精确的频率空间域黏声波有限差分数值模拟
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摘要
在时间空间域,模拟吸收衰减效应时对计算机内存需求大,计算效率不高、非常难以进行模拟吸收衰减;频率空间域通过引入品质因子和复值速度,使用经验物理、数学公式进行数值模拟吸收衰减就容易多了。笔者使用十分节省计算机内存需求的嵌套剖分法,使用Kjartansson模型高效率地进行模拟吸收衰减。数值试验证实吸收衰减影响地震场的所有频率、对高频的影响最为明显,降低了地震记录的质量;频率空间域非常容易模拟吸收衰减效应,为黏声波全波形反演实际地震资料而奠定很好的基础。
Modeling absorption and attenuation in time-space domain requiring a lot of computer memory with low computational efficiency,it is hard to simulate attenuation in time-space domain.We can use an empirical physical or mathematical formulation to simulate absorption and attenuation in frequency-space domain through introducing complex velocity and Q values.We can easily describe attenuation with high efficiency in frequency-space domain using nested dissection and Kjartansson's model.Numerical experiments demonstrate that absorption and attenuation affects all the frequency components of the wavefield and affects a greater impact on the higher frequency components,so it decreases the seismic record's resolution.It is very easy to simulate absorption and attenuation effects in frequency-space domain,providing a good foundation for visco-acoustic wave full waveform inversion on real data.
Modeling absorption and attenuation in time-space domain requiring a lot of computer memory with low computational efficiency,it is hard to simulate attenuation in time-space domain.We can use an empirical physical or mathematical formulation to simulate absorption and attenuation in frequency-space domain through introducing complex velocity and Q values.We can easily describe attenuation with high efficiency in frequency-space domain using nested dissection and Kjartansson's model.Numerical experiments demonstrate that absorption and attenuation affects all the frequency components of the wavefield and affects a greater impact on the higher frequency components,so it decreases the seismic record's resolution.It is very easy to simulate absorption and attenuation effects in frequency-space domain,providing a good foundation for visco-acoustic wave full waveform inversion on real data.
引文
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[6]Kjartansson E.Constant Q-wave propagation and attenuation[J].Journal of Geophysical Research,1979,84:4737-4748.
[7]Churl-Hyun Jo.An optimal 9-point,finite-difference frequency-space 2-D scalar wave extrapolator[J].Geophysics,1996,61(2):529-537.
[8]Pratt R G,Worthington M H.Inverse theory applied to multi-source cross-hole tomography:PartⅠ:Acoustic wave-equationmethod[J].Geophys Prosp,1990,38:287-310.
[9]Gerhard Pratt R.Frequency-domain elastic wave modeling by finitedifferences:A tool for crosshole seismic imaging[J].Geophysics,1990,55(5):625-632.
[10]George A,Liu J W.Computer Solution of Large Sparse PositiveDefinite Systems[M].New York:Prentice Hall,1981.
[11]任浩然,王华忠,龚婷.标量地震波频率—空间域有限差分法数值模拟[J].石油物探,2009,48(1):20-26.
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[13]Clayton R,Engquist B.Absorbing boundary conditions for acousticand elastic wave equations[J].Bull Seis Soc Am,1977,67:1529-1540.
[2]Carcione J M.Wave fields in real media:Wave propagation in an-isotropic,anelastic and porous media[R].Pergamon,Amsterdam,2001.
[3]Ursin.Comparison of seismic dispersion and attenuation models[R].CWP408-References,2002.
[4]谢里夫R E.勘探地震学[M].初英等译.第二版.北京:石油工业出版社,1999.
[5]李庆忠.走向精确勘探的道路[M].北京:石油工业出版社,1994.
[6]Kjartansson E.Constant Q-wave propagation and attenuation[J].Journal of Geophysical Research,1979,84:4737-4748.
[7]Churl-Hyun Jo.An optimal 9-point,finite-difference frequency-space 2-D scalar wave extrapolator[J].Geophysics,1996,61(2):529-537.
[8]Pratt R G,Worthington M H.Inverse theory applied to multi-source cross-hole tomography:PartⅠ:Acoustic wave-equationmethod[J].Geophys Prosp,1990,38:287-310.
[9]Gerhard Pratt R.Frequency-domain elastic wave modeling by finitedifferences:A tool for crosshole seismic imaging[J].Geophysics,1990,55(5):625-632.
[10]George A,Liu J W.Computer Solution of Large Sparse PositiveDefinite Systems[M].New York:Prentice Hall,1981.
[11]任浩然,王华忠,龚婷.标量地震波频率—空间域有限差分法数值模拟[J].石油物探,2009,48(1):20-26.
[12]廖建平.频率空间域地震波数值模拟方法研究[D].上海:同济大学海洋与地球科学学院,2009.
[13]Clayton R,Engquist B.Absorbing boundary conditions for acousticand elastic wave equations[J].Bull Seis Soc Am,1977,67:1529-1540.
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