多次各向异性散射模式对S波能量密度包络曲线的影响
摘要
在多次各向异性散射理论的基础上,本文重新推导了方向性散射系数的球函数展开式.引入特征时间的概念,来定义震源处初始地震波脉冲宽度,并在地震波能量密度积分方程中引入任意给定频率的初始脉冲能量谱密度的解析表达.通过离散波数方法求解了修正的地震波能量密度积分方程.基于积分方程的数值解,研究了不同散射模式对S波能量密度包络曲线的影响.计算结果表明:随着震源距的增加,在S波到时之后,多次各向异性散射模式与多次各向同性散射模式合成的能量密度包络差异逐渐增大.其中通过多次前散射模式,我们可以得到不同震源距的尾波能量密度包络的同一衰减趋势,以及S波能量密度包络随着震源距的增加而出现的展宽现象.最后,利用美国内华达州Wells地震余震的台站记录验证了多次前散射模式的实用性与有效性.
Based on the multiple anisotropic scattering theory,we reevaluate the spherical harmonic series expansion of directional scattering coefficient.A characteristic source time is introduced to define the initial impulse width of energy density at the source.We use an analytical expression of the initial spectral energy intensity in the integral equation of seismic wave energy density at any given frequency.The modified integral equation is solved by a discrete wave number method.Based on this solution,we investigate the effect of scattering pattern on S wave energy density envelope.And the numerical simulation shows that after the S arrival time the difference of the energy density envelope between the multiple anisotropic scattering pattern and the isotropic scattering pattern increases with distances.Using forward anisotropic scattering pattern,we successfully reproduce the common decay of the seismic coda wave energy density envelopes at different hypocentral distances.For the same pattern,the S wave energy density envelope broadens with increasing hypocentral distance.Finally,we verify the forward anisotropic scattering pattern with the observation from the aftershock of the 2008 Wells,Nevada earthquake in USA.
Based on the multiple anisotropic scattering theory,we reevaluate the spherical harmonic series expansion of directional scattering coefficient.A characteristic source time is introduced to define the initial impulse width of energy density at the source.We use an analytical expression of the initial spectral energy intensity in the integral equation of seismic wave energy density at any given frequency.The modified integral equation is solved by a discrete wave number method.Based on this solution,we investigate the effect of scattering pattern on S wave energy density envelope.And the numerical simulation shows that after the S arrival time the difference of the energy density envelope between the multiple anisotropic scattering pattern and the isotropic scattering pattern increases with distances.Using forward anisotropic scattering pattern,we successfully reproduce the common decay of the seismic coda wave energy density envelopes at different hypocentral distances.For the same pattern,the S wave energy density envelope broadens with increasing hypocentral distance.Finally,we verify the forward anisotropic scattering pattern with the observation from the aftershock of the 2008 Wells,Nevada earthquake in USA.
引文
[1]吴如山.地震波散射:理论与应用.地球物理学进展,1989,4(4):1-23.Wu R S.Seismic scattering:Theory and application.Progress in Geophysics(in Chinese),1989,4(4):1-23.
[2]Sato H,Fehler M.Seismic Wave Propagation and Scatteringin the Heterogenous Earth.New York:AIP Press,1998.
[3]李灿苹.散射波特征与非均匀地质体对应关系研究[博士论文].北京:中国地质大学,2006.Li C P.A study on corresponding relationship betweenscattering wave characteristic and heterogeneous geologicbodies[Ph.D.thesis](in Chinese).Beijing:China Universityof Geosciences,2006.
[4]尹军杰.地震散射波场特征的数值模拟研究[博士论文].北京:中国地质大学,2005.Yin J J.A study on seismic scattered wave characteristics bynumerical simulating[Ph.D.thesis](in Chinese).Beijing:China University of Geosciences,2005.
[5]尹军杰,刘学伟,李文慧.地震波散射理论及应用研究综述.地球物理学进展,2005,20(1):123-134.Yin J J,Liu X W,Li W H.The view of seismic wavescattering theory and its applications.Progress in Geophysics(in Chinese),2005,20(1):123-134.
[6]Zeng Y H,Anderson J G,Su F.Subevent rake and randomscattering effects in realistic strong ground motion simulation.Geophys.Res.Lett.,1995,22(1):17-20.
