Low-rank one-step wave extrapolation for pure qP-wave forward modeling in viscoacoustic anisotropic media
GU Hanming1, ZHANG Kuitao1, LIU Chuncheng2, WANG Jianhua2
1. Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan, Hubei 430074, China; 2. CNOOC Research Institute, Beijing 100028, China
Abstract:Forward modelling and reverse time migration (RTM) of pure quasi-P (qP) waves in anisotropic media have attracted a lot of attentions in recent years. However,the results have serious noises and low resolution because of neglecting the viscosity although considering the anisotropy of the media. The application of the conventional quasi-acoustic equation is limited due to the interference from quasi-shear waves,limitation of model parameters and instability of the simulating process. This paper introduces a one-step wave field continuation method,deduces the expression for viscoelastic media in space-wavenumber domain,and constructs a pure qP wave field continuation operator in space-wavenumber domain for viscoacoustic anisotropic media,and finally realizes the forward modeling of pure qP waves in viscoacoustic anisotropic media based on the Low-Rank decomposition algorithm. The modelling results indicate that:a. the seismic wavefield can simulate the anisotropy and viscosity of underground media,so it is consistent with underground conditions; the Low-Ran method is not limited by the weak points of the quasi-acoustic equation which is interfered by quasi-shear waves,restricted by model parameters and with instable simulating process;c. no numerical aliasing appears when the time step is appropriately increased. By improving computational efficiency while ensuring accuracy,the Low-Ran method is stable and effective in calculation.It provides a theoretical basis for reverse time migration for anisotropic media based on Q compensation.
Chichinina T,Obolentseva I,Gik L,et al.Attenuation anisotropy in the linear-slip model:Interpretation of physical modeling data[J].Geophysics,2009,74(5):WB165-WB176.
[2]
丁亮,刘洋.逆时偏移成像技术研究进展[J].地球物理学进展,2011,26(3):1085-1100.DING Liang,LIU Yang.Progress in reverse time migration imaging[J].Progress in Geophysics,2011,26(3):1085-1100.
[3]
Alkhalifah T.Acoustic approximations for processing in transversely isotropic media[J].Geophysics,1998,63(2):623-631.
[4]
Alkhalifah T.An acoustic wave equation for anisotropic media[J].Geophysics,2000,65(4):1239-1250.
[5]
Du X,Bancroft J C,Lines L R.Reverse-time migration for tilted TI media[C].SEG Technical Program Expanded Abstracts,2005,24:1930-1933.
[6]
Zhou H B,Zhang G Q,Bloor R.An anisotropic acoustic wave qeuation for modeling and migration in 2D TTI media[C].SEG Technical Program Expanded Abstracts,2006,25:194-198.
[7]
Duveneck E,Milcik P,Bakker P M,et al.Acoustic VTI wave equations and their application for anisotrpic reverse-time migration[J].SEG Technical Program Expanded Abstracts,2008,27:2186-2190.
[8]
程玖兵,陈茂根,王腾飞,等.各向异性介质qP波传播描述Ⅱ:分离纯模式标量波[J].地球物理学报,2014,57(10):3389-3401.CHENG Jiubing,CHEN Maogen,WANG Tengfei,et al.Description of qP-wave propagation in anisotropic media,Part Ⅱ:Separation of pure-mode scalar waves[J].Chinese Journal of Geophysics,2014,57(10):3389-3410.
[9]
程玖兵,康玮,王腾飞.各向异性介质qP波传播描述Ⅰ:伪纯模式波动方程[J].地球物理学报,2013,56(10):3474-3486.CHENG Jiubing,KANG Wei,WANG Tengfei.Description of qP-wave propagation in anisotropic media,Part Ⅰ:Pseudo-pure-mode scalar wave equa-tions[J].Chinese Journal of Geophysics,2013,56(10):3474-3486.
[10]
Zhang Y,Zhang P,Zhang H Z.Compensating for visco-acoustic effects in reverse-time migration[C].SEG Technical Program Expanded Abstracts,2010,29:3160-3164.
[11]
Suh S,Yoon K,Cai J,et al.Compensating visco-acoustic effects in anisotropic resverse-time migration[C].SEG Technical Program Expanded Abstracts,2012,31:1-5.
[12]
Xu W C,Li Z C,Deng W Z,et al.Anisotropic visco-acoustic wave RTM based on second-order quasi-differential equation[C].SEG Technical Program Expanded Abstracts,2015,34:4013-4017.
[13]
李金丽,刘建勋,姜春香,等.黏声VTI介质正演模拟与照明分析[J].石油地球物理勘探,2017,52(5):906-914.LI Jinli,LIU Jianxun,JIANG Chunxiang,et al.Forward modeling and illumination analysis in visco-acoustic VTI media[J].Oil Geophysical Prospecting,2017,52(5):906-914.
[14]
Duveneck E,Bakker P M.Stable P-wave modeling for reverse-time migration in tilted TI media[J].Geophysics,2011,76(2):S65-S75.
[15]
Grechka V,Zhang L B,Rector J W.Shear waves in a-coustic anisotropic media[J].Geophysics,2004,69(2):576-582.
