基于Aki公式的主动源瑞雷波频散曲线提取方法研究
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摘要
瑞雷波成像是一种有效探测近地表横波速度结构的方法,准确提取频散曲线是该方法的关键。本文提出了利用噪声理论中的Aki公式提取主动源瑞雷波频散曲线的方法,在频率域中,两道记录互相关后的频谱能够被贝塞尔函数所描述,利用频谱实部的零点与贝塞尔函数根的对应关系,即可以获得离散频点处的相速度值,进而提取出频散曲线。首先介绍了Aki法应用于主动源瑞雷波数据的理论基础与计算流程;然后,利用该方法对三组理论模型数值模拟记录进行了计算,得到了与理论频散曲线一致的结果;最后,对一组实际采集的瑞雷波数据进行处理得到相速度剖面,并与多道面波分析方法得到的剖面结果对比,验证了Aki法在主动源数据处理中的有效性与适用性。与多道面波处理技术相比,Aki法的优势在于仅利用单炮记录中的两道数据进行相速度的计算,当某炮记录的采集道数不足或存在坏道时,可以保证提取的频散曲线的质量。
Rayleigh wave imaging is efficient in estimating the shear-(S) wave velocity in near-surface exploration. The key is to accurately extract the dispersion of Rayleigh wave. We propose a method to calculate the dispersion of the active-source Rayleigh wavefield by using the Aki formulation. The spectrum after the cross correlation of two-channel records in the frequency domain is expressed by the Bessel function. Using the corresponding relation between the zero point of the spectrum real part and the Bessel function root, the phase velocity at the discrete frequency point is obtained and the dispersion curve is extracted. First, the theoretical basis and calculation method used in the active-source Rayleigh wave data are introduced. Then, three sets of theoretical models are calculated by this method and the results are consistent with the theoretical dispersion. Finally, we process a group of real Rayleigh wave data and obtain the phase velocity profiles and compared them with the results obtained by the multichannel surface wave analysis method. The effectiveness and applicability of the Aki method in active-source data processing are verified. Compared with multichannel wave processing, the advantage of the Aki method lies in the use of two-channel data in a single-shot record. When the number of acquisition channels in a shot gathers is insufficient or there is a bad channel, the quality of the extracted dispersion is guaranteed.
Rayleigh wave imaging is efficient in estimating the shear-(S) wave velocity in near-surface exploration. The key is to accurately extract the dispersion of Rayleigh wave. We propose a method to calculate the dispersion of the active-source Rayleigh wavefield by using the Aki formulation. The spectrum after the cross correlation of two-channel records in the frequency domain is expressed by the Bessel function. Using the corresponding relation between the zero point of the spectrum real part and the Bessel function root, the phase velocity at the discrete frequency point is obtained and the dispersion curve is extracted. First, the theoretical basis and calculation method used in the active-source Rayleigh wave data are introduced. Then, three sets of theoretical models are calculated by this method and the results are consistent with the theoretical dispersion. Finally, we process a group of real Rayleigh wave data and obtain the phase velocity profiles and compared them with the results obtained by the multichannel surface wave analysis method. The effectiveness and applicability of the Aki method in active-source data processing are verified. Compared with multichannel wave processing, the advantage of the Aki method lies in the use of two-channel data in a single-shot record. When the number of acquisition channels in a shot gathers is insufficient or there is a bad channel, the quality of the extracted dispersion is guaranteed.
引文
Aki,K.,1957,Space and time spectra of stationary stochastic wave,with special reference to microtremors:Bulletin of the Earthquake Research Institute,35,415-456.
Asten,M.W.,2006,On bias and noise in passive seismic data from finite circular array data processed using spac methods:Geophysics,71(6),V153-V162.
Buchen,P.W.,and Ben-Hedor,R.,1996,Free-mode surface-wave computations:Geophysical Journal International,124,869-887.
Chávez-García,F.J.,and Luzón,F.,2005,On the correlation of seismic microtremors:Journal of Geophysical Research,110,B11313.
