P波和S波接收函数的贝叶斯联合反演
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摘要
S波接收函数对于研究岩石圈速度结构具有重要价值.本文利用合成地震图技术研究了S波接收函数的动力学特征.在接收函数非线性复谱比反演方法的基础上,发展了基于贝叶斯理论的P波和S波接收函数的非线性联合反演方法.结果表明:(1)适用于S波接收函数反演的震中距范围约为55°～80°,S波接收函数反演要求所用远震事件的震级大于5级;(2)与陡变的岩石圈底部界面(LAB)相比,梯度带类型LAB上生成的SLP转换波相对较弱,台站下方的沉积盖层有助于相对增强SLP震相;(3)由于S波接收函数径向分量不符合δ脉冲,不依赖于等效震源假定的三分量接收函数多道最大或然性反褶积方法更适合S波接收函数的估计;(4)数值检验的结果表明,在初始模型速度参数偏离真实模型20%的情况下,本文的方法能够预测300km深度范围内的P波和S波速度结构;(5)观测数据的反演结果表明,由于P波接收函数低频分量相对不足,本文的联合反演方法对于大于100km深度上地幔的S波速度结构约束相对较弱.
S-receiver function is valuable for investigating the lithosphere velocity structure.Using synthetic seismogram technique,we have studied dynamic characteristics of S-receiver functions.Based on the Bayesian inversion theory and non-linear inversion technique of the complex spectral ratio of the P-receiver function,a joint P-and S-receiver function inversion technique is proposed in this study.Our results show that(1) epicenter distances are limited to 55°~80° for the S-receiver function inversion and the magnitude of events used in the inversion should be larger than 5.0 for a good enough signal to noise ratio;(2) the SLP conversion on the lithosphere-asthenosphere boundary(LAB) with gradient structure is weaker than that on the sharp LAB,and the sediment is in favor of the SLP conversion at LAB;(3) since the radial component of S-receiver functions is not a delta pulse,the multi-channel maximal likelihood deconvolution technique for three-component receiver function estimation not relying on the source equalization assumption is more suitable for estimating S-receiver function;(4) numerical tests demonstrate that when the deviation of initial model is within 20% from the true model,our method can well predict the model parameters of the crust and upper mantle down to 300 km depth;(5) observational data tests demonstrate that the resultant S-wave velocities at depth larger than 100 km are less well constrained.
S-receiver function is valuable for investigating the lithosphere velocity structure.Using synthetic seismogram technique,we have studied dynamic characteristics of S-receiver functions.Based on the Bayesian inversion theory and non-linear inversion technique of the complex spectral ratio of the P-receiver function,a joint P-and S-receiver function inversion technique is proposed in this study.Our results show that(1) epicenter distances are limited to 55°~80° for the S-receiver function inversion and the magnitude of events used in the inversion should be larger than 5.0 for a good enough signal to noise ratio;(2) the SLP conversion on the lithosphere-asthenosphere boundary(LAB) with gradient structure is weaker than that on the sharp LAB,and the sediment is in favor of the SLP conversion at LAB;(3) since the radial component of S-receiver functions is not a delta pulse,the multi-channel maximal likelihood deconvolution technique for three-component receiver function estimation not relying on the source equalization assumption is more suitable for estimating S-receiver function;(4) numerical tests demonstrate that when the deviation of initial model is within 20% from the true model,our method can well predict the model parameters of the crust and upper mantle down to 300 km depth;(5) observational data tests demonstrate that the resultant S-wave velocities at depth larger than 100 km are less well constrained.
引文
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[2]刘启元,Kind R,李顺成.接收函数复谱比的最大或然性估计及非线性反演.地球物理学报,1996,39(4):502-513.Liu Q Y,Kind R,Li S C.Maximal likelihood estimation andnonlinear inversion of the complex receiver function spectrumratio.Chinese J.Geophys.(in Chinese),1996,39(4):502-513.
[3]Farra V,Vinnik L.Upper mantle stratification by P and Sreceiver functions.Geophys.J.Int.,2000,141(3):699-712.
[4]Oreshin S,Vinnik L,Peregoudov D,et al.Lithosphere andasthenosphere of the Tien Shan imaged by S receiverfunctions.Geophys.Res.Lett.,2002,29(8):1191,doi:1029/2001GL014441.
[5]Kumar P,Yuan X,Kind R,et al.The lithosphere-asthenosphere boundary in the Tien Shan-Karakoram regionfrom S receiver functions:Evidence for continental subduction.Geophys.Res.Lett.,2005,32,L07305,doi:10.1029/2004GL022291,1-4.
