波动方程保幅叠前深度偏移与AVO响应
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摘要
从全声波方程出发,基于严格的解耦理论进行单程波保幅分解,得到直观、高效率的直接面对地震波传播波场的压力分量进行延拓的单程波动方程;按照叠前深度偏移方法中的波场双重向下延拓理论实现共炮域公式到CMP(共中心点)域公式的转换,推导出由双平方根方程定义的保幅单程波动方程,从而将振幅误差补偿作为偏移的一部分在偏移过程中实现,使得地震成像在给出正确位置的同时也给出真实振幅。在此基础上获得的CRP(共反射点)道集在保证真实振幅的前提下,有效解决了绕射波干涉、反射点弥散、与倾角有关的NMO等问题,使AVO响应更加清晰,提高了AVO资料的分析精度。
The high efficient and direct-viewing one-way wave equation,which was started from full acoustic wave equation,was derived by using one-way wave s preserved-amplitude decomposition based on strict decoupling theory.This kind of one-way wave equation is to do continuation for pressure components of seismic wavefield directly.The formula transformation from common-shot domain to common midpoint(CMP) domain was achieved according to the theory of wavefield double downward continuation in prestack depth migration.Then the preserved-amplitude one-way wave equation defined by double-square-root equation was derived.So the amplitude error compensation as one part of migration can be realized during migration period.Furthermore,this method has a special function that can give true amplitudes as well as the correct locations at the same time.Under the condition of preserving true amplitudes,the common reflection point(CRP) gathers based on this method efficiently solve diffracted wave interference,reflection point dispersion and NMO problem connected with angle of dip.This method makes AVO response clearer and improves the precision of AVO analysis.
The high efficient and direct-viewing one-way wave equation,which was started from full acoustic wave equation,was derived by using one-way wave s preserved-amplitude decomposition based on strict decoupling theory.This kind of one-way wave equation is to do continuation for pressure components of seismic wavefield directly.The formula transformation from common-shot domain to common midpoint(CMP) domain was achieved according to the theory of wavefield double downward continuation in prestack depth migration.Then the preserved-amplitude one-way wave equation defined by double-square-root equation was derived.So the amplitude error compensation as one part of migration can be realized during migration period.Furthermore,this method has a special function that can give true amplitudes as well as the correct locations at the same time.Under the condition of preserving true amplitudes,the common reflection point(CRP) gathers based on this method efficiently solve diffracted wave interference,reflection point dispersion and NMO problem connected with angle of dip.This method makes AVO response clearer and improves the precision of AVO analysis.
引文
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[4]董渊,杨慧珠,杜启振.有限元-有限差分法二维波动逆时偏移初探[J].石油大学学报:自然科学版,2003,27(6):25-29.DONG Yuan,YANG Hui-zhu,DU Qi-zhen.Study onreverse-time migration of two-dimensional wave equa-tion with element-finite difference method[J].Journalof the University of Petroleum,China(Edition of Nat-ural Science),2003,27(6):25-29.
[5]陈天胜,刘洋,魏修成.纵波和转换波联合AVO反演方法研究[J].中国石油大学学报:自然科学版,2006,30(1):33-37.CHEN Tian-sheng,LIU Yang,WEI Xiu-cheng.Jointamplitude verse offset inversion of P-P and P-SV seis-mic data[J].Journal of China University of Petroleum(Edition of Natural Science),2006,30(1):33-37.
[6]陈建江,印兴耀,张广智.基于贝叶斯理论的振幅随炮检距变化三参数同步反演[J].中国石油大学学报:自然科学版,2007,31(3):33-38.CHEN Jian-jiang,YIN Ying-yao,ZHANG Guang-zhi.Simultaneous three-term AVO inversion based onBayesian theorem[J].Journal of China University ofPetroleum(Edition of Natural Science),2007,31(1):33-38.
[7]张关泉.波动方程的上行波和下行波的耦合方程组[J].应用数学学报,1993,16(2):251-263.ZHANG Guan-quan.System of coupled equations fordowngoing and upcoming waves[J].Acta Math ApplSinica(in Chinese),1993,16(2):251-263.
[8]GRAY S.The Marmousi2 model elastic synthetic dataand an analysis of imaging and AVO structurally com-plex environment[D].Houston:University of Hous-ton,2004.
[2]RISTOW D,RUHL T.Fourier finite-difference mi-gration[J].Geophysics,1994,59(12):1882-1893.
[3]李振春,张建磊,王延光,等.基于共聚焦点道集的叠前深度偏移及其应用[J].石油大学学报:自然科学版,2003,27(4):27-31.LI Zhen-chun,ZHANG Jian-lei,WANG Yan-guang,et al.Prestack depth migration based on common fo-cus point gather and its application[J].Journal of theUniversity of Petroleum,China(Edition of NaturalScience),2003,27(4):27-31.
[4]董渊,杨慧珠,杜启振.有限元-有限差分法二维波动逆时偏移初探[J].石油大学学报:自然科学版,2003,27(6):25-29.DONG Yuan,YANG Hui-zhu,DU Qi-zhen.Study onreverse-time migration of two-dimensional wave equa-tion with element-finite difference method[J].Journalof the University of Petroleum,China(Edition of Nat-ural Science),2003,27(6):25-29.
[5]陈天胜,刘洋,魏修成.纵波和转换波联合AVO反演方法研究[J].中国石油大学学报:自然科学版,2006,30(1):33-37.CHEN Tian-sheng,LIU Yang,WEI Xiu-cheng.Jointamplitude verse offset inversion of P-P and P-SV seis-mic data[J].Journal of China University of Petroleum(Edition of Natural Science),2006,30(1):33-37.
[6]陈建江,印兴耀,张广智.基于贝叶斯理论的振幅随炮检距变化三参数同步反演[J].中国石油大学学报:自然科学版,2007,31(3):33-38.CHEN Jian-jiang,YIN Ying-yao,ZHANG Guang-zhi.Simultaneous three-term AVO inversion based onBayesian theorem[J].Journal of China University ofPetroleum(Edition of Natural Science),2007,31(1):33-38.
[7]张关泉.波动方程的上行波和下行波的耦合方程组[J].应用数学学报,1993,16(2):251-263.ZHANG Guan-quan.System of coupled equations fordowngoing and upcoming waves[J].Acta Math ApplSinica(in Chinese),1993,16(2):251-263.
[8]GRAY S.The Marmousi2 model elastic synthetic dataand an analysis of imaging and AVO structurally com-plex environment[D].Houston:University of Hous-ton,2004.
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