Cox,H.,1973,Spatial correlation in arbitrary noise fields with application to ambient sea noise:Journal of the Acoustical Society of America,54(5),1289-1301.
Dal,G.,Pipan,M.,and Forte,E.,et al.,2003,Determination of Rayleigh wave dispersion curves for near surface applications in unconsolidated sediments:73th Annual International Meeting,SEG Expanded Abstracts,1247-1250.
Dorman,J.,and Ewing,M.,1962,Numerical inversion of seismic surface wave dispersion data and crust-mantle structure in the New York-Pennsylvania area:Journal of Geophysical Research,67(13),5227-5241.
Ekstr?m,G.,Abers,G.A.,and Webb,S.C.,2009,Determination of surface-wave phase velocities across Usarray from noise and Aki's spectral formulation:Geophysical Research Letters,2009,36(18),64-66.
Herrmann,R.B.,2013,Computer programs in seismology,an evolving tool for instruction and research,Seismological Research Letters,84(6),1081-1088.
Lee,W.B.,and Solomon,S.C.,1979,Simultaneous inversion of surface wave phase velocity and attenuation,Rayleigh and Love waves over continental and oceanic paths:Bulletin of the Seismological Society of America,69,65-95.
Lin,F.,Ritzwoller,M.H.,and Snieder,R.,2009,Eikonal tomography,surface wave tomography by phase front tracking across a regional broad-band seismic array:Geophysical Journal International,177(3),1091-1110.
Lobkis,O.I.,and Weaver,R.L.,2001,On The emergence of the green's function in the correlations of a diffuse field:Journal of the Acoustical Society of America,110(6),3011-3017.
Luo,Y.,Xia,J.,and Miller,R.D.,et al.,2008,Rayleighwave Dispersive energy imaging using a high-resolution linear radon transform:Pure and Applied Geophysics,165(5),903-922.
Luo,Y.,Xia,J.,and Miller,R.D.,et al.,2009a,Rayleighwave mode separation by high-resolution linear radon transform:Geophysical Journal International,179(1),254-264.
Luo,Y.,Xia,J.,and Xu,Y.,et al.,2009b,Dipping-interface mapping using mode-separated Rayleigh waves:Pure and Applied Geophysics,166(3),353-347.
Mcmechan,G.A.,and Yedlin,M.J.,1981,Analysis of dispersive waves by wave field transformation:Geophysics,46,101-113.
Nakahara,H.,2006,A systematic study of theoretical relations between spatial correlation and Green's function in one-,two-and three-dimensional random scalar wavefields:Geophysical Journal International,167(3),1097-1105.
Pan,Y.,Xia,J.,and Zeng,C.,2013,Verification of correctness of using real part of complex root as rayleigh-wave phase velocity with synthetic data,Journal of Applied Geophysics,88(1),94-100.
Park,C.B.,Miller,R.D.,and Xia,J.,1998,Imaging dispersion curves of surface waves on multi-channel record:68th Annual International Meeting,SEGExpanded Abstracts,1377-1380.
Sanchez-sesma,F.,and Campillo,M.,2006,Retrieval of the Green's function from cross-correlation,the canonical elastic problem:Bulletin of the Seismological Society of America,96(3),1182-1191.
Song,Y.,Castagna,J.P.,and Black,R.A.,et al.,1989,Sensitivity of near-surface shear-wave velocity determination from Rayleigh and Love waves:59th Annual International Meeting,SEG Expanded Abstracts1989,509-512.
Stephenson,W.J.,Louie,J.N.,and Pullammanappallil,S.,et al.,2006,Blind shear-wave velocity comparison of Remi and MASW results with boreholes to 200 m in Santa Clara valley,implications for earthquake groundmotion assessment:Bulletin of the Seismological Society of America,95(6),2506-2516.
Sun,C.Y.,Wang,Y.Y.,and Wu,D.S.,et al.,2017,Nonlinear Rayleigh wave inversion based on the shuffled frog-leaping algorithm:Applied Geophysics,14(4),551-558.
Tsai,V.C.,and Moschetti,M.P.,2010,An explicit relationship between time-domain noise correlation and spatial autocorrelation(SPAC)results:Geophysical Journal International,182(1),454-460.
