Past,present and future of seismic migration imaging
Sa Liming1, Yang Wuyang2,3, Du Qizheng4, Wang Chengxiang5, Zhou Hui2, Zhang Houzhu6
1. China National Petroleum Corporation, Beijing 100007, China;
2. China University of Petroleum (Beijing), Beijing 102249, China;
3. Northwest Branch, Research Institute of Petroleum Exploration & Development, PetroChina, Lanzhou 730020, China;
4. China University of Petroleum (East China), Qingdao, Shandong 266580, China;
5. BGP Inc., CNPC, Zhuozhou, Hebei 072750, China;
6. Houston, Texas, USA
Abstract:In this paper, we first give a brief review of the history of seismic imaging. Then we discuss the common used migration approaches such as acoustic migrations on P-wave velocity, elastic migrations on both P- and S-wave velocity, anisotropic migrations on three weak anisotropy parameters, and visco-elastic migration on viscosity parameters. Meanwhile, we look at velocity model building and computer hardware developments which are very important for seismic migration. After that, we state some applications of seismic migration imaging in the aspects of structural interpretation, parameter inversion, amplitude attribute extraction, joint analysis of well logging and seismic attributes, and even seismic acquisition design. Finally we anticipate more magnificent achievements of seismic imaging based on elastic, complex anisotropy and visco-elastic prestack depth migrations in the near future era of cloud computing and massive data.
Bednar J B. A brief history of seismic migration. Geophysics, 2005, 70(3): 3MJ-20MJ.
[2]
Loewenthal D L, Roberson L R and Sherwood J. The wave equation applied to migration. Geophysical Prospecting, 1976,24(2): 380-399.
[3]
Claerbout J F. Coarse grid calculations of waves in inhomogeneous media with application to delineation of complicated seismic structure. Geophysics, 1970, 35(3): 407-418
[4]
Claerbout J F. Toward a unified theory of reflector mapping. Geophysics, 1971, 36(3): 467-481.
[5]
Stolt R H. Migration by Fourier transform. Geo-physics, 1978, 43(1): 23-48.
[6]
Gazdag J. Wave equation migration with the phase-shift method. Geophysics, 1978, 43(7): 1342-1351.
[7]
Schneider W A. Developments in seismic data pro-cessing and analysis. Geophysics, 1971, 36(6):1043-1073.
[8]
French W S. Two-dimensional and three-dimensional migration of model experiment reflection profiles.Geophysics, 1974, 39(3): 265-277.
[9]
French W S. Computer migration of oblique seismic reflection profiles. Geophysics, 1975, 40(6): 961-980.
[10]
Schneider W A. Integral formulation for migration in two and three dimensions. Geophysics, 1978, 43(1):49-76.
[11]
Hubral P. Time migration some theoretical aspects. Geophysical Prospecting, 1977, 25(4): 738-745.
[12]
Larner K L, Hatton L, Gibson B S et al. Depth migration of imaged time sections. Geophysics, 1981, 46(5): 734-750.
[13]
马在田. 高阶方程偏移的分裂算法. 地球物理学报, 1983, 26(4): 377-388.
Ma Zaitian. A splitting-up method for solution of higher-order migration equation by finite-difference scheme. Chinese Journal of Geophysics,1983,26(4):377-388.
Zhang Guanquan. Steep dip finite-difference migration using the system of lower-order partial differential equations. Chinese Journal of Geophysics, 1986, 29(3):273-282.
[15]
McMechan G A. Migration by extrapolation of time-dependent boundary values. Geophysical Prospecting, 1983,31(2):413-420.
[16]
Chang W F and McMechan G A. Elastic reverse-time migration. Geophysics, 1987, 52(10): 1365-1375.
[17]
Chang W F and McMechan G A. 3-D elastic prestack, reverse-time depth migration. Geophysics, 1994, 59(4): 597-409.
[18]
Yan J and Sava P. Isotropic angle-domain elastic reverse-time migration. Geophysics, 2008, 73(6): 229-239.
[19]
Zhang L, Rector J W and Hoversten G M. An acoustic wave equation for modeling in tilted TI media. SEG Technical Program Expanded Abstracts, 2003, 22:153-156.
[20]
Fletcher R P, Du X and Fowler P J. Reverse time migration in tilted transversely isotropic (TTI) media. Geophysics, 2009, 74(6): WCA179-WCA187.
[21]
Zhang Y, Zhang H, Zhang G. A stable TTI reverse time migration and its implementation. Geophysics, 2011, 76(3): WA3-WA11.
[22]
Beylkin G. Imaging of discontinuities in the inverse scattering problem byinversion of a generalized Radon transform. Journal of Mathematical Physics, 1985,26:99-108.
[23]
Bleistein N. On the imaging of reflectors in the earth. Geophysics, 1987, 52(7): 931-942.