[6]Soudoudi F,Yuan X,Liu Q Y,et al.Lithospheric thinknessbeneath the Dabie Shan,central eastern China from S receiverfunctions.Geophys.J.Int.,2006,166(3):1363-1367.
[7]Vinnik L P,Reigber C,Aleshin I M,et al.Receiver functiontomography of the central Tien Shan.Earth Planet.Sci.Lett.,2004,225(1-2):131-146.
[8]Ammon C J,Randall G,Zandt G.On the nonuniqueness ofreceiver function inversion.J.Geophys Res.,1990,95(B10):15303-15318.
[9]Wu Q,Li Y,Zhang R,et al.Wavelet modeling of broad-band receiver functions.Geophys.J.Int.,2007,170(2):534-544.
[10]Liu Q Y,Li Y,Chen J H,et al.Joint inversion of receiverfunction and ambient noise based on Bayesian theory.Chin.J.Geophys.,2010,53(11):961-972.
[11]Scales J A,Snieder R.The anatomy of inverse problems.Geophysics,2000,65(6):1708-1710.
[12]Yuan X H,Kind R,Li X Q,et al.The S receiver functions:synthetics and data example.Geophys.J.Int.,2006,165(2):555-564.
[13]Aki K,Richards P G.Quantitative Seismology:Theory andMethods.San Francisco:W.H.Freeman and Company,1980,133-155.
[14]刘启元,范会吉.震源区和接收区结构不同情况下体波合成地震图的矩阵-射线方法.地球物理学报,1992,35(2):193-203.Liu Q Y,Fan H J.The ray-matrix method of syntheticseismograms for different source and receiver structure.Chinese J.Geophys.(in Chinese),1992,35(2):193-203.
[15]刘启元,邵学钟.天然地震PS转换波动力学特征的初步研究.地球物理学报,1985,28(3):291-302.Liu Q Y,Shao X Z.A study of the dynamic characteristics ofPS converted waves with synthetic seismogram.Chinese J.Geophys.(in Chinese),1985,28(3):291-302.
[16]刘启元,Kind R.远震接收函数及非线性复谱波形反演.∥中国地球物理学会年刊.北京:地震出版社,1992,18.Liu Q Y,Kind R.Lithospheric receiver function and its non-linear complex spectrum inversion.∥Annual of the ChineseGeophysical Society(in Chinese).Beijing:SeismologicalPress,1992,18.
[17]刘启元,KindR.分离三分量远震接收函数的多道最大或然性反褶积方法.地震地质,2004,26(3):416-425.Liu Q Y,Kind R.Multi-channel maximal likelihooddeconvolution method for isolating 3-component teleseismicreceiver function.Seismology and Geology(in Chinese),2004,26(3):416-425.
[18]Ligorria J P,Ammon C J.Iterative Deconvolution andReceiver-Function Estimation.Bull.Seism.Soc.Am.,1999,89(5):1395-1400.
[19]李顺成,刘启元,陈九辉等.横跨天山的宽频带流动地震台阵观测.地球物理学进展,2005,20(4):955-960.Li S C,Liu Q Y,Chen J H,et al.Passive broadband seismicarray observation across Tianshan.Progress in Geophysics(in Chinese),2005,20(4):955-960.
[20]Tarantola A.Inversion Problem Theory,Method for DataFitting and Model Parameter Estimation.Amsterdam:Elsevier,1987.
[21]Tarantola A.Inverse Problem Theory,and Methods forModel Parameter Estimation.SIAM,PA 19104-2688USA,2005.
[22]Müller G.The reflectivity method:a turtorial.J.Geophys.,1985,58(3):153-174.
[23]Randall G E.Efficient calculation of differential seismogramsfor lithospheric receiver functions.J.Geophys.Int.,1989,99(3):469-481.
[24]Li Y,Liu Q Y,Chen J H,et al.Shear wave velocitystructure of the crust and upper mantle underneath theTianshan orogenic belt.Science in China(Series D),2007,50(3):321-330.
[2]刘启元,Kind R,李顺成.接收函数复谱比的最大或然性估计及非线性反演.地球物理学报,1996,39(4):502-513.Liu Q Y,Kind R,Li S C.Maximal likelihood estimation andnonlinear inversion of the complex receiver function spectrumratio.Chinese J.Geophys.(in Chinese),1996,39(4):502-513.
[3]Farra V,Vinnik L.Upper mantle stratification by P and Sreceiver functions.Geophys.J.Int.,2000,141(3):699-712.