Wapenaar,K.,Slob,E.,and Snieder,R.,2006,Unified Green's function retrieval by cross-correlation:Physical Review Letters,97(23),234-301.
Xia,J.,Miller,R.D.,and Park,C.B.,1999,Estimation of near-surface shear-wave velocity by inversion of Rayleigh waves:Geophysics,64(3),691-700.
Xia,J.,Miller,R.D.,and Park,C.B.,et al.,2002,Determining Q of near-surface materials from Rayleigh waves.Journal of Applied Geophysics,51(2-4),121-129.
Xia,J.,Xu,Y.,and Miller,R.D.,2007,Generating an image of dispersive energy by frequency decomposition and slant stacking:Pure and Applied Geophysics,164(5),941-956.
Xu,C.,and Butt,S.D.,2006,Evaluation of masw techniques to image steeply dipping cavities in laterally inhomogeneous terrain:Journal of Applied Geophysics,59(2),106-116.
Yao,H.,Campman,X.,and Hoop,M.V.D.,et al.,2009,Estimation of surface wave green's functions from correlation of direct waves,coda waves,and ambient noise in SE Tibet:Physics of the Earth&Planetary Interiors,77(1-2),1-11.
Yilmaz,?.,1987,Seismic data processing,society of exploration geo-physicists,Tulsa,OK.
Yilmaz,?.,Eser,M.,and Berilgen,M.,2006,A case study of seismic zonation in municipal areas:The Leading Edge,25(3),319-330.
Zhou,T.F.,Peng,G.X.,and Hu,T.Y.,et al.,2014,Rayleigh wave nonlinear inversion based on the firefly algorithm:Applied Geophysics,11(2),167-178.
Asten,M.W.,2006,On bias and noise in passive seismic data from finite circular array data processed using spac methods:Geophysics,71(6),V153-V162.
Buchen,P.W.,and Ben-Hedor,R.,1996,Free-mode surface-wave computations:Geophysical Journal International,124,869-887.
Chávez-García,F.J.,and Luzón,F.,2005,On the correlation of seismic microtremors:Journal of Geophysical Research,110,B11313.
Cox,H.,1973,Spatial correlation in arbitrary noise fields with application to ambient sea noise:Journal of the Acoustical Society of America,54(5),1289-1301.
Dal,G.,Pipan,M.,and Forte,E.,et al.,2003,Determination of Rayleigh wave dispersion curves for near surface applications in unconsolidated sediments:73th Annual International Meeting,SEG Expanded Abstracts,1247-1250.
Dorman,J.,and Ewing,M.,1962,Numerical inversion of seismic surface wave dispersion data and crust-mantle structure in the New York-Pennsylvania area:Journal of Geophysical Research,67(13),5227-5241.
Ekstr?m,G.,Abers,G.A.,and Webb,S.C.,2009,Determination of surface-wave phase velocities across Usarray from noise and Aki's spectral formulation:Geophysical Research Letters,2009,36(18),64-66.
Herrmann,R.B.,2013,Computer programs in seismology,an evolving tool for instruction and research,Seismological Research Letters,84(6),1081-1088.
Lee,W.B.,and Solomon,S.C.,1979,Simultaneous inversion of surface wave phase velocity and attenuation,Rayleigh and Love waves over continental and oceanic paths:Bulletin of the Seismological Society of America,69,65-95.
Lin,F.,Ritzwoller,M.H.,and Snieder,R.,2009,Eikonal tomography,surface wave tomography by phase front tracking across a regional broad-band seismic array:Geophysical Journal International,177(3),1091-1110.
Lobkis,O.I.,and Weaver,R.L.,2001,On The emergence of the green's function in the correlations of a diffuse field:Journal of the Acoustical Society of America,110(6),3011-3017.
Luo,Y.,Xia,J.,and Miller,R.D.,et al.,2008,Rayleighwave Dispersive energy imaging using a high-resolution linear radon transform:Pure and Applied Geophysics,165(5),903-922.
