7.
Crossley D J.1992.Eigensolutions and seismic excitation of theSlichter mode triplet for a fully rotating Earth model.EOS,73:60.
Crossley D J,Rochester M G,Peng Z R.1992.Slichter modes andLove numbers.Geophysical Research Letters,19(16):1679-1682,doi:10.1029/92GL01574.
Dahlen F A,Smith M L.1975.The influence of rotation on the freeoscillations of the Earth.Philosophical Transactions of theRoyal Society of London.Series A,Mathematical and PhysicalSciences,279(1292):583-624,doi:10.1098/rsta.1975.0087.
Ding H,Shen W B.2013.Search for the Slichter modes based on anew method:Optimal sequence estimation.Journal of GeophysicalResearch:Solid Earth,118(9):5018-5029,doi:10.1002/jgrb.50344.
Geller R J,Stein S.1979.Time-domain attenuation measurementsfor fundamental spheroidal modes(0S6to0S21)for the 1977Indonesian earthquake.Bulletin of the Seismological Societyof America,69(6):1671-1691.
Gilbert F.1971.The diagonal sum rule and averaged eigenfrequencies.Geophysical Journal of the Royal Astronomical Society,23(1):119-123,doi:10.1111/j.1365-246X.1971.tb01806.x.
Greff-Lefftz M,Legros H.2007.Fluid core dynamics and degreeone deformations:Slichter mode and geocenter motions.Physics ofthe Earth and Planetary Interiors,161(3-4):150-160,doi:10.1016/j.pepi.2006.12.003.
Guo J Y,Dierks O,Neumeyer J,et al.2006.Weighting algorithmsto stack superconducting gravimeter data for the potentialdetection of the Slichter modes.J.Geodyn.,41(1):326-333,doi:10.1016/j.jog.2005.08.014.
Hinderer J,Crossley D J,Jensen O A.1995.A search for theSlichter triplet in superconducting gravimeter data.Physics ofthe Earth and Planetary Interior,90(3):183-195,doi:10.1016/0031-9201(95)05083-N.
Jiang Y,Xu J Q,Sun H P.2013.Detection of inner coretranslational oscillations using superconducting gravimeters.Journal of Earth Science,24(5):750-758,doi:10.1007/s12583-013-0370-x.
Jiang Y,Hu X G,Liu C L,Sun H.2014.Constraining focalmechanism of Lushan earthquake by observations of the Earth′sfree oscillation.Science China Earth Sciences,57(9):2064-2070,doi:10.1007/s11430-014-4913-5.
Jiang Y,Xu J Q,Sun H P.2014.The influence of eigenperiod ofinner core′s translational oscillations caused by deep interiorstructure.Chinese Journal of Geophysics(in Chinese),57(4):1041-1048,doi:10.6038/cjg20140403.
Kanamori H,Cipar J J.1974.Focal process of the great Chileanearthquake May 22,1960.Physics of the Earth and PlanetaryInteriors,9(2):128-136,doi:10.1016/0031-9201(74)90029-6.
Kennet B L N.1991.IASPEI 1991seismological tables.TerraNova,3(2):122,doi:10.1111/j.1365-3121.1991.tb00863.x.
Pagiatakis S D,Yin H,El-Gelil M A.2007.Least-squares selfcoherency analysis of superconducting gravimeter records insearch for the Slichter triplet.Physics of the Earth and PlanetaryInteriors,160(2):108-123,doi:10.1016/j.pepi.2006.10.002.
Peng Z R.1997.Effects of a mushy transition zone at the inner coreboundary on Slichter modes.Geophysical Journal International,131(3):607-617,doi:10.1111/j.1365-246X.1997.tb06602.x.
Richter B.1987.Parallel registration with two superconductinggravimeters.Bull.Inf.Marees.Terr.,99:6757-6758.
Rochester M,Peng Z R.1993.The Slichter modes of the rotatingEarth:A test the sub seismic approximation.GeophysicalJournal International,113(3):575-585,doi:10.1111/j.1365-246X.1993.tb04653.x.
Rogister V.2003.Splitting of seismic-free oscillations and of theSlichter triplet using the normal mode theory of a rotating,ellipsoidal Earth.Geophysics of the Earth and Planetary Interiors,140(1):169-182,doi:10.1016/j.pepi.2003.08.002.
