Seismic scatterring data migration based on scattering wave equation
HU Ziduo1, YONG Xueshan1, LIU Wei1, CHEN Shengchang2, WANG Yanxiang1
1. Northwest Branch, Research Institute of Petroleum Exploration & Development, PetroChina, Lanzhou, Gansu 730020, China; 2. School of Earth Sciences, Zhejiang University, Hangzhou, Zhejiang 310027, China
Abstract：Present reverse time migration methods don’t distinguish scattering data from reflection data,and the imaging formula is established with the concept of reflected wave propagation.In this study,starting from the perturbation form of wave equation,we defined the scatterer generating scattering wave and the reflector generating reflected wave according to the relationship between the size of a underground heterogeneous body and the wavelength of seismic wave,and formulated a linear forward equation of primary scattering data,then derived the formula of calculating seismic reverse time migration on the spatial scattering location by the linear inverse theory,and finally tested the method on Sigbee2A model data.Theory and numerical test have demonstrated that the scattering data migration method can provide migration results with more correct phase and higher resolution than those from the conventional reverse time migration method based on the concept of reflection.
Gray S,Etgen J,Dellinger J,et al.Seismic migration problems and solutions[J].Geophysics,2001,66(5):1622-1640.
[2]
Yilmaz O.Seismic Data Analysis[M].SEG,Tulsa,2001.
[3]
Claerbout J.Toward a unified theory of reflector mapping[J].Geophysics,1971,36(3):467-481.
[4]
Claerbout J.Fundamentals of Geophysical Data Processing[M].McGraw-Hill Book Co Inc,New York,1976.
[5]
Berkhout A.Seismic Migration:Imaging of Acoustic Energy by Wavefield Extrapolation,Part A:Theoretical Aspects(2nd Edition)[M]. Elsevier,Amsterdam,1982.
[6]
Du Q,Zhu Y,Ba J.Polarity reversal correction for elastic reverse time migration[J].Geophysics,2012,77(2):S31-S41.
Zhang Y,Duan L and Xie Y.A stable and practical implementation of least-squares reverse time migration[J].Geophysics,2015,80(1):V23-V31.
[9]
Yao G,Jakubowicz H.Least-squares reverse time migration[C].SEG Technical Program Expanded Abstracts,2012,31:1-5.
[10]
Yao G,Jakubowicz H.Non-linear least-squares reverse time migration[C].SEG Technical Program Expanded Abstracts,2012,31:1-5.
[11]
Dong S,Cai J,Guo M,et al.Least-squares reverse time migration:towards true amplitude imaging and improving the resolution[C].SEG Technical Program Expanded Abstracts,2012,31:1-5.
[12]
Gray S.True-amplitude seismic migration:A comparison of three approaches[J].Geophysics,1997,62(3):926-936.
[13]
郭振波,李振春.最小平方逆时偏移真振幅成像[J].石油地球物理勘探,2014,49(1):113-120.GUO Zhenbo,LI Zhenchun.True amplitude imaging based on least-squares reverse time migration[J].Oil Geophysical Prospecting,2014,49(1):113-120.
[14]
黄建平,孙陨松,李振春,等.一种基于分频编码的最小二乘裂步偏移方法[J].石油地球物理勘探,2014,49(4):702-707.HUANG Jianping,SUN Yunsong,LI Zhenchun,et al.Least-squares split step migration based on frequency division encoding[J].Oil Geophysical Prospecting,2014,49(4):702-709.
[15]
周华敏,陈生昌,任浩然,等.基于照明补偿的单程波最小二乘偏移[J].地球物理学报,2014,57(8):2644-2655.ZHOU Huamin,CHEN Shengchang,REN Haoran,et al.One way wave equation least squares migration based on illumination compensation[J].Chinese Journal of Geophysics,2014,57(8):2644-2655.
[16]
Zhang Y,Ratcliffe A,Duan L.Velocity and impedance inversion based on true amplitude reverse time migration[C].SEG Technical Program Expanded Abstracts,2013,32:949-953.
[17]
Duan L,Zhang Y and Peng L.Band-limited impedance perturbation inversion using cross-correlative least-squares RTM[C].SEG Technical Program Expanded Abstracts,2014,33:3720-3725.
[18]
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.
[19]
段沛然,谷丙洛,李振春.基于优化算子边界存储策略的高效逆时偏移方法[J].石油地球物理勘探,2019,54(1):93-101.DUAN Peiran,GU Bingluo,LI Zhenchun.An efficient reverse time migration in the vertical time domain based on optimal operator boundary storage strategy[J].Oil Geophysical Prospecting,2019,54(1):93-101.
[20]
李闯,黄建平,李振春,等.基于混合随机共轭梯度的最小二乘逆时偏移[J].石油地球物理勘探,2018,53(6):1188-1197.LI Chuang,HUANG Jianping,LI Zhenchun,et al.Least-squares reverse time migration with a hybrid stochastic conjugate gradient[J].Oil Geophysical Prospecting,2018,53(6):1188-1197.
[21]
陈可洋,王建民,关昕,等.逆时偏移技术在VSP数据成像中的应用[J].石油地球物理勘探,2018,53(增刊1):89-93.CHEN Keyang,WANG Jianmin,GUAN Xin,et al.VSP data imaging with reverse time migration[J].Oil Geophysical Prospecting,2018,53(S1):89-93.
[22]
Leveille J,Jones I,Zhou Z,et al.Subsalt imaging for exploration,production,and development:A review[J].Geophysics,2011,76(5):WB3-WB20.
[23]
Schuster G.Seismic Inversion[M].SEG,Tulsa,2017.
[24]
马在田.地震成像技术——有限差分偏移[M].北京:石油工业出版社,1989.
[25]
Robein E.Seismic Imaging:A Review of the Tech-niques,Their Principles,Merits and Limitations[M].EAGE,Houten,2010.
[26]
Stolt R,Benson A.Seismic Migration:Theory and Practice[M].Geophysical Press,London,1986.
[27]
Beylkin G.Imaging of discontinuities in the inverse scattering problem by the inversion of a causal Radon transform[J].Journal of Mathematics Physics,1985,26(1):99-108.
[28]
Bleistein N.On the imaging of reflectors in the earth[J].Geophysics,1987,52(7):931-942.
[29]
Bleistein N,Cohen J,Stockwell J.Mathematics of Multidimensional Seismic Imaging,Migration,and Inversion[M].Springer,New York,2001.
[30]
李振春等编著.地震叠前成像理论与方法[M].山东东营:中国石油大学出版社,2011.
[31]
李振春.地震偏移成像技术研究现状与发展趋势[J].石油地球物理勘探,2014,49(1):1-21.LI Zhenchun.Research status and development trends for seismic migration technology[J].Oil Geophysical Prospecting,2014,49(1):1-21.
[32]
Aki K,Richards P.Quantitative Seismology(2nd edition)[M].University Science Books,Sausalito,2002.
[33]
Devaney A.Mathematical Foundations of Imaging,Tomography and Wavefield Inversion[M].Cambridge University Press,New York,2012.
[34]
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.