[7]Mai P M,Imperatori W,Olsen K B.Hybrid broadbandground-motion simulations:Combining long-period deterministicsynthesis with high-frequency multiple S-to-S backscattering.Bull.Seism.Soc.Am.,2010,100(5A):2124-2142.
[8]刘建华,刘福田,王凤霞等.单台Lg尾波QCLg的测量研究.地球物理学报,1999,42(3):371-382.Liu J H,Liu F T,Wang F X,et al.A measuring study forsingle-trace Lg coda QCLg.Chinese J.Geophys.(in Chinese),1999,42(3):371-382.
[9]胡家富,丛连理,苏有锦等.云南及周边地区Lg尾波Q值的分布特征.地球物理学报,2003,46(6):809-814.Hu J F,Cong L L,Su Y J,et al.Distribution characteristicsof Qvalue of the Lg coda in Yunnan and its adjacent regions.Chinese J.Geophys.(in Chinese),2003,46(6):809-814.
[10]张天中,马云生,张焕生等.震源谱的尾波多台多震综合求解方法.地球物理学报,2004,40(5):702-709.Zhang T Z,Ma Y S,Zhang H S,et al.A multi-station andmulti-event coda method to study seismic source spectrum.Chinese J.Geophys.(in Chinese),2004,40(5):702-709.
[11]刘建华,刘福田,阎晓蔚等.华北地区Lg尾波衰减研究——Lg尾波Q的测量.地球物理学报,2004,47(5):822-831.Liu J H,Liu F T,Yan X W,et al.A study of Lg codaattenuation in North China-the measurement of Lg coda Q.Chinese J.Geophys.(in Chinese),2004,47(5):822-831.
[12]刘建华,刘福田,阎晓蔚等.华北地区Lg尾波衰减研究——Lg尾波Q0地震成像.地球物理学报,2004,47(6):1044-1052.Liu J H,Liu F T,Yan X W,et al.A study of Lg codaattenuation beneath North China:seismic imaging of Lg codaQ0.Chinese J.Geophys.(in Chinese),2004,47(6):1044-1052.
[13]贾豫葛,李小凡,张美根等.地震波散射研究的若干重要进展.地球物理学进展,2005,20(4):939-949.Jia Y G,Li X F,Zhang M G,et al.Some important progressin research upon seismic wave scattering.Progress inGeophysics(in Chinese),2005,20(4):939-949.
[14]Aki K.Analysis of the seismic coda of local earthquakes asscattered waves.J.Geophys.Res.,1969,74(2):615-631.
[15]Aki K,Chouet B.Origin of coda waves:source,attenuation,and scattering effects.J.Geophys.Res.,1975,80(23):3322-3342.
[16]Sato H.Energy propagation including scattering effectssingle isotropic scattering approximation.J.Phys.Earth,1977,25(1):27-41.
[17]Gao L S,Lee L C,Biswas N N,et al.Comparison of theeffects between single and multiple scattering on coda wavesfor local earthquakes.Bull.Seism.Soc.Am.,1983,73(2):377-389.
[18]Gao L S,Biswas N N,Lee L C,et al.Effects of multiplescattering on coda waves in three-dimensional medium.PureAppl.Geophys.,1983,121(1):3-15.
[19]尚铁梁,高龙生.多次散射的传输理论及其在脉冲源的地震尾波问题上的应用.中国科学(B辑),1988,(1):85-94.Shang T L,Gao L S.Multiple scattering energy transporttheory and its application on seismic coda wave.Science inChina(Series B),1988,(1):85-94.
[20]Zeng Y H,Su F,Aki K.Scattering wave energy propagationin a random isotropic scattering medium 1.Theory.J.Geophys.Res.,1991,96(B1):607-619.
[21]Hoshiba M.Simulation of multiple-scattered coda waveexcitation based on the energy conservation law.Phys.EarthPlanet.Inter.,1991,67(1-2):123-136.
[22]曾健,聂永安.单次与多次散射对地方震尾波的作用.地震学报,1989,11(1):12-23.Zeng J,Nie Y A.The effects of single and multiple scatteringon coda waves for local earthquakes.Acta SeismologicaSinica(in Chinese),1989,11(1):12-23.