[4]Oreshin S,Vinnik L,Peregoudov D,et al.Lithosphere andasthenosphere of the Tien Shan imaged by S receiverfunctions.Geophys.Res.Lett.,2002,29(8):1191,doi:1029/2001GL014441.
[5]Kumar P,Yuan X,Kind R,et al.The lithosphere-asthenosphere boundary in the Tien Shan-Karakoram regionfrom S receiver functions:Evidence for continental subduction.Geophys.Res.Lett.,2005,32,L07305,doi:10.1029/2004GL022291,1-4.
[6]Soudoudi F,Yuan X,Liu Q Y,et al.Lithospheric thinknessbeneath the Dabie Shan,central eastern China from S receiverfunctions.Geophys.J.Int.,2006,166(3):1363-1367.
[7]Vinnik L P,Reigber C,Aleshin I M,et al.Receiver functiontomography of the central Tien Shan.Earth Planet.Sci.Lett.,2004,225(1-2):131-146.
[8]Ammon C J,Randall G,Zandt G.On the nonuniqueness ofreceiver function inversion.J.Geophys Res.,1990,95(B10):15303-15318.
[9]Wu Q,Li Y,Zhang R,et al.Wavelet modeling of broad-band receiver functions.Geophys.J.Int.,2007,170(2):534-544.
[10]Liu Q Y,Li Y,Chen J H,et al.Joint inversion of receiverfunction and ambient noise based on Bayesian theory.Chin.J.Geophys.,2010,53(11):961-972.
[11]Scales J A,Snieder R.The anatomy of inverse problems.Geophysics,2000,65(6):1708-1710.
[12]Yuan X H,Kind R,Li X Q,et al.The S receiver functions:synthetics and data example.Geophys.J.Int.,2006,165(2):555-564.
[13]Aki K,Richards P G.Quantitative Seismology:Theory andMethods.San Francisco:W.H.Freeman and Company,1980,133-155.
[14]刘启元,范会吉.震源区和接收区结构不同情况下体波合成地震图的矩阵-射线方法.地球物理学报,1992,35(2):193-203.Liu Q Y,Fan H J.The ray-matrix method of syntheticseismograms for different source and receiver structure.Chinese J.Geophys.(in Chinese),1992,35(2):193-203.
[15]刘启元,邵学钟.天然地震PS转换波动力学特征的初步研究.地球物理学报,1985,28(3):291-302.Liu Q Y,Shao X Z.A study of the dynamic characteristics ofPS converted waves with synthetic seismogram.Chinese J.Geophys.(in Chinese),1985,28(3):291-302.
[16]刘启元,Kind R.远震接收函数及非线性复谱波形反演.∥中国地球物理学会年刊.北京:地震出版社,1992,18.Liu Q Y,Kind R.Lithospheric receiver function and its non-linear complex spectrum inversion.∥Annual of the ChineseGeophysical Society(in Chinese).Beijing:SeismologicalPress,1992,18.
[17]刘启元,KindR.分离三分量远震接收函数的多道最大或然性反褶积方法.地震地质,2004,26(3):416-425.Liu Q Y,Kind R.Multi-channel maximal likelihooddeconvolution method for isolating 3-component teleseismicreceiver function.Seismology and Geology(in Chinese),2004,26(3):416-425.
[18]Ligorria J P,Ammon C J.Iterative Deconvolution andReceiver-Function Estimation.Bull.Seism.Soc.Am.,1999,89(5):1395-1400.
[19]李顺成,刘启元,陈九辉等.横跨天山的宽频带流动地震台阵观测.地球物理学进展,2005,20(4):955-960.Li S C,Liu Q Y,Chen J H,et al.Passive broadband seismicarray observation across Tianshan.Progress in Geophysics(in Chinese),2005,20(4):955-960.
[20]Tarantola A.Inversion Problem Theory,Method for DataFitting and Model Parameter Estimation.Amsterdam:Elsevier,1987.
[21]Tarantola A.Inverse Problem Theory,and Methods forModel Parameter Estimation.SIAM,PA 19104-2688USA,2005.
[22]Müller G.The reflectivity method:a turtorial.J.Geophys.,1985,58(3):153-174.
[23]Randall G E.Efficient calculation of differential seismogramsfor lithospheric receiver functions.J.Geophys.Int.,1989,99(3):469-481.
[24]Li Y,Liu Q Y,Chen J H,et al.Shear wave velocitystructure of the crust and upper mantle underneath theTianshan orogenic belt.Science in China(Series D),2007,50(3):321-330.
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