高分辨率的频率空间域声波全波形速度反演-理论模型
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摘要
使用最速下降法进行二维频率空间域声波波动方程全波形速度反演,讨论了如何快速实现高精度的二维频率空间域声波波动方程全波形速度反演.多尺度的思想耦合在反演框架中.把非线性问题化为逐步线性问题是我们关注的焦点,目的是把整个非线性反演的黑匣子转化成为每一步可控的过程,尽可能得到想要的反演解.仅仅使用3个离散的频率,每个频率迭代10次,对广角Marmousi模型进行地面地震声波全波形速度反演,反演得到高分辨率、高精度的速度,为全波形反演实际资料奠定了很好的基础.
We use the steepest descent method based on two-dimensional frequency space domain acoustic wave equation for full waveform velocity inversion,discuss how to quickly realize high precision two-dimensional frequency domain full waveform velocity inversion.Multi-scale criterial is coupling in the inversion framework.The nonlinear problem changes into gradually linear problem is our focus.The purpose is the whole nonlinear inverse black box into every step of controllable process as far as possible,getting an inversion solution we want.Use only three discrete frequencies,each frequency iterative ten times,we make surface seismic acoustic wave full waveform inversion on extended Marmousi and get a high resolution and high precision imaging of velocity.This gives a good foundation for full waveform inversion on real field data.
We use the steepest descent method based on two-dimensional frequency space domain acoustic wave equation for full waveform velocity inversion,discuss how to quickly realize high precision two-dimensional frequency domain full waveform velocity inversion.Multi-scale criterial is coupling in the inversion framework.The nonlinear problem changes into gradually linear problem is our focus.The purpose is the whole nonlinear inverse black box into every step of controllable process as far as possible,getting an inversion solution we want.Use only three discrete frequencies,each frequency iterative ten times,we make surface seismic acoustic wave full waveform inversion on extended Marmousi and get a high resolution and high precision imaging of velocity.This gives a good foundation for full waveform inversion on real field data.
引文
[1]杨文采.地球物理反演的理论与方法[M].北京:地质出版社,1997. Yang W C.Theory and Methods in Geophysical Inversion(in Chinese)[M].Beijing:Geological Publishing House,1997.
[2]Pratt R G,Worthington M H.Inverse theory applied to multisource cross-hole tomography.PartⅠ:Acoustic waveequation method[J].Geophys.Prosp.,1990,38(3):287- 310.
[3]Tarantola A.Inversion of seismic reflection data in the acoustic approximation[J].Geophysics,1984,49(8):1259- 1266.
[4]Claerbout J F.Toward a unified theory of reflector mapping [J].Geophysics,1971,36(3):467-481.
[5]Claerbout J F.Fundamentals of Geophysical Data Processing [M].McGraw-Hill Book Co.,1976.
[6]Gauthier O.Virieux J,Tarantola A.Two-dimensional nonlinear inversion of seismic waveforms:Numerical results [J].Geophysics,1986,51(7):1387-1403.
[7]Zhou C X,Cai W Y,Luo Y,et al.Acoustic wave-equation traveltime and waveform inversion of crosshole seismic data [J].Geophysics,1995,60(3):765-773.
[8]Pratt R G,Shin C,Hicks G J.Gauss-Newton and full Newton methods in frequency-space seismic waveform inversion[J]. Geophys.J.Int.,1998,133(2):341-362.
[9]Pratt R G.Seismic waveform inversion in the frequency domain,Part 1:Theory and verification in a physical scale model[J].Geophysics,1999a,64(3):888-901.
[10]Pratt R G,Shipp R M.Seismic waveform inversion in the frequency domain,Part 2:Fault delineation in sediments using crosshole data[J].Geophysics,1999b,64(3):902- 914.
[11]Sirgue L,Pratt R G.Efficient waveform inversion and imaging:A strategy for selecting temporal frequencies[J]. Geophysics,2004,69(1):231-248.
[12]Mora P.Nonlinear two-dimensional elastic inversion of multioffset seismic data[J].Geophysics,1987,52(9):1211 -1228.
[13]Vigh D,Starr E W.Comparisons for waveform inversion, time domain or frequency domain? SEG Expanded Abstract, 2008,27:1890-1894.
