黏声波介质傅里叶有限差分法正演模拟
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摘要
大地吸收效应主要由地球介质本身的黏滞性所致,黏滞性会影响波场的所有频率成分,且对高频成分的影响更大,从而导致地震垂向分辨率的降低。本文将完全弹性介质中的傅里叶有限差分法推广到黏声波介质的正演领域,该法是一种频率域的单程波方法,较双程波法具有计算效率上的优势,较时间域法更容易模拟衰减和频散效应。文中对Marmousi模型进行了黏声波介质的正演模拟,数值算例表明:①黏声波介质和完全弹性介质的振幅和相位特征只有在传播时间短且距炮点近的部位才较吻合,表明黏滞吸收作用对地震波波形、频带以及振幅等产生很大影响;②随着传播距离(时间)的增加,波场的高频成分明显衰减,波形逐渐变宽,能量逐渐变弱。文中方法适应强空间变速介质的正演模拟,且具有较高的计算效率,为深入研究大地吸收效应进而提高地震分辨率奠定了基础。
Earth absorption effect mainly resulted from the viscosity of earth media itself,which can affect all frequency components of wavefield,especially for high-frequency elements,leading vertical resolution of seismic data to reduce.The paper popularizes the Fourier finite-difference method in full-elastic media to the forward field in viso-acoustic media,which is one-way wave method in frequency domain and has superiority in computational efficiency if comparison with two-way wave method,and is easier simulation of attenuation and dispersion effects than in time domain.The paper carried out forward modeling for Marmousi model in visco-acoustic media,and the numeric case showed:①the consistency of feature of amplitude and phase between the viso-acoustic media and full-elastic media is only in the part of short travel time and near shot points at the same time,showing absorption effect by viscosity has large influence on waveform,frequency band and amplitude of seismic wave;②along with increasing of the travel distance(time),the high-frequency components in wavefield show clear attenuation,the waveform is gradually widening and the energy is gradually weakening.The method presented in the paper is suitable for forward simulation in large velocity-changed media in space,and has higher computational efficiency,laying the foundation for deep study of earth absorption effect and further improvement of seismic resolution.
Earth absorption effect mainly resulted from the viscosity of earth media itself,which can affect all frequency components of wavefield,especially for high-frequency elements,leading vertical resolution of seismic data to reduce.The paper popularizes the Fourier finite-difference method in full-elastic media to the forward field in viso-acoustic media,which is one-way wave method in frequency domain and has superiority in computational efficiency if comparison with two-way wave method,and is easier simulation of attenuation and dispersion effects than in time domain.The paper carried out forward modeling for Marmousi model in visco-acoustic media,and the numeric case showed:①the consistency of feature of amplitude and phase between the viso-acoustic media and full-elastic media is only in the part of short travel time and near shot points at the same time,showing absorption effect by viscosity has large influence on waveform,frequency band and amplitude of seismic wave;②along with increasing of the travel distance(time),the high-frequency components in wavefield show clear attenuation,the waveform is gradually widening and the energy is gradually weakening.The method presented in the paper is suitable for forward simulation in large velocity-changed media in space,and has higher computational efficiency,laying the foundation for deep study of earth absorption effect and further improvement of seismic resolution.
引文
[1]安艺敬一等著,李钦祖等译.定量地震学:理论与方法(第1卷).北京:地震出版社,1986
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[6]Varela C L et al.Modeling of attenuation and disper-sion.Geophysics,1993,58(8):1167～1173
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[9]崔建军等.粘弹性波动方程正演和偏移.中南工业大学学报,2001,32(5):441～444
[10]Ristow D et al.Fourier finite-difference migration.Geophysics,1994,59(12):1882～1893
[11]He Z Het al.Nonzero offset seismic forward model-ing by one-way acoustic wave-equation.Expanded Abstracts of68th SEG Mtg,1998,1921～1924
[12]熊高君等.多次反射可控制的波动方程共炮记录正演模拟.石油地球物理勘探,1998,33(5):585～590
[13]熊高君等.改进的正演模拟定位原理.石油地球物理勘探,1998,33(6):742～748
[14]熊高君等.三维混合延拓一步法波动方程正演模拟.成都理工学院学报,1999,26(1):48～51
[15]张金海等.傅里叶有限差分法三维波动方程正演模拟.地球物理学报,2007,50(6):1854～1862
[16]Stoffa P L et al.Split-step Fourier migration.Geo-physics,1990,55(4):410～421
[17]Wu R S.Wide-angle elastic wave one-way propaga-tionin heterogeneous media and an elastic wave com-plex-screen method.Journal of Geophysics Re-search,1994,99(B1):751～766
[18]罗娣华等.东川地区深井Q值与频率的关系.地球物理学报,2001,44(增刊):170～178
[19]姚振兴等.用于深度域地震剖面衰减与频散补偿的反Q滤波方法.地球物理学报,2003,46(2):229～233
[2]俞寿朋.高分辨率地震勘探.北京:石油工业出版社,1993
[3]李庆忠.走向精确勘探的道路.北京:石油工业出版社,1994
[4]凌云等.时频空间域球面发散与吸收补偿.石油地球物理勘探,2005,40(2):176～182,189
[5]赵连锋.井间地震波速与衰减联合层析成像方法研究[博士论文].成都:成都理工大学,2003
[6]Varela C L et al.Modeling of attenuation and disper-sion.Geophysics,1993,58(8):1167～1173
[7]常新伟.衰减与频散的补偿方法.石油地球物理勘探,1996,31(3):442～447
[8]Stolt R H.Migration by Fourier transform.Geophys-ics,1978,43(1):23～48
[9]崔建军等.粘弹性波动方程正演和偏移.中南工业大学学报,2001,32(5):441～444
[10]Ristow D et al.Fourier finite-difference migration.Geophysics,1994,59(12):1882～1893
[11]He Z Het al.Nonzero offset seismic forward model-ing by one-way acoustic wave-equation.Expanded Abstracts of68th SEG Mtg,1998,1921～1924
[12]熊高君等.多次反射可控制的波动方程共炮记录正演模拟.石油地球物理勘探,1998,33(5):585～590
[13]熊高君等.改进的正演模拟定位原理.石油地球物理勘探,1998,33(6):742～748
[14]熊高君等.三维混合延拓一步法波动方程正演模拟.成都理工学院学报,1999,26(1):48～51
[15]张金海等.傅里叶有限差分法三维波动方程正演模拟.地球物理学报,2007,50(6):1854～1862
[16]Stoffa P L et al.Split-step Fourier migration.Geo-physics,1990,55(4):410～421
[17]Wu R S.Wide-angle elastic wave one-way propaga-tionin heterogeneous media and an elastic wave com-plex-screen method.Journal of Geophysics Re-search,1994,99(B1):751～766
[18]罗娣华等.东川地区深井Q值与频率的关系.地球物理学报,2001,44(增刊):170～178
[19]姚振兴等.用于深度域地震剖面衰减与频散补偿的反Q滤波方法.地球物理学报,2003,46(2):229～233
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