基于谱元-简正振型耦合方法的核幔边界D″区地震波波形模拟方法研究
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摘要
本文拓展了一种模拟地震波在地球核幔边界D″区各向异性介质中传播的数值方法:谱元-简正振型耦合方法(CSEM).该方法通过在球对称各向同性介质空间采用简正振型方法,在各向异性的D″区采用谱元方法,并在两种介质的边界采用"DtN"算子耦合的策略计算一维模型PREM(见文献[1])或修改后的D″区横向各向同性VTI-PREM模型的理论地震图.模拟所得数值解结果与采用简正振型方法得到的解析解结果进行对比以验证方法的精度.在中国科学院地球深部结构重点实验室高性能计算机上使用128个CPU计算得到的结果显示,在10-5～0.125Hz的频率范围内谱元简正振型法得到的波形与简正振型方法能很好拟合.此外,对于VTI介质结构模型,谱元简正振型法能够准确模拟S波分裂现象,从而验证了谱元简正振型耦合方法对各向异性介质中地震波传播数值模拟是一种有效的方法.
We extended a coupled mode/spectral element method(CSEM hereafter),which can efficiently modeling the seismic waves propagation in the anisotropic D″ region.Using the original PREM and a modified transverse isotropic PREM model in D″ region,we calculated synthetic seismograms with a new PC cluster with 128 CPUs and 160GB memory in the Key Laboratory of Earth Deep Interior.The numerical solution was compared with the analytical solution by normal mode method in order to verify the accuracy of CSEM.Comparison shows that in a broad frequency band(10-5~0.125 Hz) the results of the two methods match very well.Besides,the synthetic seismograms of the transverse isotropic PREM model show obvious arrival time differences between SH and SV components.This proved the capability of CSEM to modeling S wave splitting caused by anisotropic media.
We extended a coupled mode/spectral element method(CSEM hereafter),which can efficiently modeling the seismic waves propagation in the anisotropic D″ region.Using the original PREM and a modified transverse isotropic PREM model in D″ region,we calculated synthetic seismograms with a new PC cluster with 128 CPUs and 160GB memory in the Key Laboratory of Earth Deep Interior.The numerical solution was compared with the analytical solution by normal mode method in order to verify the accuracy of CSEM.Comparison shows that in a broad frequency band(10-5~0.125 Hz) the results of the two methods match very well.Besides,the synthetic seismograms of the transverse isotropic PREM model show obvious arrival time differences between SH and SV components.This proved the capability of CSEM to modeling S wave splitting caused by anisotropic media.
引文
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[23]Komatitsch D,Vinnik L P,Chevrot S.SHdiff-SVdiffsplitting in an isotropic Earth.J.Geophys.Res.,2010,115(B7):B07312.
[24]Grand S P.Mantle shear-wave tomography and the fate ofsubducted slabs.Philosophical Transactions of the RoyalSociety of London.Series A:Mathematical.Physical andEngineering Sciences,2002,360(1800):2475-2491.
[25]He Y M,Wen L X,Zheng T Y.Geographic boundary andshear wave velocity structure of the"Pacific anomaly"nearthe core-mantle boundary beneath western Pacific.Earth andPlanetary Science Letters,2006,244(1-2):302-314.
[26]Panning M,Romanowicz B.A three-dimensional radiallyanisotropic model of shear velocity in the whole mantle.Geophysical Journal International,2006,167(1):361-379.
[27]Yang H Y Y,Zhao L,Hung S H.Synthetic seismograms bynormal-mode summation:a new derivation and numericalexamples.Geophysical Journal International,2010,183(3):1613-1632.
[28]Al-Attar D,Woodhouse J H,Deuss A.Calculation of normalmode spectra in laterally heterogeneous earth models using aniterative direct solution method.Geophysical JournalInternational,2012,189(2):1038-1046.
[2]Thomas C,Kendall J M.The lowermost mantle beneathnorthern Asia-II.Evidence for lower-mantle anisotropy.Geophys.J.Int.,2002,151(1):296-308.
[3]Wookey J,Kendall J M,Rümpker G.Lowermost mantleanisotropy beneath the north Pacific from differential S-ScSsplitting.Geophysical Journal International,2005,161(3):829-838.
[4]Nowacki A,Wookey J,Kendall J M.New advances in usingseismic anisotropy,mineral physics and geodynamics tounderstand deformation in the lowermost mantle.J.Geod.,2011,52(3-4):205-228.
[5]杨凤琴,刘斌,倪四道等.西伯利亚下地幔底部的剪切波各向异性.地震学报,2008,30(2):209-213.Yang F Q,Liu B,Ni S D,et al.Shear velocity anisotropy ofthe lowermost mantle beneath the Siberia.Acta SeismologicaSinica(in Chinese),2008,30(2):209-213.
