地震激发地球自由振荡过程的数值模拟初步探索
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摘要
地球自由振荡的固有频率与地球内部结构密切相关,研究地球自由振荡可以深入研究地球内部结构。传统的解析方法侧重于本征频率的确定,但对从地震发生到地球自由振荡被激发的全过程难以研究。从弹性波动理论基础出发,试采用谱元法结合高性能并行计算数值模拟特大地震激发的弹性波在地球内部传播过程。在不考虑地球重力情况下,对数值模拟激发地球自由振荡的结果进行功率谱密度分析,通过对谱结果的观察并与理论值进行对比分析,认识到环型振型数值模拟结果可以准确重现其长周期理论频率值,地球重力对球型振型有重要影响。探讨了是否可以通过这种方法真实重现地球自由振荡激发的过程。以期利用此方法深入探讨地球横向不均匀性对地球自由振荡的影响。
The eigenfrequencies of the Earth′s free oscillations are closely related to the Earth′s internal structures.Elaborately investigating the characteristics of the Earth′s free oscillations can open another window to address the hierarchical structures with variations of this mysterious planet on which we are living.The traditional method mainly focused on calculating the eigenfrequencies by analytical ways,whereas it lacks the advantage of modeling a realistic earth model with lateral heterogeneity,from studying on the process from earthquake occurrence to the Earth′s free oscillations inspired.We proposed numerical simulation method which is based on the elastic propagation theory;the spectral element method and high performance parallel computing were incorporated to simulate the seismic wave propagation process in the Earth's interior.As a preliminary study,we neglected the effects of the Earth′s gravitational potential.The seismographic data recorded by synthetic stations were analyzed by power spectral density distribution analysis,and compared with those from the theoretical values of PREM model.We found that the simulated results of toroidal modes agreed well with the theoretical values.
The eigenfrequencies of the Earth′s free oscillations are closely related to the Earth′s internal structures.Elaborately investigating the characteristics of the Earth′s free oscillations can open another window to address the hierarchical structures with variations of this mysterious planet on which we are living.The traditional method mainly focused on calculating the eigenfrequencies by analytical ways,whereas it lacks the advantage of modeling a realistic earth model with lateral heterogeneity,from studying on the process from earthquake occurrence to the Earth′s free oscillations inspired.We proposed numerical simulation method which is based on the elastic propagation theory;the spectral element method and high performance parallel computing were incorporated to simulate the seismic wave propagation process in the Earth's interior.As a preliminary study,we neglected the effects of the Earth′s gravitational potential.The seismographic data recorded by synthetic stations were analyzed by power spectral density distribution analysis,and compared with those from the theoretical values of PREM model.We found that the simulated results of toroidal modes agreed well with the theoretical values.
引文
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[16]Sinha S,Routh P S,Anno P D,et al.Spectral decomposition ofseismic data with continuous-wavelet transform[J].Geophysics,2005,70(6):19-25.
[17]Shen J.Efficient chebyshev-legendre galerkin methods for ellipticproblems[J].Houston Journal ofMathematics,1996,31:233-239.
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[19]Kennett B L N,Engdahl E R,Buland R.Constraints on seismicvelocities in the earth from traveltimes[J].Geophysical JournalInternational,1995,122:108-124.
[20]Komatitsch D,Tromp J.Introduction to the spectral elementmethod for three-dimensional seismic wave propagation[J].Geo-physical Journal International,1999,139:806-822.
[21]Woodhouse J H,Deuss A.Theory and observations—Earth′s freeoscillations[M]∥Treatise on Geophysics(Volume 1).Elsevier,2007:31-65.
[22]Lapwood E R,Usami T.Free Oscillations of the Earth[M].New York:Cambridge University Press,1981:94-115.
[23]Aki K,Richards P G.Quantitiative Seismology:Theory andMethods[M].San Francisco:WHFreeman and Company,1980:375-425.
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[25]Robert A P,Robert B.Representation of the elastic-gravitationalexcitation of a spherical earth model by generalized spherical har-monics[J].Geological and Geophysical Sciences,1973,34:451-487.