[14]许琨,王妙月.声波方程频率域有限元参数反演[J].地球物理学报,2001,44(6):852-864.Xu K,Wang M Y.Finite element inversion of the coefficients of acoustic equation in frequency domain[J].Chinese J. Geophys.(in Chinese),2001,44(6):852-864.
[15]许琨,王妙月.利用地质规则块体建模方法的频率域有限元弹性波速度反演[J].地球物理学报,2004,47(4):708- 717. Xu K,Wang M Y.Frequency-domain finite-element inversion of elastic-wave velocity using the geological regularblocky -model method[J].Chinese J.Geophys.(in Chinese), 2004,47(4):708-717.
[16]吴永栓,曹辉,陈国金,等.井间地震波形反演与应用[J].勘探地球物理进展,2006,29(5):337-340 Wu Y S,Cao H,Chen G J,et al.Crosswell seismic waveform inversion and its application[J].Progress in Exploration Geophysics(in Chinese),2006,29(5):337- 340.
[17]曹辉,陈国金,郭建,等.频率域2.5-D井间波形层析成像及其实际应用[J].地球物理学报,2008,51(3):91 5-923. Cao H,Chen G J,Guo J,et al.The 2.5-D cross-well waveform tomography in the frequent domain and its practical application[J].Chinese J.Geophys.(in Chinese),2008,51 (3):915-923.
[18]张荣忠,袁诚.地震波形反演技术的应用[J].天然气工业, 2009,29(2):52-54. Zhang R Z,Yuan C.Application of the seismic waveform inversion technique[J].Natural Gas Industry,2009,29(2): 52-54.
[19]龙桂华,李小凡,张美根,等.频率域粘弹性声波透射波形速度反演[J].地震学报,2009,31(1):32-41. Long G H,Li X F,Zhang M G,et al.Visco-acoustic transmission waveform inversion for velocity structure in space-frequency domain[J].Acta Seismologica Sinica(in Chinese),2009,31(1):32-41.
[20]卞爱飞,於文辉,周华伟.频率域全波形反演方法研究进展[J].地球物理学进展,2010,25(3):982-993. Bian A F,Yu W H,Zhou H W.Progress in the frequencydomain full waveform inversion method[J].Progress in Geophys.(in Chinese),2010,25(3):982-993.
[21]Jo C H,Shin C,Suh J H.An optimal 9-point,finitedifference, frequency-space,2-D scalar wave extrapolator [J].Geophysics,1996,61(2):529-537
[22]廖建平,刘和秀,王华忠,等.快速高精度的频率空间域声波数值模拟方法研究[J].地球物理学进展,2011,26(4): 1359-1363. Liao J P,Liu H X,Wang H Z,et al.Study on rapid highly accurate acoustic wave numerical simulation in frequency space domain[J].Progress in Geophys.(in Chinese),2011, 26(4):1359-1363.
[23]Versteeg R.The Marmousi experience:Velocity model determination on a synthetic complex data set[J].The Leading Edge,1994,13(9):927-936.
[24]Stockwell J W Jr,Cohen J K.The New SU User's Manual (Version 4.0).2008.
[25]George A,Liu J W H.Computer Solution of Large Sparse Positive Definite Systems.New York:Prentice Hall,1981.
[2]Pratt R G,Worthington M H.Inverse theory applied to multisource cross-hole tomography.PartⅠ:Acoustic waveequation method[J].Geophys.Prosp.,1990,38(3):287- 310.
[3]Tarantola A.Inversion of seismic reflection data in the acoustic approximation[J].Geophysics,1984,49(8):1259- 1266.
[4]Claerbout J F.Toward a unified theory of reflector mapping [J].Geophysics,1971,36(3):467-481.
[5]Claerbout J F.Fundamentals of Geophysical Data Processing [M].McGraw-Hill Book Co.,1976.
[6]Gauthier O.Virieux J,Tarantola A.Two-dimensional nonlinear inversion of seismic waveforms:Numerical results [J].Geophysics,1986,51(7):1387-1403.
[7]Zhou C X,Cai W Y,Luo Y,et al.Acoustic wave-equation traveltime and waveform inversion of crosshole seismic data [J].Geophysics,1995,60(3):765-773.
