Abstract：Stratigraphic imaging, an approximate inversion of the spatial variation of the physical properties of subsurface strata, is of great value for the exploration and development of lithological and unconventional reservoirs. In this paper, a stratigraphic imaging method involving the relative perturbation of wave impedance of the reflector is proposed according to the idea of wave equation migration. On the basis of a smooth subsurface me-dium model featuring accurate kinematic characte-ristics of seismic waves, a linear forward expression of seismic data based on the relative perturbation of wave impedance of the reflector is derived by applying the seismic wave propagation theory. Then, the relative perturbation of wave impedance is obtained through approximate inversion from seismic data according to the linear inversion theory. A method of stratigraphic imaging with seismic data that is based on wave equation migration and takes wave impedance variation as the main target is constructed. During stratigraphic imaging, angle decomposition of the wavefield generates angle-domain common imaging-point gathers for stratigraphic imaging. In contrast, stratigraphic imaging results under an angle-domain average can be obtained quickly when angle decomposition of the wavefield is not performed. When the seismic data are described by the acoustic wave equation, the proposed stratigraphic imaging method can be employed to obtain stratum imaging based on the relative perturbation of acoustic wave impedance. When the seismic data are described by the scalar wave equation, the proposed method can be applied to attain stratum imaging based on relative velocity perturbation. Compared with the reverse time migration method based on seismic data, the proposed stratigraphic imaging method has the same calculation process and a comparable amount of calculation. This method also achieves a satisfactory stratigraphic imaging effect when it is applied to a test with synthetic seismic data.
陈生昌, 刘亚楠, 李代光. 基于波动方程偏移的地震数据地层成像[J]. 石油地球物理勘探, 2022, 57(5): 1105-1113.
CHEN Shengchang, LIU Yanan, LI Daiguang. Stratigraphic imaging with seismic data based on wave equation migration. Oil Geophysical Prospecting, 2022, 57(5): 1105-1113.
LAVERGNE M. Pseudo-diagraphics de vitesse en offshore profound[J]. Geophysical Prospecting,1975,23(4):695-711.
[2]
LINDSETH R O. Synthetic sonic logs:a process for stratigraphic interpretation[J]. Geophysics,1979,44(1):3-26.
[3]
COOKE D A,SCHNEIDER W A. Generalized linear inversion of reflection seismic data[J]. Geophysics,1983,48(6):665-676.
[4]
OLDENBURG D W,SCHEUER T,LEVY S. Reco-very of the acoustic impedance from reflection seismograms[J]. Geophysics,1983,48(10):1318-1337.
[5]
伊小蝶,吴帮玉,孟德林,等. 数据增广和主动学习在波阻抗反演中的应用[J]. 石油地球物理勘探,2021,56(4):707-715.YI Xiaodie,WU Bangyu,MENG Delin,et al. Application of data augmentation and active learning to seismic wave impedance inversion[J]. Oil Geophysical Prospecting,2021,56(4):707-715.
[6]
王泽峰,许辉群,杨梦琼,等. 应用时域卷积神经网络的地震波阻抗反演方法[J]. 石油地球物理勘探,2022,57(2):279-286,296.WANG Zefeng,XU Huiqun,YANG Mengqiong,et al. Seismic impedance inversion method based on temporal convolutional neural network[J]. Oil Geophysical Prospecting,2022,57(2):279-286,296.
[7]
CONNOLLY P. Elastic impedance[J]. The Leading Edge,1999,18(4):438-452.
[8]
WHITECOMBE D N. Elastic impedance normalization[J]. Geophysics,2002,67(1):60-62.
[9]
LU J,YANG Z,WANG Y,et al. Joint PP and PS AVA seismic inversion using exact Zoeppritz equations[J]. Geophysics,2015,80(5):R239-R250.
[10]
宗兆云,印兴耀,张峰,等. 杨氏模量和泊松比反射系数近似方程及叠前地震反演[J]. 地球物理学报,2012,55(11):3786-3794.ZONG Zhaoyun,YIN Xingyao,ZHANG Feng,et al. Reflection coefficient equation and pre-stack seismic inversion with Young’s modulus and Poisson ratio[J]. Chinese Journal of Geophysics,2012,55(11):3786-3794.
[11]
ZONG Z Y,YIN X Y,WU G C. Elastic impedance parameteriztion and inversion with Yong’s modulus and Poisson’s ratio[J]. Geophysics,2013,78(6):N35-N42.