Rosat S,Hinderer J,Crossley D,et al.2003.The search for theSlichter mode:comparison of noise levels of superconductinggravimeters and investigation of a stacking method.Phys.EarthPlanet.Inter.,140(1-3):183-202,doi:10.1016/J.PEPI.2003.07.010.
Rosat S.2007.Optimal seismic source mechanisms to excite theSlichter mode.Dynamic Planet,130:571-577,doi:10.1007/978-3-540-49350-1_83.
Rosat S,Hinderer J.2011.Noise levels of superconductinggravimeters:updated comparison and time stability.Bulletin ofthe Seismological Society of America,101(3):1233-1241,doi:10.1785/0120100217.
Rosat S,Rogister Y.2012.Excitation of the Slichter mode bycollision with a meteoroid or pressure variations at the surfaceand core boundaries.Physics of the Earth and PlanetaryInteriors,190-191:25-33,doi:10.1016/j.pepi.2011.10.007.
Rosat S,Boy J P,Rogister Y.2014.Surface atmospheric pressureexcitation of the translational mode of the inner core.Physics ofthe Earth and Planetary Interiors,227:55-60,doi:10.1016/j.pepi.2013.12.005.
Shen W B,Ding H.2013.Detection of the inner core translationaltriplet using superconducting gravimetric observations.Journalof Earth Science,24(5):725-735,doi:10.1007/s12583-013-0369-3.
Slichter L B.1961.The fundamental free mode of the Earth′s innercore.Proceedings of the National Academy of Sciences of theUnited States of America,47(2):186-190.
Smith M L.1976.Translational inner core oscillations of a rotating,slightly elliptical Earth.Journal of Geophysical Research,81(17):3055-3065,doi:10.1029/JB081i017p03055.
Smylie D E.1992.The inner core translational triplet and thedensity near the Earth′s center.Science,255(5052):1678-1682,doi:10.1126/science.255.5052.1678.
Smylie D E,Jiang X H,Brennan B J,et al.1992.Numericalcalculation of modes of oscillation of the Earth′s core.GeophysicalJournal International,108(2):465-490,doi:10.1111/j.1365-246X.1992.tb04629.x.
Smylie D E,Jiang X H.1993.Core oscillations and their detectionin superconducting gravimeter records.J.Geomagnet.Geoelectr.,45(11-12):1347-1369.
Smylie D E.1999.Viscosity near the Earth′s solid inner core.Science,284(5413):461-463,doi:10.1126/science.284.5413.461.
Stein S,Okal E A.2005.Seismology:Speed and size of the Sumatraearthquake.Nature,434(7033):581-582,doi:10.1038/434581a.
Sun H P,Xu J Q,Ducarme B.2004.Detection of the translationaloscillation of the Earth′s solid inner core based on the internationalsuperconducting gravimeter observations.Chinese Science Bulletin,49(11):1165-1176,doi:10.1360/03wd0242.
Won I J,Kuo J T.1973.Oscillation of the Earth′s inner core and itsrelation to the generation of geomagnetic field.Journal of GeophysicalResearch,78(5):905-911,doi:10.1029/JB078i005p00905.
Xu J Q,Sun H P,Fu R S.2005.Detection of long-period coremodes by using the data from global superconducting gravimeters.Chinese Journal of Geophysics(in Chinese),48(1):69-77,doi:10.3321/j.issn:0001-5733.2005.01.012.
Xu J Q,Sun H P,Zhou J C.2010.Experimental detection of theinner core translational triplet.Chinese Science Bulletin,55(3):276-283,doi:10.1007/s11434-009-0479-6.
江颖,徐建桥,孙和平.2014.深内部地球结构对内核平动振荡本征周期的影响.地球物理学报,57(4):1041-1048,doi:10.6038/cjg20140403.
孙和平,徐建桥,Ducarme B.2004.基于国际超导重力仪观测资料检测地球固态内核的平动振荡.科学通报,49(8):610-614.
徐建桥,孙和平,傅容珊.2005.利用全球超导重力仪数据检测长周期核模.地球物理学报,48(1):69-77,doi:10.3321/j.issn:0001-5733.2005.01.012.
徐建桥,孙和平,周江存.2009.内核平动三重谱线探测的实验探测.科学通报,54(22):3483-3490.