[23]聂永安,曾健,冯德益.三维尾波散射问题的理论研究.地震学报,1995,17(1):68-71.Nie Y A,Zeng J,Feng D Y.The research on seismic codawave scattering in three dimension space.Acta SeismologicaSinica(in Chinese),1995,17(1):68-71.
[24]Wu R S.Seismic wave scattering and the small scaleinhomogeneities in the lithosphere[Ph.D.thesis].Massachusetts Institute of Technology,1984.
[25]Wu R S,Aki K.Multiple scattering and energy transfer ofseismic waves-Separation of scattering effect from intrinsicattenuation.II.Application of the theory to Hindu Kushregion.Pure Appl.Geophys.,1988,128(1-2):49-80.
[26]Sato H.Energy transportation in one-and two-dimensionalscattering media:analytic solutions of the multiple isotropicscattering model.Geophys.J.Int.,1993,112(1):141-146.
[27]Ugalde A,Tripathi J N,Hoshiba M,et al.Intrinsic andscattering attenuation in western India from aftershocks ofthe 26January,2001Kachchh earthquake.Tectonophysics,2007,429(1-2):111-123.
[28]Padhy S,Wegler U,Korn M.Seismogram envelopeinversion using a multiple isotropic scattering model:application to aftershocks of the 2001Bhuj earthquake.Bull.Seism.Soc.Am.,2007,97(1B):222-233.
[29]Lee W S,Yun S,Do J Y.Scattering and intrinsic attenuationof short-period S waves in the Gyeongsang Basin,SouthKorea,revealed from S-wave seismogram envelopes based onthe radiative transfer theory.Bull.Seism.Soc.Am.,2010,100(2):833-840.
[30]Wegler U,Korn M,Przybilla J.Modeling full seismogramenvelopes using radiative transfer theory with Born scatteringcoefficients.Pure Appl.Geophys.,2006,163(2-3):503-531.
[31]Sato H.Coda wave excitation due to nonisotropic scatteringand nonspherical source radiation.J.Geophys.Res.,1982,87(B10):8665-8674.
[32]Sato H.Formulation of the multiple non-isotropic scatteringprocess in 2-D space on the basis of energy-transport theory.Geophys.J.Int.,1994,117(3):727-732.
[33]Sato H.Formulation of the multiple non-isotropic scatteringprocess in 3-D space on the basis of energy transport theory.Geophys.J.Int.,1995,121(2):523-531.
[34]Hoshiba M.Estimation of nonisotropic scattering in westernJapan using coda wave envelopes:Application of a multiplenonisotropic scattering model.J.Geophys.Res.,1995,100(B1):645-657.
[35]Gusev A A,Abubakirov I R.Simulated envelopes of non-isotropically scattered body waves as compared to observedones:Another manifestation of fractal heterogeneity.Geophys.J.Int.,1996,127(1):49-60.
[36]Ishimaru A.Wave Propagation and Scattering in RandomMedia,2vols.San Diego,Calif.Academic Press,1978.
[37]季效达,薛兴恒,陆英.数学物理方程.北京:科学出版社,2005.Ji X D,Xue X H,Lu Y.Equations of Mathematical Physics(in Chinese).Beijing:Science Press,2005.
[38]Zeng Y H.Theory of scattered P-and S-wave energy in arandom isotropic scattering medium.Bull.Seism.Soc.Am.,1993,83(4):1264-1276.
[39]Zhang S J,Jin J M.Computation of Special Functions.NewYork:John Wiley&Sons,1996.
[2]Sato H,Fehler M.Seismic Wave Propagation and Scatteringin the Heterogenous Earth.New York:AIP Press,1998.
[3]李灿苹.散射波特征与非均匀地质体对应关系研究[博士论文].北京:中国地质大学,2006.Li C P.A study on corresponding relationship betweenscattering wave characteristic and heterogeneous geologicbodies[Ph.D.thesis](in Chinese).Beijing:China Universityof Geosciences,2006.