Luo,Y.,Xia,J.,and Miller,R.D.,et al.,2009a,Rayleighwave mode separation by high-resolution linear radon transform:Geophysical Journal International,179(1),254-264.
Luo,Y.,Xia,J.,and Xu,Y.,et al.,2009b,Dipping-interface mapping using mode-separated Rayleigh waves:Pure and Applied Geophysics,166(3),353-347.
Mcmechan,G.A.,and Yedlin,M.J.,1981,Analysis of dispersive waves by wave field transformation:Geophysics,46,101-113.
Nakahara,H.,2006,A systematic study of theoretical relations between spatial correlation and Green's function in one-,two-and three-dimensional random scalar wavefields:Geophysical Journal International,167(3),1097-1105.
Pan,Y.,Xia,J.,and Zeng,C.,2013,Verification of correctness of using real part of complex root as rayleigh-wave phase velocity with synthetic data,Journal of Applied Geophysics,88(1),94-100.
Park,C.B.,Miller,R.D.,and Xia,J.,1998,Imaging dispersion curves of surface waves on multi-channel record:68th Annual International Meeting,SEGExpanded Abstracts,1377-1380.
Sanchez-sesma,F.,and Campillo,M.,2006,Retrieval of the Green's function from cross-correlation,the canonical elastic problem:Bulletin of the Seismological Society of America,96(3),1182-1191.
Song,Y.,Castagna,J.P.,and Black,R.A.,et al.,1989,Sensitivity of near-surface shear-wave velocity determination from Rayleigh and Love waves:59th Annual International Meeting,SEG Expanded Abstracts1989,509-512.
Stephenson,W.J.,Louie,J.N.,and Pullammanappallil,S.,et al.,2006,Blind shear-wave velocity comparison of Remi and MASW results with boreholes to 200 m in Santa Clara valley,implications for earthquake groundmotion assessment:Bulletin of the Seismological Society of America,95(6),2506-2516.
Sun,C.Y.,Wang,Y.Y.,and Wu,D.S.,et al.,2017,Nonlinear Rayleigh wave inversion based on the shuffled frog-leaping algorithm:Applied Geophysics,14(4),551-558.
Tsai,V.C.,and Moschetti,M.P.,2010,An explicit relationship between time-domain noise correlation and spatial autocorrelation(SPAC)results:Geophysical Journal International,182(1),454-460.
Wapenaar,K.,Slob,E.,and Snieder,R.,2006,Unified Green's function retrieval by cross-correlation:Physical Review Letters,97(23),234-301.
Xia,J.,Miller,R.D.,and Park,C.B.,1999,Estimation of near-surface shear-wave velocity by inversion of Rayleigh waves:Geophysics,64(3),691-700.
Xia,J.,Miller,R.D.,and Park,C.B.,et al.,2002,Determining Q of near-surface materials from Rayleigh waves.Journal of Applied Geophysics,51(2-4),121-129.
Xia,J.,Xu,Y.,and Miller,R.D.,2007,Generating an image of dispersive energy by frequency decomposition and slant stacking:Pure and Applied Geophysics,164(5),941-956.
Xu,C.,and Butt,S.D.,2006,Evaluation of masw techniques to image steeply dipping cavities in laterally inhomogeneous terrain:Journal of Applied Geophysics,59(2),106-116.
Yao,H.,Campman,X.,and Hoop,M.V.D.,et al.,2009,Estimation of surface wave green's functions from correlation of direct waves,coda waves,and ambient noise in SE Tibet:Physics of the Earth&Planetary Interiors,77(1-2),1-11.
Yilmaz,?.,1987,Seismic data processing,society of exploration geo-physicists,Tulsa,OK.
Yilmaz,?.,Eser,M.,and Berilgen,M.,2006,A case study of seismic zonation in municipal areas:The Leading Edge,25(3),319-330.
Zhou,T.F.,Peng,G.X.,and Hu,T.Y.,et al.,2014,Rayleigh wave nonlinear inversion based on the firefly algorithm:Applied Geophysics,11(2),167-178.