[8]Pratt R G,Shin C,Hicks G J.Gauss-Newton and full Newton methods in frequency-space seismic waveform inversion[J]. Geophys.J.Int.,1998,133(2):341-362.
[9]Pratt R G.Seismic waveform inversion in the frequency domain,Part 1:Theory and verification in a physical scale model[J].Geophysics,1999a,64(3):888-901.
[10]Pratt R G,Shipp R M.Seismic waveform inversion in the frequency domain,Part 2:Fault delineation in sediments using crosshole data[J].Geophysics,1999b,64(3):902- 914.
[11]Sirgue L,Pratt R G.Efficient waveform inversion and imaging:A strategy for selecting temporal frequencies[J]. Geophysics,2004,69(1):231-248.
[12]Mora P.Nonlinear two-dimensional elastic inversion of multioffset seismic data[J].Geophysics,1987,52(9):1211 -1228.
[13]Vigh D,Starr E W.Comparisons for waveform inversion, time domain or frequency domain? SEG Expanded Abstract, 2008,27:1890-1894.
[14]许琨,王妙月.声波方程频率域有限元参数反演[J].地球物理学报,2001,44(6):852-864.Xu K,Wang M Y.Finite element inversion of the coefficients of acoustic equation in frequency domain[J].Chinese J. Geophys.(in Chinese),2001,44(6):852-864.
[15]许琨,王妙月.利用地质规则块体建模方法的频率域有限元弹性波速度反演[J].地球物理学报,2004,47(4):708- 717. Xu K,Wang M Y.Frequency-domain finite-element inversion of elastic-wave velocity using the geological regularblocky -model method[J].Chinese J.Geophys.(in Chinese), 2004,47(4):708-717.
[16]吴永栓,曹辉,陈国金,等.井间地震波形反演与应用[J].勘探地球物理进展,2006,29(5):337-340 Wu Y S,Cao H,Chen G J,et al.Crosswell seismic waveform inversion and its application[J].Progress in Exploration Geophysics(in Chinese),2006,29(5):337- 340.
[17]曹辉,陈国金,郭建,等.频率域2.5-D井间波形层析成像及其实际应用[J].地球物理学报,2008,51(3):91 5-923. Cao H,Chen G J,Guo J,et al.The 2.5-D cross-well waveform tomography in the frequent domain and its practical application[J].Chinese J.Geophys.(in Chinese),2008,51 (3):915-923.
[18]张荣忠,袁诚.地震波形反演技术的应用[J].天然气工业, 2009,29(2):52-54. Zhang R Z,Yuan C.Application of the seismic waveform inversion technique[J].Natural Gas Industry,2009,29(2): 52-54.
[19]龙桂华,李小凡,张美根,等.频率域粘弹性声波透射波形速度反演[J].地震学报,2009,31(1):32-41. Long G H,Li X F,Zhang M G,et al.Visco-acoustic transmission waveform inversion for velocity structure in space-frequency domain[J].Acta Seismologica Sinica(in Chinese),2009,31(1):32-41.
[20]卞爱飞,於文辉,周华伟.频率域全波形反演方法研究进展[J].地球物理学进展,2010,25(3):982-993. Bian A F,Yu W H,Zhou H W.Progress in the frequencydomain full waveform inversion method[J].Progress in Geophys.(in Chinese),2010,25(3):982-993.
[21]Jo C H,Shin C,Suh J H.An optimal 9-point,finitedifference, frequency-space,2-D scalar wave extrapolator [J].Geophysics,1996,61(2):529-537
[22]廖建平,刘和秀,王华忠,等.快速高精度的频率空间域声波数值模拟方法研究[J].地球物理学进展,2011,26(4): 1359-1363. Liao J P,Liu H X,Wang H Z,et al.Study on rapid highly accurate acoustic wave numerical simulation in frequency space domain[J].Progress in Geophys.(in Chinese),2011, 26(4):1359-1363.
[23]Versteeg R.The Marmousi experience:Velocity model determination on a synthetic complex data set[J].The Leading Edge,1994,13(9):927-936.
[24]Stockwell J W Jr,Cohen J K.The New SU User's Manual (Version 4.0).2008.
[25]George A,Liu J W H.Computer Solution of Large Sparse Positive Definite Systems.New York:Prentice Hall,1981.
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