[6]戴志阳,刘斌,王宵翔等.西太平洋下D″区的剪切波各向异性.地震学报,2007,29(5):459-466.Dai Z Y,Liu B,Wang X X,et al.Shear wave anisotropy inD"region beneath the western Pacific.Acta SeismologicaSinica(in Chinese),2007,29(5):459-466.
[7]戴志阳.西太平洋下地幔D"层的地震波速度各向异性研究[博士论文].合肥:中国科学技术大学,2008.Dai Z Y.Seismic velocity anisotropy in D′layer of mantlebeneath the Western Pacific(in Chinese)[Ph.D.Thesis].Hefei:University of Science and Technology of China.
[8]Zhao L,Wen L X,Chen L,et al.A two-dimensional hybridmethod for modeling seismic wave propagation in anisotropicmedia.J.Geophys.Res.,2008,113:B12307,doi:10.1029/2008JB005733.
[9]Komatitsch D,Tromp J.Spectral-element simulations ofglobal seismic wave propagation-I.Validation.Geophys.J.Int.,2002,149(2):390-412.
[10]Komatitsch D,Tromp J.Spectral-element simulations ofglobal seismic wave propagation-II.3-D models,oceans,rotation and self-gravitation.Geophys.J.Int.,2002,150(1):303-318.
[11]Liu Q,Polet J,Komatitsch D,et al.Spectral-elementmoment tensor inversions for earthquakes in southernCalifornia.Bull.Seismol.Soc.Am.,2004,94(5):1748-1761.
[12]Capdeville Y,Chaljub E,Vilotte J P,et al.Coupling thespectral element method with a modal solution for elasticwave propagation in global earth models.Geophys.J.Int.,2003,152(1):34-66.
[13]Capdeville Y,To A,Romanowicz B.Coupling spectralelements and modes in a spherical Earth:an extension to the'sandwich'case.Geophys.J.Int.,2003,154(1):44-57.
[14]Givoli D,Keller J B.Non-reflecting boundary conditions forelastic waves.Wave Motion,1990,12(3):261-279.
[15]Chaljub E,Komatitsch D,Vilotte J P,et al.Spectral-element analysis in seismology.∥Wu R S,Maupin V.Advances in Geophysics,Advances in Wave Propagation inHeterogeneous Earth.San Diego:Elsevier Academic PressInc.,2007,48:365-419.
[16]Love A E H.A Treatise on the Mathematical Theory ofElasticity.New York:Dover Publications,1944.
[17]Komatitsch D,Vilotte J P,Vai R,et al.The spectralelement method for elastic wave equations:application to 2Dand 3D seismic problems.International Journal forNumerical Methods in Engineering,1999,45:1139-1164.
[18]Ronchi C,Ianoco R,Paolucci P S.The Cubed Sphere:a newmethod for the solution of partial differential equations inspherical geometry.J.Comput.Phys.,1996,124(1):93-114.
[19]Phinney R A,Burridge R.Representation of the elastic-gravitational excitation of a spherical earth model bygeneralized spherical harmonics.Geophysical JournalInternational,1973,34(4):451-487.
[20]To A,Romanowicz B,Capdeville Y,et al.3Deffects ofsharp boundaries at the borders of the African and Pacificsuperplumes:Observation and modeling.Earth Planet.Sci.Lett.,2005,233(1-2):137-153.
[21]Qin Y L,Capdeville Y,Montagner J P,et al.Reliability ofmantle tomography models assessed by spectral elementsimulation.Geophysical Journal International,2009,177(1):125-144.
[22]Dahlen F A,Tromp J.Theoretical Global Seismology.Princeton:Princeton University Press,1998.
[23]Komatitsch D,Vinnik L P,Chevrot S.SHdiff-SVdiffsplitting in an isotropic Earth.J.Geophys.Res.,2010,115(B7):B07312.
[24]Grand S P.Mantle shear-wave tomography and the fate ofsubducted slabs.Philosophical Transactions of the RoyalSociety of London.Series A:Mathematical.Physical andEngineering Sciences,2002,360(1800):2475-2491.
[25]He Y M,Wen L X,Zheng T Y.Geographic boundary andshear wave velocity structure of the"Pacific anomaly"nearthe core-mantle boundary beneath western Pacific.Earth andPlanetary Science Letters,2006,244(1-2):302-314.
[26]Panning M,Romanowicz B.A three-dimensional radiallyanisotropic model of shear velocity in the whole mantle.Geophysical Journal International,2006,167(1):361-379.
[27]Yang H Y Y,Zhao L,Hung S H.Synthetic seismograms bynormal-mode summation:a new derivation and numericalexamples.Geophysical Journal International,2010,183(3):1613-1632.
[28]Al-Attar D,Woodhouse J H,Deuss A.Calculation of normalmode spectra in laterally heterogeneous earth models using aniterative direct solution method.Geophysical JournalInternational,2012,189(2):1038-1046.
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