基于贝叶斯理论的接收函数与环境噪声联合反演
|
摘要
基于Bayes反演理论(Tarantola,1987,2005),在接收函数非线性复谱比反演方法基础上(刘启元等,1996),本文讨论了接收函数与地震环境噪声Rayleigh波相速度频散的联合反演.本文采用修正后的快速广义反射/透射系数方法(Pei et al.,2008,2009)计算Rayleigh波相速度频散,并引入地壳泊松比的全局性搜索.数值检验表明:(1)接收函数与环境噪声的联合反演能够有效地解决反演结果对初始模型依赖的问题,即使对地壳速度结构仅有非常粗略的初始估计(例如,垂向均匀模型),本文方法仍能给出模型参数的可靠估计;(2)由于环境噪声与接收函数在频带上的适配性明显优于地震面波,接收函数与环境噪声的非线性联合反演能更好地约束台站下方近地表的速度结构;对于周期范围为2～40s的环境噪声相速度频散,利用本文方法能够可靠推测台站下方0～80km深度范围的S波速度结构,其浅表速度结构的分辨率可达到1km(3)本文方法能够可靠地估计地壳泊松比,泊松比的全局性搜索有助于合理解释接收函数和环境噪声的面波频散数据.利用本文方法对川西台阵KWC05台站观测的接收函数与环境噪声的联合反演表明,该台站下方地壳厚度为44km,上地壳具有明显的高速结构,24～42km范围的中下地壳具有低速结构.该台站下方地壳的平均泊松比为0.262,壳内低速带的泊松比为0.27.
In this study, we present a method for the joint inversion of receiver function and ambient noise based on Bayesian inverse theory (Tarantola, 1987, 2005). In our method, the nonlinear inversion method of the complex spectrum ratio of receiver functions (Liu et al. , 1996) has been extended to perform the joint inversion of the receiver function and ambient noise with global scanning of the crustal Poisson s ratio. The forward problem of the Rayleigh-wave phase dispersion is solved in terms of a modified version of the fast generalized R/T method proposed by Pei et al. (2008,2009). Our numerical tests show that (1) the dependency of inversion results on initial models has been removed and the model s parameter is estimated reliably even in the case of using a vertically homogeneous model as the initial guess for the crust structure; (2) since the consistency of the frequency band of the receiver function with the phase dispersion obtained from ambient noise is much better than that with seismic surface waves, the S-wave velocity structure in depth of 0～80 km can be well estimated in terms of the joint inversion of receiver function and ambient noise for the phase velocity dispersion in the period of 2～40 s, and the space resolution of the shallow structure nearby the surface can reach to 1 km; (3) global scanning of the Poisson's ratio is not only in favor of data interpretation of the receiver function and ambient noise, but also provides a reliable estimation of the crustal Poisson's ratio. The joint inversion of receiver function and ambient noise recorded at Station KWC05 of the western Sichuan seismic array shows that the crustal thickness beneath the station reaches to 44 km and the crustal S-wave velocity structure manifests the high-speed upper crust and low-speed middle-lower crust in depth of 24～42 km. The Poisson's ratio averaged over the crust is 0. 262 and that over the low-velocity zone is 0. 27.
In this study, we present a method for the joint inversion of receiver function and ambient noise based on Bayesian inverse theory (Tarantola, 1987, 2005). In our method, the nonlinear inversion method of the complex spectrum ratio of receiver functions (Liu et al. , 1996) has been extended to perform the joint inversion of the receiver function and ambient noise with global scanning of the crustal Poisson s ratio. The forward problem of the Rayleigh-wave phase dispersion is solved in terms of a modified version of the fast generalized R/T method proposed by Pei et al. (2008,2009). Our numerical tests show that (1) the dependency of inversion results on initial models has been removed and the model s parameter is estimated reliably even in the case of using a vertically homogeneous model as the initial guess for the crust structure; (2) since the consistency of the frequency band of the receiver function with the phase dispersion obtained from ambient noise is much better than that with seismic surface waves, the S-wave velocity structure in depth of 0～80 km can be well estimated in terms of the joint inversion of receiver function and ambient noise for the phase velocity dispersion in the period of 2～40 s, and the space resolution of the shallow structure nearby the surface can reach to 1 km; (3) global scanning of the Poisson's ratio is not only in favor of data interpretation of the receiver function and ambient noise, but also provides a reliable estimation of the crustal Poisson's ratio. The joint inversion of receiver function and ambient noise recorded at Station KWC05 of the western Sichuan seismic array shows that the crustal thickness beneath the station reaches to 44 km and the crustal S-wave velocity structure manifests the high-speed upper crust and low-speed middle-lower crust in depth of 24～42 km. The Poisson's ratio averaged over the crust is 0. 262 and that over the low-velocity zone is 0. 27.