[4]尹军杰.地震散射波场特征的数值模拟研究[博士论文].北京:中国地质大学,2005.Yin J J.A study on seismic scattered wave characteristics bynumerical simulating[Ph.D.thesis](in Chinese).Beijing:China University of Geosciences,2005.
[5]尹军杰,刘学伟,李文慧.地震波散射理论及应用研究综述.地球物理学进展,2005,20(1):123-134.Yin J J,Liu X W,Li W H.The view of seismic wavescattering theory and its applications.Progress in Geophysics(in Chinese),2005,20(1):123-134.
[6]Zeng Y H,Anderson J G,Su F.Subevent rake and randomscattering effects in realistic strong ground motion simulation.Geophys.Res.Lett.,1995,22(1):17-20.
[7]Mai P M,Imperatori W,Olsen K B.Hybrid broadbandground-motion simulations:Combining long-period deterministicsynthesis with high-frequency multiple S-to-S backscattering.Bull.Seism.Soc.Am.,2010,100(5A):2124-2142.
[8]刘建华,刘福田,王凤霞等.单台Lg尾波QCLg的测量研究.地球物理学报,1999,42(3):371-382.Liu J H,Liu F T,Wang F X,et al.A measuring study forsingle-trace Lg coda QCLg.Chinese J.Geophys.(in Chinese),1999,42(3):371-382.
[9]胡家富,丛连理,苏有锦等.云南及周边地区Lg尾波Q值的分布特征.地球物理学报,2003,46(6):809-814.Hu J F,Cong L L,Su Y J,et al.Distribution characteristicsof Qvalue of the Lg coda in Yunnan and its adjacent regions.Chinese J.Geophys.(in Chinese),2003,46(6):809-814.
[10]张天中,马云生,张焕生等.震源谱的尾波多台多震综合求解方法.地球物理学报,2004,40(5):702-709.Zhang T Z,Ma Y S,Zhang H S,et al.A multi-station andmulti-event coda method to study seismic source spectrum.Chinese J.Geophys.(in Chinese),2004,40(5):702-709.
[11]刘建华,刘福田,阎晓蔚等.华北地区Lg尾波衰减研究——Lg尾波Q的测量.地球物理学报,2004,47(5):822-831.Liu J H,Liu F T,Yan X W,et al.A study of Lg codaattenuation in North China-the measurement of Lg coda Q.Chinese J.Geophys.(in Chinese),2004,47(5):822-831.
[12]刘建华,刘福田,阎晓蔚等.华北地区Lg尾波衰减研究——Lg尾波Q0地震成像.地球物理学报,2004,47(6):1044-1052.Liu J H,Liu F T,Yan X W,et al.A study of Lg codaattenuation beneath North China:seismic imaging of Lg codaQ0.Chinese J.Geophys.(in Chinese),2004,47(6):1044-1052.
[13]贾豫葛,李小凡,张美根等.地震波散射研究的若干重要进展.地球物理学进展,2005,20(4):939-949.Jia Y G,Li X F,Zhang M G,et al.Some important progressin research upon seismic wave scattering.Progress inGeophysics(in Chinese),2005,20(4):939-949.
[14]Aki K.Analysis of the seismic coda of local earthquakes asscattered waves.J.Geophys.Res.,1969,74(2):615-631.
[15]Aki K,Chouet B.Origin of coda waves:source,attenuation,and scattering effects.J.Geophys.Res.,1975,80(23):3322-3342.
[16]Sato H.Energy propagation including scattering effectssingle isotropic scattering approximation.J.Phys.Earth,1977,25(1):27-41.
[17]Gao L S,Lee L C,Biswas N N,et al.Comparison of theeffects between single and multiple scattering on coda wavesfor local earthquakes.Bull.Seism.Soc.Am.,1983,73(2):377-389.
[18]Gao L S,Biswas N N,Lee L C,et al.Effects of multiplescattering on coda waves in three-dimensional medium.PureAppl.Geophys.,1983,121(1):3-15.
[19]尚铁梁,高龙生.多次散射的传输理论及其在脉冲源的地震尾波问题上的应用.中国科学(B辑),1988,(1):85-94.Shang T L,Gao L S.Multiple scattering energy transporttheory and its application on seismic coda wave.Science inChina(Series B),1988,(1):85-94.