Courtier N,Ducarme B,Goodkind J,et al.2000.Globalsuperconducting gravimeter observations and the search for thetranslational modes of the inner core.Phys.Earth Planet.Inter.,117(1-4):3-20,doi:10.1016/S0031-9201(99)00083-7.
Crossley D J.1992.Eigensolutions and seismic excitation of theSlichter mode triplet for a fully rotating Earth model.EOS,73:60.
Crossley D J,Rochester M G,Peng Z R.1992.Slichter modes andLove numbers.Geophysical Research Letters,19(16):1679-1682,doi:10.1029/92GL01574.
Dahlen F A,Smith M L.1975.The influence of rotation on the freeoscillations of the Earth.Philosophical Transactions of theRoyal Society of London.Series A,Mathematical and PhysicalSciences,279(1292):583-624,doi:10.1098/rsta.1975.0087.
Ding H,Shen W B.2013.Search for the Slichter modes based on anew method:Optimal sequence estimation.Journal of GeophysicalResearch:Solid Earth,118(9):5018-5029,doi:10.1002/jgrb.50344.
Geller R J,Stein S.1979.Time-domain attenuation measurementsfor fundamental spheroidal modes(0S6to0S21)for the 1977Indonesian earthquake.Bulletin of the Seismological Societyof America,69(6):1671-1691.
Gilbert F.1971.The diagonal sum rule and averaged eigenfrequencies.Geophysical Journal of the Royal Astronomical Society,23(1):119-123,doi:10.1111/j.1365-246X.1971.tb01806.x.
Greff-Lefftz M,Legros H.2007.Fluid core dynamics and degreeone deformations:Slichter mode and geocenter motions.Physics ofthe Earth and Planetary Interiors,161(3-4):150-160,doi:10.1016/j.pepi.2006.12.003.
Guo J Y,Dierks O,Neumeyer J,et al.2006.Weighting algorithmsto stack superconducting gravimeter data for the potentialdetection of the Slichter modes.J.Geodyn.,41(1):326-333,doi:10.1016/j.jog.2005.08.014.
Hinderer J,Crossley D J,Jensen O A.1995.A search for theSlichter triplet in superconducting gravimeter data.Physics ofthe Earth and Planetary Interior,90(3):183-195,doi:10.1016/0031-9201(95)05083-N.
Jiang Y,Xu J Q,Sun H P.2013.Detection of inner coretranslational oscillations using superconducting gravimeters.Journal of Earth Science,24(5):750-758,doi:10.1007/s12583-013-0370-x.
Jiang Y,Hu X G,Liu C L,Sun H.2014.Constraining focalmechanism of Lushan earthquake by observations of the Earth′sfree oscillation.Science China Earth Sciences,57(9):2064-2070,doi:10.1007/s11430-014-4913-5.
Jiang Y,Xu J Q,Sun H P.2014.The influence of eigenperiod ofinner core′s translational oscillations caused by deep interiorstructure.Chinese Journal of Geophysics(in Chinese),57(4):1041-1048,doi:10.6038/cjg20140403.
Kanamori H,Cipar J J.1974.Focal process of the great Chileanearthquake May 22,1960.Physics of the Earth and PlanetaryInteriors,9(2):128-136,doi:10.1016/0031-9201(74)90029-6.
Kennet B L N.1991.IASPEI 1991seismological tables.TerraNova,3(2):122,doi:10.1111/j.1365-3121.1991.tb00863.x.
Pagiatakis S D,Yin H,El-Gelil M A.2007.Least-squares selfcoherency analysis of superconducting gravimeter records insearch for the Slichter triplet.Physics of the Earth and PlanetaryInteriors,160(2):108-123,doi:10.1016/j.pepi.2006.10.002.
Peng Z R.1997.Effects of a mushy transition zone at the inner coreboundary on Slichter modes.Geophysical Journal International,131(3):607-617,doi:10.1111/j.1365-246X.1997.tb06602.x.
Richter B.1987.Parallel registration with two superconductinggravimeters.Bull.Inf.Marees.Terr.,99:6757-6758.
Rochester M,Peng Z R.1993.The Slichter modes of the rotatingEarth:A test the sub seismic approximation.GeophysicalJournal International,113(3):575-585,doi:10.1111/j.1365-246X.1993.tb04653.x.
Rogister V.2003.Splitting of seismic-free oscillations and of theSlichter triplet using the normal mode theory of a rotating,ellipsoidal Earth.Geophysics of the Earth and Planetary Interiors,140(1):169-182,doi:10.1016/j.pepi.2003.08.002.