引文
[1] Langston C A.Structure under Mount Rainier,Washington,inferred from teleseismic body waves.J.Geophys.Res.,1979,84:4749～4762
[2] Ammon C J,Randall G,Zandt G.On the nonuniqueness of receiver function inversions.J.Geophys.Res.,1990,95(B10) :15303～15318
[3] Wu Q,Li Y,Zhang R,et al.Wavelet modeling of broadband receiver functions.Geophys.J.Int.,2007,170(2) :534～544
[4] Scales J A,Snieder R.The anatomy of inverse problems.Geophysics,2000,65(6) :1708～1710
[5] (O|¨)zalaybey S,Savage M K,Sheehan A F,et al.Shear-wave velocity structure in the northern Basin and Range province from the combined analysis of receiver functions and surface waves.Bull.Seism.Soc.Am.,1997,87(1) :183～199．
[6] Julia J,Ammon C J,Herrmann R B,et al.Joint inversion of receiver function and surface wave dispersion observations.Geophys.J.Int.,2000,143(1) :1～19
[7] Sung J C,Chang-Eob B,Langston C A.Joint analysis of teleseismic receiver functions and surface wave dispersion using the Genetic algorithm.Bull.Seism.Soc.Am.,2004,94(2) :691～704
[8] Lawrence J F,Wiens D A.Combined receiver-function and surface wave phase-velocity inversion using a niching genetic algorithm:application to Patagonia.Bull.Seism.Soc.Am.,2004,94(3) :977～987
[9] 胡家富,朱雄关,夏静瑜等.利用面波和接收函数联合反演滇西地区壳幔速度结构.地球物理学报,2005,48(5) :1069～1076 Hu J F,Zhu X G,Xia J Y,et al.Using surface wave and receiver function to jointly inverse the crust-mantle velocity structure in the West Yunnan area.Chinese J.Geophys.(in Chinese),2005,48(5) :1069～1076
[10] Lobkis O I,Weaver R L.On the emergence of the Green's function in the correlations of a diffusive field.J.Acoust.Soc.Am.,2001,110(6) :3011～3017
[11] Weaver R L,Lobkis O I.Diffuse fields in open systems and the emergence of the Green's function.J.Acoust.Soc.Am.,2004,116(5) :2731～2734
[12] Campillo M,Paul A.Long-Range correlations in the diffuse seismic coda.Science,2003,299(5606) :547～549
[13] Shapiro N M,Campillo M.Emergence of broadband Rayleigh waves from correlations of the ambient seismic noise.Geophys.Res.Lett.,2004,31(7) :1615～1619
[14] Shapiro N M,Campillo M,Stehly L,et al.High-resolution surface-wave tomography from ambient seismic noise.Science,2005,307:1615～1618
[15] Yao H J,van der Hilst R D.Analysis of ambient noise energy distribution and phase velocity bias in ambient noise tomography,with application to SE Tibet.Geophys.J.Int.,2009,179(4) :1113～1132
[16] 李昱,姚华建,刘启元等.川西地区台阵环境噪声瑞利波相速度层析成像.地球物理学报,2010,53(4) :842～852 Li Y,Yao H J,Liu Q Y,et al.Phase velocity array tomography of Rayleigh waves in western Sichuan from ambient noise.Chinese J.Geophys.(in Chinese),2010,53(4) :842～852
[17] 刘启元,Kind R,李顺成.接收函数复频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 and nonlinear inversion of the complex receiver function spectrum ratio.Chinese J.Geophys.(in Chinese),1996,39(4) :502～513
[18] Müller G.The reflectivity method:a tutorial.J.Geophys.,1985,58(3) :153～174
[19] Randall G E.Efficient calculation of differential seismograms for lithospheric receiver functions.J.Geophys.Int.,1989,99(3) :469～481
[20] Scherbaum F.Seismic imaging of the site response using micro earthquake recordings,part Ⅰ:method.Bull.Seism.Soc.Am.,1987,77:1905～1923
[21] Thomson W T.Transmission of elastic waves through a stratified solid medium.J.Appl.Physics,1950,21(2) :89～93