[12]
周林,廖建平,李景叶,等. 基于精确Zoeppritz方程的储层含油气性预测方法[J]. 地球物理学报,2021,64(10):3788-3806.ZHOU Lin,LIAO Jianping,LI Jingye,et al. Prediction method of reservoir oil-gas potential based on exact Zoeppritz equations[J]. Chinese Journal of Geo-physics,2021,64(10):3788-3806.
[13]
宋磊,印兴耀,宗兆云,等. 基于先验约束的深度学习地震波阻抗反演方法[J]. 石油地球物理勘探,2021,56(4):716-727.SONG Lei,YIN Xingyao,ZONG Zhaoyun,et al. Deep learning seismic impedance inversion based on prior constraints[J]. Oil Geophysical Prospecting,2021,56(4):716-727.
[14]
TARANTOLA A. Inversion of seismic reflection data in the acoustic approximation[J]. Geophysics,1984,49(8):1259-1266.
[15]
TARANTOLA A. A strategy for nonlinear inversion of seismic reflection data[J]. Geophysics,1986,51(4):1893-1903.
[16]
VIRIEUX J,OPERTO S. An overview of full-waveform inversion in exploration geophysics[J]. Geophysics,2009,74(6):WCC1-WCC26.
[17]
AKI K,RICHARDS P G. Quantitative Seismology(2nd Edition)[M]. University Science Books,Sau-salito,2002.
[18]
SIRGUE L. The importance of low frequency and large offset in waveform inversion[C]. Extended Abstracts of 68th EAGE Conference & Exhibition，2006，A037.
[19]
BLEISTEIN N,STOCKWELL J W,COHEN J K. Mathematics of Multidimensional Seismic Imaging,Migration,and Inversion[M]. Springer,New York, 2001.
[20]
陈生昌,周华敏. 再论地震数据偏移成像[J]. 地球物理学报,2016,59(2):643-654.CHEN Shengchang,ZHOU Huamin. Re-exploration to migration of seismic data[J]. Chinese Journal of Geophysics,2016,59(2):643-654.
[21]
ZHANG Y,RATCLIFFE A,DUAN L,et al. Velocity and impedance inversion based on true amplitude reverse time migration[C]. SEG Technical Program Expanded Abstracts,2013,32:949-953.
[22]
DUAN L,PENG L Z,ZHANG Y. Band-limited impedance perturbation inversion using cross-correlative least-squares RTM[C]. SEG Technical Program Expanded Abstracts,2014,33:3720-3725.
[23]
BLEISTEIN N,ZHANG Y,XU S,et al. Migration/inversion:think image point coordinates,process in acquisition surface coordinates[J]. Inverse Problem,2005,21(5):1715-1744.
[24]
陈生昌,周华敏. 基于反射波动方程的叠前地震反射数据波阻抗相对变化成像研究[J]. 石油物探,2017,56(5):651-657.CHEN Shengchang,ZHOU Huamin. A relative impedance variation imaging of pre-stack seismic reflection data based on reflection wave equation[J]. Geophysical Prospecting for Petroleum,2017,56(5):651-657.
[25]
陈生昌. 基于反射波动方程的地震反射数据波形成像[J]. 石油地球物理勘探,2018,53(3):487-501.CHEN Shengchang. Waveform imaging of seismic reflection data based on reflection wave equation[J]. Oil Geophysical Prospecting,2018,53(3):487-501.
[26]
陈生昌. 用于地震反射数据偏移的反射波方程[J]. 石油物探,2019,58(3):433-443.CHEN Shengchang. Reflection wave equations for the migration of seismic reflected data[J]. Geophysical Prospecting for Petroleum,2019,58(3):433-443.
[27]
TARANTOLA A. Inverse Problem Theory and Methods for Model Parameter Estimation[M]. Society for Industrial and Applied Mathematics,Philadelphia,2004.
[28]
STOLT R H,WEGLEIN A B. Seismic Imaging and Inversion:Application of Linear Inverse Theory[M]. Cambridge University Press,New York,2012.
[29]
DEVANEY J. Mathematical Foundations of Imaging,Tomography and Wavefield Inversion[M]. Cambridge University Press,New York,2012.
[30]
SAVA P C,FOMEL S. Angle-domain common-image gathers by wavefield continuation methods[J]. Geophysics,2003,68(3):1065-1074.
[31]
YOON K,MARFURT K J. Reverse-time migration using the Poynting vector[J]. Exploration Geophy-sics,2006,37(1):102-107.