Rosat S,Hinderer J,Crossley D,et al.2003.The search for theSlichter mode:comparison of noise levels of superconductinggravimeters and investigation of a stacking method.Phys.EarthPlanet.Inter.,140(1-3):183-202,doi:10.1016/J.PEPI.2003.07.010.
Rosat S.2007.Optimal seismic source mechanisms to excite theSlichter mode.Dynamic Planet,130:571-577,doi:10.1007/978-3-540-49350-1_83.
Rosat S,Hinderer J.2011.Noise levels of superconductinggravimeters:updated comparison and time stability.Bulletin ofthe Seismological Society of America,101(3):1233-1241,doi:10.1785/0120100217.
Rosat S,Rogister Y.2012.Excitation of the Slichter mode bycollision with a meteoroid or pressure variations at the surfaceand core boundaries.Physics of the Earth and PlanetaryInteriors,190-191:25-33,doi:10.1016/j.pepi.2011.10.007.
Rosat S,Boy J P,Rogister Y.2014.Surface atmospheric pressureexcitation of the translational mode of the inner core.Physics ofthe Earth and Planetary Interiors,227:55-60,doi:10.1016/j.pepi.2013.12.005.
Shen W B,Ding H.2013.Detection of the inner core translationaltriplet using superconducting gravimetric observations.Journalof Earth Science,24(5):725-735,doi:10.1007/s12583-013-0369-3.
Slichter L B.1961.The fundamental free mode of the Earth′s innercore.Proceedings of the National Academy of Sciences of theUnited States of America,47(2):186-190.
Smith M L.1976.Translational inner core oscillations of a rotating,slightly elliptical Earth.Journal of Geophysical Research,81(17):3055-3065,doi:10.1029/JB081i017p03055.
Smylie D E.1992.The inner core translational triplet and thedensity near the Earth′s center.Science,255(5052):1678-1682,doi:10.1126/science.255.5052.1678.
Smylie D E,Jiang X H,Brennan B J,et al.1992.Numericalcalculation of modes of oscillation of the Earth′s core.GeophysicalJournal International,108(2):465-490,doi:10.1111/j.1365-246X.1992.tb04629.x.
Smylie D E,Jiang X H.1993.Core oscillations and their detectionin superconducting gravimeter records.J.Geomagnet.Geoelectr.,45(11-12):1347-1369.
Smylie D E.1999.Viscosity near the Earth′s solid inner core.Science,284(5413):461-463,doi:10.1126/science.284.5413.461.
Stein S,Okal E A.2005.Seismology:Speed and size of the Sumatraearthquake.Nature,434(7033):581-582,doi:10.1038/434581a.
Sun H P,Xu J Q,Ducarme B.2004.Detection of the translationaloscillation of the Earth′s solid inner core based on the internationalsuperconducting gravimeter observations.Chinese Science Bulletin,49(11):1165-1176,doi:10.1360/03wd0242.
Won I J,Kuo J T.1973.Oscillation of the Earth′s inner core and itsrelation to the generation of geomagnetic field.Journal of GeophysicalResearch,78(5):905-911,doi:10.1029/JB078i005p00905.
Xu J Q,Sun H P,Fu R S.2005.Detection of long-period coremodes by using the data from global superconducting gravimeters.Chinese Journal of Geophysics(in Chinese),48(1):69-77,doi:10.3321/j.issn:0001-5733.2005.01.012.
Xu J Q,Sun H P,Zhou J C.2010.Experimental detection of theinner core translational triplet.Chinese Science Bulletin,55(3):276-283,doi:10.1007/s11434-009-0479-6.
江颖,徐建桥,孙和平.2014.深内部地球结构对内核平动振荡本征周期的影响.地球物理学报,57(4):1041-1048,doi:10.6038/cjg20140403.
孙和平,徐建桥,Ducarme B.2004.基于国际超导重力仪观测资料检测地球固态内核的平动振荡.科学通报,49(8):610-614.
徐建桥,孙和平,傅容珊.2005.利用全球超导重力仪数据检测长周期核模.地球物理学报,48(1):69-77,doi:10.3321/j.issn:0001-5733.2005.01.012.
徐建桥,孙和平,周江存.2009.内核平动三重谱线探测的实验探测.科学通报,54(22):3483-3490.
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