[22] Haskell N A.The dispersion of surface waves on a multilayered medium.Bull.Seism.Soc.Am.,1953,43(1) :17～34
[23] Dunkin J W.Computation of modal solution in layered,elastic media at high frequencies.Bull.Seism.Soc.Am.,1965,53(2) :335～358
[24] Herrmann R B,Ammon C J.Computer programs in seismology version 3． 20:Surface waves,receiver functions,and crustal structure.St.Louis University,Missouri.2002,Available at http://mnw.eas.slu.edu/People/RBHerrmann
[25] Kennett B L N.Seismic Wave Propagation in Stratified Media.Cambridge University Press,1983
[26] Luco J E,Apsel R J.On the Green's function for a layered halbspace,part Ⅰ.Bull.Seism.Soc.Am.1983,73(4) :909～929
[27] Chen X.A systematic and efficient method of computing normal modes for multilayered half-space.Geophy.J Int.,1993,115(2) :391～409
[28] Pei D H,John N L,Pullammanappallil S K,et al.Improvements on computation of phase velocities of Rayleigh waves based on the generalized R/T coefficient method.Bull.Seism.Soc.Am.,2008,98(1) .280～287
[29] Pei D H,John N L,Pullammanappallil S K,et al.Erratum to improvements on computation of phase velocities of Raylcigh waves based on the generalized R/T coefficient method.Bull.Seism.Soc.Am.,2009,99(4) :2610～2611
[30] 潘佳铁,吴庆举,李永华等.基于快速广义反射透射系数方法的面波群速度计算.地球物理学进展,2009,24(6) :2030～2035 Pan J T,Wu Q J,Li Y H.Group velocities computation of surface waves based on the fast generalized R/T coefficient method.(in Chinese),2009,24(6) .2030～2035
[31] Aki K,Richards P G.Quantitative Seismology,Second Ed.University Science Books,Sausalito,Californian,2002
[32] Tarantola A.Inverse Problem Theory,Methods for Data Fitting and Model Parameter Estimation.Elsevier,Amsterdam,1987
[33] Tarantola A.Inverse Problem Theory,and Methods for Model Parameter Estimation.SIAM,PA 19104-2688 USA,2005
[34] Scales J A,Snieder R.To Bayes or not to Bayes.Geophysics,1997,62(4) :1045～1046
[35] Gouveia W P,Scales J A.Bayesian seismic waveform inversion:parameter estimation and uncertainty analysis.J.Geophys.Res.,1998,103(2) :2759～2779
[36] Gao S.A Bayesian nonlinear inversion of seismic body-wave attenuation factors.Bull.Seism.Soc.Am,1997,87(4) :961～970
[37] Cercato M.Computation of partial derivatives of Rayleighwave phase velocity using second-order subdeterminants.Geophys.J.Int.,2007,170(1) .217～238
[38] Novotiny O.Partial derivatives of dispersion curves of Love waves in layered medium.Studia Geoph.et Geod.,1970,14(1) :36～50
[39] Novotiny O.Methods of computing the partial derivatives ot dispersion curves.Pure.Appl.Geophys.,1976,114(5) :765～775
[40] Dziewonski A M,Anderson D L.Preliminary reference Earth model.Phys.Earth Planet.Int.,1981,25(4) :297～356
[41] 刘启元,陈九辉,李顺成等.汶川M_S8． 0地震:川西流动地震台阵观测数据的初步分析.地震地质,2008,30(3) :584～596 Liu Q Y,Chen J H,Li S C,et al.The M_S8． 0 Wenchuan earthquake:Preliminary results from the western Sichuan mobile seismic array observations.Seismology and Geology(in Chinese),2008,30(3) :584～596
[42] 刘启元,李昱,陈九辉等.汶川M_S8． 0地震:地壳上地幔S波速度结构的初步研究.地球物理学报,2009,52(2) :309～319 Liu Q Y,Li Y,Chen J H.Wenchuan M_S8． 0 earthquake:Swave velocity structure of the crust and upper mantle.Chinese J.Geophys.(in Chinese),2009,52(2) .309～319
[43] Ligorria J P,Ammon C J.Iterative deconvolution of teleseismic seismograms and receiver function estimation.Bull.Seism.Soc.Am.,1999,89(5) :1395～1400