[16]
郭成锋,杜启振,张明强,等.改进的TTI介质纯P波方程正演模拟与逆时偏移[J].地球物理学报,2017,60(1):258-270.GUO Chengfeng,DU Qizhen,ZHANG Mingqiang,et al.Numerical simulation and reverse time migration using an improved pure P wave equation in tilted transversely isotropic media[J].Chinese Journal of Geophysics,2017,60(1):258-270.
[17]
Zhang Y,Zhang H Z,Zhang G Q.A stable TTI re-verse time migration and its implementation[J].Geophysics,2011,76(3):WA3-WA11.
[18]
Zhan G,Pestana R C,Stiffa P L.Decoupled equations for reverse time migration in tilted transversely isotropic media[J].Geophysics,2012,77(2):T37-T45.
[19]
Xu S,Tang B,Mu J,et al.Quasi-P wave propagation with an elliptic differential operator[C].SEG Technical Program Expanded Abstracts,2015,34:4380-4384.
[20]
杨鹏,李振春,谷丙洛.一种TI介质纯qP波正演方法及其在逆时偏移中的应用[J].地球物理学报,2017,60(11):4447-4467.YANG Peng,LI Zhenchun,GU Bingluo.Pure quasi-P wave forward modeling method in TI media and its application to RTM[J].Chinese Journal of Geophy-sics,2017,60(11):4447-4467.
张庆朝,朱国维,周俊杰,等.TTI介质qP波伪谱法正演模拟[J].石油地球物理勘探,2019,54(2):302-311.ZHANG Qingchao,ZHU Guowei,ZHOU Junjie,et al.qP-wave numerical simulation in TTI media with pseudo-spectral method[J].Oil Geophysical Prospecting, 2019,54(2):302-311.
[23]
Du X,Fowler P J,Fletcher R P.Recursive integral time extrapolation methods for waves:A comparative review[J].Geophysics,2014,79(1):T9-T26.
[24]
Fomel S,Ying L X,Song X L.Seismic wave extrapolation using lowrank symbol approximation[J].Geophysical Prospecting,2012,61(3):526-536.
[25]
Song X L,Alkhalifah T.Modeling of pseudoacoustic P-waves in orthorhombic media with a low-rank approximation[J].Geophysics,2013,78(4):C33-C40.
[26]
Fang G,Fomel S,Du Q Z,et al.Lowrank seismic-wave extrapolation on a staggered grid[J].Geophy-sics,2014,79(3):T157-T168.
[27]
Sun J Z,Fomel S,Ying L X.Low-rank one-step wave extrapolation for reverse time migration[J].Geophy-sics,2015,81(1):S39-S54.
[28]
黄金强,李振春,江文.TTI介质Low-rank有限差分法高效正演模拟及逆时偏移[J].石油地球物理勘探,2018,53(6):1198-1209.HUANG Jinqiang,LI Zhenchun,JIANG Wen.An efficient forward modeling with the Low-rank finite-difference algorithm for complex TTI media and its application in inverse time migration[J].Oil Geophy-sical Prospecting,2018,52(5):915-927.
[29]
黄金强,李振春.基于Low-rank分解的复杂TI介质纯qP波正演模拟与逆时偏移[J].地球物理学报,2017,60(2):704-721.HUANG Jinqiang,LI Zhenchun.Modeling and reverse time migration of pure quasi-P-waves in complex TI media with a Low-rank decomposition[J].Chinese Journal of Geophysics,2017,60(2):704-721.
[30]
袁雨欣,胡婷,王之洋,等.求解二阶解耦弹性波方程的低秩分解法和低秩有限差分法[J].地球物理学报,2018,61(8):3324-3333.YUAN Yuxin,HU Ting,WANG Zhiyang,et al.Solving second-order decoupled elastic wave equations using low-rank decomposition method and low-rank finite differences[J].Chinese Journal of Geophysics,2018,61(8):3324-3333.
[31]
Zhang Y,Zhang G Q.One-step extrapolation method for reverse time migration[J].Geophysics,2009,74(4):A29-A33.
[32]
Wards B D,Margrave G F,Lamoureux M P.Phase-shift time-stepping for reverse-time migration[C].SEG Technical Program Expanded Abstracts,2008,27:2262-2266.
[33]
Fomel S.On anelliptic approximations for qP velocities in VTI media[J].Geophysical Prospecting,2004,52(3):247-259.
[34]
李振春,郭振波,田坤.黏声介质最小平方逆时偏移[J].地球物理学报,2014,57(1):214-228.LI Zhenchun,GUO Zhenbo,TIAN Kun.Least-squares inverse time migration in visco-acoustic media[J].Chinese Journal of Geophysics,2014,57(1):214-228.
[35]
Engquist B,Ying L.A fast directional algorithm for high frequency acoustic scattering in two dimensions[J].Communications in Mathematical Sciences,2009,7(2):327-345.
[36]
李庆忠.走向精确勘探的道路[M].北京:石油工业出版社,1993.LI Qingzhong.Road to Precise Exploration[M].Petroleum Industry Press,Beijing,1993.