[2]Lei X E,Sun H P,Hsu H T.Check of Earth′s free oscillationsexcited by Sumatra-Andaman Large earthquake and discussions onthe anistropy of inner core[J].Science in China(Series D:EarthSciences),2007,50(6):909-917.
[3]Qiu Zehua,Ma Jin,Chi Shunliang.Earth′s free torsional oscilla-tions of the great Sumatra earthquake observed with borehole shearstrainmeter[J].Chinese Journal Geophysics,2007,50(3):797-805.[邱泽华,马瑾,池顺良.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[J].地球物理学报,2007,50(3):797-805.]
[4]Widmer-Schnidrig R.Free oscillations illuminate the mantle[J].Nature,1999,398:292-293.
[5]Tsuboi N.Free oscillations of a laterally heterogeneous and anelas-tic earth[J].Pageoph,1995,145:445-457.
[6]Dahlen F A,Sailor R V.Rotational and elliptical splitting of thefree oscillations of the Earth[J].Geological and Geophysica Sci-ences,1979,58:609-623.
[7]Luh P C,Dziewonski A M.Theoretical normal-mode spectra of arotating elliptical earth[J].Geophysical Journal,1976,45(3):617-645.
[8]Tromp J.Support for anisotropy of the Earth′s inner core from freeoscillations[J].Nature,1993,366(16):678-681.
[9]Woodhouse J H,Giardini D,Li X D.Evidence for inner core ani-sotropy from free oscillations[J].Geophysical Research Letters,1986,13(13):1 549-1 552.
[10]Masters TG,Widmer R.Free Oscillations:Frequencies and At-tenuations[M].Americal Geophysical Union,1995:104-125.
[11]Park J,Song TR A,Tromp J,et al.Earth′s free oscillations ex-cited by the 26 December 2004 Sumatra-Andaman earthquake[J].Science,2005,308:1 139-1 144.
[12]Park J.Free-oscillation coupling theory[C]∥Cloetingh S AP L,ed.Mathematical Geophysics.D.Reidel Publishing Company,1988:31-52.
[13]Komatitsch D,Ritsema J,Tromp J.The spectral-element meth-od,beowulf computing,and global seismology[J].Science,2002,298:1 737-1 742.
[14]Komatitsch D,Tromp J.Spectral-element simulations of globalseismic wave propagation-I.Validation[J].Geophysical JournalInternational,2002,149:390-412.
[15]Komatitsch D,Tromp J.Spectral-element simulations of globalseismic wave propagation-II.Three-dimensional models,oceans,rotation and self-gravitation[J].Geophysical Journal Internation-al,2002,150:303-318.
[16]Sinha S,Routh P S,Anno P D,et al.Spectral decomposition ofseismic data with continuous-wavelet transform[J].Geophysics,2005,70(6):19-25.
[17]Shen J.Efficient chebyshev-legendre galerkin methods for ellipticproblems[J].Houston Journal ofMathematics,1996,31:233-239.
[18]Guo B Y,Shen J,Wang L L.Optimal spectral-galerkin methodsusing generalized jacobiI polynomials[J].Journal ofScientificComputing,2006,27(1):305-322.
[19]Kennett B L N,Engdahl E R,Buland R.Constraints on seismicvelocities in the earth from traveltimes[J].Geophysical JournalInternational,1995,122:108-124.
[20]Komatitsch D,Tromp J.Introduction to the spectral elementmethod for three-dimensional seismic wave propagation[J].Geo-physical Journal International,1999,139:806-822.
[21]Woodhouse J H,Deuss A.Theory and observations—Earth′s freeoscillations[M]∥Treatise on Geophysics(Volume 1).Elsevier,2007:31-65.
[22]Lapwood E R,Usami T.Free Oscillations of the Earth[M].New York:Cambridge University Press,1981:94-115.
[23]Aki K,Richards P G.Quantitiative Seismology:Theory andMethods[M].San Francisco:WHFreeman and Company,1980:375-425.
[24]Luh P C.Normal modes of a rotating,self-gravitating inhomoge-neous earth[J].Geological and Geophysical Sciences,1974,38:187-224.
[25]Robert A P,Robert B.Representation of the elastic-gravitationalexcitation of a spherical earth model by generalized spherical har-monics[J].Geological and Geophysical Sciences,1973,34:451-487.
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