[2] Ammon C J,Randall G,Zandt G.On the nonuniqueness of receiver function inversions.J.Geophys.Res.,1990,95(B10) :15303～15318
[3] Wu Q,Li Y,Zhang R,et al.Wavelet modeling of broadband receiver functions.Geophys.J.Int.,2007,170(2) :534～544
[4] Scales J A,Snieder R.The anatomy of inverse problems.Geophysics,2000,65(6) :1708～1710
[5] (O|¨)zalaybey S,Savage M K,Sheehan A F,et al.Shear-wave velocity structure in the northern Basin and Range province from the combined analysis of receiver functions and surface waves.Bull.Seism.Soc.Am.,1997,87(1) :183～199．
[6] Julia J,Ammon C J,Herrmann R B,et al.Joint inversion of receiver function and surface wave dispersion observations.Geophys.J.Int.,2000,143(1) :1～19
[7] Sung J C,Chang-Eob B,Langston C A.Joint analysis of teleseismic receiver functions and surface wave dispersion using the Genetic algorithm.Bull.Seism.Soc.Am.,2004,94(2) :691～704
[8] Lawrence J F,Wiens D A.Combined receiver-function and surface wave phase-velocity inversion using a niching genetic algorithm:application to Patagonia.Bull.Seism.Soc.Am.,2004,94(3) :977～987
[9] 胡家富,朱雄关,夏静瑜等.利用面波和接收函数联合反演滇西地区壳幔速度结构.地球物理学报,2005,48(5) :1069～1076 Hu J F,Zhu X G,Xia J Y,et al.Using surface wave and receiver function to jointly inverse the crust-mantle velocity structure in the West Yunnan area.Chinese J.Geophys.(in Chinese),2005,48(5) :1069～1076
[10] Lobkis O I,Weaver R L.On the emergence of the Green's function in the correlations of a diffusive field.J.Acoust.Soc.Am.,2001,110(6) :3011～3017
[11] Weaver R L,Lobkis O I.Diffuse fields in open systems and the emergence of the Green's function.J.Acoust.Soc.Am.,2004,116(5) :2731～2734
[12] Campillo M,Paul A.Long-Range correlations in the diffuse seismic coda.Science,2003,299(5606) :547～549
[13] Shapiro N M,Campillo M.Emergence of broadband Rayleigh waves from correlations of the ambient seismic noise.Geophys.Res.Lett.,2004,31(7) :1615～1619
[14] Shapiro N M,Campillo M,Stehly L,et al.High-resolution surface-wave tomography from ambient seismic noise.Science,2005,307:1615～1618
[15] Yao H J,van der Hilst R D.Analysis of ambient noise energy distribution and phase velocity bias in ambient noise tomography,with application to SE Tibet.Geophys.J.Int.,2009,179(4) :1113～1132
[16] 李昱,姚华建,刘启元等.川西地区台阵环境噪声瑞利波相速度层析成像.地球物理学报,2010,53(4) :842～852 Li Y,Yao H J,Liu Q Y,et al.Phase velocity array tomography of Rayleigh waves in western Sichuan from ambient noise.Chinese J.Geophys.(in Chinese),2010,53(4) :842～852
[17] 刘启元,Kind R,李顺成.接收函数复频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 and nonlinear inversion of the complex receiver function spectrum ratio.Chinese J.Geophys.(in Chinese),1996,39(4) :502～513
[18] Müller G.The reflectivity method:a tutorial.J.Geophys.,1985,58(3) :153～174
[19] Randall G E.Efficient calculation of differential seismograms for lithospheric receiver functions.J.Geophys.Int.,1989,99(3) :469～481
[20] Scherbaum F.Seismic imaging of the site response using micro earthquake recordings,part Ⅰ:method.Bull.Seism.Soc.Am.,1987,77:1905～1923
[21] Thomson W T.Transmission of elastic waves through a stratified solid medium.J.Appl.Physics,1950,21(2) :89～93
[22] Haskell N A.The dispersion of surface waves on a multilayered medium.Bull.Seism.Soc.Am.,1953,43(1) :17～34