[20]Zeng Y H,Su F,Aki K.Scattering wave energy propagationin a random isotropic scattering medium 1.Theory.J.Geophys.Res.,1991,96(B1):607-619.
[21]Hoshiba M.Simulation of multiple-scattered coda waveexcitation based on the energy conservation law.Phys.EarthPlanet.Inter.,1991,67(1-2):123-136.
[22]曾健,聂永安.单次与多次散射对地方震尾波的作用.地震学报,1989,11(1):12-23.Zeng J,Nie Y A.The effects of single and multiple scatteringon coda waves for local earthquakes.Acta SeismologicaSinica(in Chinese),1989,11(1):12-23.
[23]聂永安,曾健,冯德益.三维尾波散射问题的理论研究.地震学报,1995,17(1):68-71.Nie Y A,Zeng J,Feng D Y.The research on seismic codawave scattering in three dimension space.Acta SeismologicaSinica(in Chinese),1995,17(1):68-71.
[24]Wu R S.Seismic wave scattering and the small scaleinhomogeneities in the lithosphere[Ph.D.thesis].Massachusetts Institute of Technology,1984.
[25]Wu R S,Aki K.Multiple scattering and energy transfer ofseismic waves-Separation of scattering effect from intrinsicattenuation.II.Application of the theory to Hindu Kushregion.Pure Appl.Geophys.,1988,128(1-2):49-80.
[26]Sato H.Energy transportation in one-and two-dimensionalscattering media:analytic solutions of the multiple isotropicscattering model.Geophys.J.Int.,1993,112(1):141-146.
[27]Ugalde A,Tripathi J N,Hoshiba M,et al.Intrinsic andscattering attenuation in western India from aftershocks ofthe 26January,2001Kachchh earthquake.Tectonophysics,2007,429(1-2):111-123.
[28]Padhy S,Wegler U,Korn M.Seismogram envelopeinversion using a multiple isotropic scattering model:application to aftershocks of the 2001Bhuj earthquake.Bull.Seism.Soc.Am.,2007,97(1B):222-233.
[29]Lee W S,Yun S,Do J Y.Scattering and intrinsic attenuationof short-period S waves in the Gyeongsang Basin,SouthKorea,revealed from S-wave seismogram envelopes based onthe radiative transfer theory.Bull.Seism.Soc.Am.,2010,100(2):833-840.
[30]Wegler U,Korn M,Przybilla J.Modeling full seismogramenvelopes using radiative transfer theory with Born scatteringcoefficients.Pure Appl.Geophys.,2006,163(2-3):503-531.
[31]Sato H.Coda wave excitation due to nonisotropic scatteringand nonspherical source radiation.J.Geophys.Res.,1982,87(B10):8665-8674.
[32]Sato H.Formulation of the multiple non-isotropic scatteringprocess in 2-D space on the basis of energy-transport theory.Geophys.J.Int.,1994,117(3):727-732.
[33]Sato H.Formulation of the multiple non-isotropic scatteringprocess in 3-D space on the basis of energy transport theory.Geophys.J.Int.,1995,121(2):523-531.
[34]Hoshiba M.Estimation of nonisotropic scattering in westernJapan using coda wave envelopes:Application of a multiplenonisotropic scattering model.J.Geophys.Res.,1995,100(B1):645-657.
[35]Gusev A A,Abubakirov I R.Simulated envelopes of non-isotropically scattered body waves as compared to observedones:Another manifestation of fractal heterogeneity.Geophys.J.Int.,1996,127(1):49-60.
[36]Ishimaru A.Wave Propagation and Scattering in RandomMedia,2vols.San Diego,Calif.Academic Press,1978.
[37]季效达,薛兴恒,陆英.数学物理方程.北京:科学出版社,2005.Ji X D,Xue X H,Lu Y.Equations of Mathematical Physics(in Chinese).Beijing:Science Press,2005.
[38]Zeng Y H.Theory of scattered P-and S-wave energy in arandom isotropic scattering medium.Bull.Seism.Soc.Am.,1993,83(4):1264-1276.
[39]Zhang S J,Jin J M.Computation of Special Functions.NewYork:John Wiley&Sons,1996.
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