[23] Dunkin J W.Computation of modal solution in layered,elastic media at high frequencies.Bull.Seism.Soc.Am.,1965,53(2) :335～358
[24] Herrmann R B,Ammon C J.Computer programs in seismology version 3． 20:Surface waves,receiver functions,and crustal structure.St.Louis University,Missouri.2002,Available at http://mnw.eas.slu.edu/People/RBHerrmann
[25] Kennett B L N.Seismic Wave Propagation in Stratified Media.Cambridge University Press,1983
[26] Luco J E,Apsel R J.On the Green's function for a layered halbspace,part Ⅰ.Bull.Seism.Soc.Am.1983,73(4) :909～929
[27] Chen X.A systematic and efficient method of computing normal modes for multilayered half-space.Geophy.J Int.,1993,115(2) :391～409
[28] Pei D H,John N L,Pullammanappallil S K,et al.Improvements on computation of phase velocities of Rayleigh waves based on the generalized R/T coefficient method.Bull.Seism.Soc.Am.,2008,98(1) .280～287
[29] Pei D H,John N L,Pullammanappallil S K,et al.Erratum to improvements on computation of phase velocities of Raylcigh waves based on the generalized R/T coefficient method.Bull.Seism.Soc.Am.,2009,99(4) :2610～2611
[30] 潘佳铁,吴庆举,李永华等.基于快速广义反射透射系数方法的面波群速度计算.地球物理学进展,2009,24(6) :2030～2035 Pan J T,Wu Q J,Li Y H.Group velocities computation of surface waves based on the fast generalized R/T coefficient method.(in Chinese),2009,24(6) .2030～2035
[31] Aki K,Richards P G.Quantitative Seismology,Second Ed.University Science Books,Sausalito,Californian,2002
[32] Tarantola A.Inverse Problem Theory,Methods for Data Fitting and Model Parameter Estimation.Elsevier,Amsterdam,1987
[33] Tarantola A.Inverse Problem Theory,and Methods for Model Parameter Estimation.SIAM,PA 19104-2688 USA,2005
[34] Scales J A,Snieder R.To Bayes or not to Bayes.Geophysics,1997,62(4) :1045～1046
[35] Gouveia W P,Scales J A.Bayesian seismic waveform inversion:parameter estimation and uncertainty analysis.J.Geophys.Res.,1998,103(2) :2759～2779
[36] Gao S.A Bayesian nonlinear inversion of seismic body-wave attenuation factors.Bull.Seism.Soc.Am,1997,87(4) :961～970
[37] Cercato M.Computation of partial derivatives of Rayleighwave phase velocity using second-order subdeterminants.Geophys.J.Int.,2007,170(1) .217～238
[38] Novotiny O.Partial derivatives of dispersion curves of Love waves in layered medium.Studia Geoph.et Geod.,1970,14(1) :36～50
[39] Novotiny O.Methods of computing the partial derivatives ot dispersion curves.Pure.Appl.Geophys.,1976,114(5) :765～775
[40] Dziewonski A M,Anderson D L.Preliminary reference Earth model.Phys.Earth Planet.Int.,1981,25(4) :297～356
[41] 刘启元,陈九辉,李顺成等.汶川M_S8． 0地震:川西流动地震台阵观测数据的初步分析.地震地质,2008,30(3) :584～596 Liu Q Y,Chen J H,Li S C,et al.The M_S8． 0 Wenchuan earthquake:Preliminary results from the western Sichuan mobile seismic array observations.Seismology and Geology(in Chinese),2008,30(3) :584～596
[42] 刘启元,李昱,陈九辉等.汶川M_S8． 0地震:地壳上地幔S波速度结构的初步研究.地球物理学报,2009,52(2) :309～319 Liu Q Y,Li Y,Chen J H.Wenchuan M_S8． 0 earthquake:Swave velocity structure of the crust and upper mantle.Chinese J.Geophys.(in Chinese),2009,52(2) .309～319
[43] Ligorria J P,Ammon C J.Iterative deconvolution of teleseismic seismograms and receiver function estimation.Bull.Seism.Soc.Am.,1999,89(5) :1395～1400
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心