[24]
Bleistein N, Cohen J K and Stockwell J W. Mathematics of Multidimensional Seismic Inversion. Sprin-ger, New York, 2001.
[25]
Zhang Y, Zhang G and Bleistein N. True amplitude wave equation migration arising from true amplitude one-way wave equations. Inverse Problem,2003,19(5): 1113.
[26]
Zhang Y, Zhang G and Bleistein N. Theory of true amplitude oneway wave equations and true amplitude common-shot migration. Geophysics, 2005, 70(4): E1-E10.
[27]
Zhang Y, Xu S and Bleistein N et al. Reverse time migration: amplitude and implementation issues. SEG Technical Program Expanded Abstracts, 2007, 26:2145-2149.
[28]
Zhang Y, Xu S and Bleistein N et al. True amplitude angle domain common image gathers from one-way wave equation migrations.Geophysics,2007,72(1):S49-S58.
[29]
Deng F and McMechan G A. True-amplitude pres-tack depth migration. Geophysics, 2007, 72(3): S155-S166.
[30]
Deng F and McMechan G A. Viscoelastic true-amplitude prestack reverse-time depth migration. Geophy-sics, 2008, 73(4):S143-S155.
[31]
Zhang Y and Sun J. Practical issues of reverse time migration: True-amplitude gathers, noise removal and harmonic-source encoding. First Break,2009,27(1):53-60.
[32]
Du Q Z, Fang G and Gong X F. Compensation of transmission losses for true-amplitude reverse time migration. Journal of Applied Geophysics, 2014, 106: 77-86.
[33]
Albertin U, Yingst D and Kitchenside P. True-amplitude beammigration. SEG Technical Program Expanded Abstracts, 2004, 23:398-401.
[34]
Gray S and Bleistein N.True-amplitude Gaussian beam migration. Geophysics, 2009, 74(2): S11-S23.
[35]
Nemeth T, Wu C and Schuster G T. Least-squares migration of incomplete reflection data. Geophysics, 1999, 64(1): 208-221.
[36]
Dai W and Schuster G T. Plane-wave least-squares reverse-time migration. Geophysics, 2013, 78(4): S165-S177.
[37]
Tarantola A. Inversion of seismic reflection data in the acoustic approximation. Geophysics, 1984,49(8): 1259-1266.
[38]
Virieux J and Operto S. An overview of full-waveform inversion in exploration. Geophysics, 2009,74(6): WCC1-WCC26.
[39]
Warne M, Ratcliffe A, Nangoo T et al. Anisotropic 3D full-waveform inversion. Geophysics, 2013,78(2): R59-R80.
Yang Wuyang, Wang Xiwen, Yong Xueshan et al. The review of seismic full waveform inrersion method. Proyress in Geophysics,2013,28(2): 766-776.
[41]
Gardner G H F. Migration of Seismic Data. Society of Exploration Geophysicists, 1985.
[42]
Bale R, Jakubowicz H. Post-stack prestack migra-tion. SEG Technical Program Expanded Abstracts,1987,6:714-717.
[43]
Berryhill J R. Wave-equation datuming. Geophysics, 1979, 44(8): 1329-1344.
[44]
Berkhout A J, Palthe D W W. Migration in the pre-sence of noise. Geophysical Prospecting, 1980,28(3):372-383.
[45]
Cerveny V, Popo M M and Psencik I. Computation of wave fieldsin inhomogeneous media Gaussian beam approach. Geophysical Journal of the Royal Astronomical Society, 1982, 70:109-128.
[46]
Costa C A, Raz S and Kosloff D. Gaussian beam mi-gration. SEG Technical Program Expanded Abstracts, 1989, 8:1169-1171.
[47]
Hill N R.Gaussian beam migration.Geophysics,1990,55(11):1416-1428.
[48]
Ting C and Wang D L. Controlled beam migration applications in Gulf of Mexico. SEG Technical Program Expanded Abstracts, 2008, 27:368-372.
[49]
张关泉. 低阶方程组求解单程波方程的解法,地球物理学报,1983, 29(3):273-282.
Zhang Guanquan. Step dip finite difference migration using lower order partial differential equations. Chinese Journal of Geophysics,1986,29(3):273-1893.
[50]
Loewenthal D and Mufti I R. Reverse time migration in the spatial frequency domain. Geophysics, 1983, 48(5): 627-635.
[51]
Baysal E, Kosloff D D and Sherwood J W C. Reverse time migration. Geophysics, 1983,48(11):1514-1524.
[52]
Kosloff D, Kessler D. Accurate depth migration by a generalized phase-shift method. Geophysics, 1987, 52(8): 1074-1084.
[53]
Wu R S and Huang L Y. Scattered field calculation in heterogeneous media using phase-screen propagation. SEG Technical Program Expanded Abstracts, 1992, 11:1289-1292.
[54]
Wu R S and de Hoop M V. Accuracy analysis of screen propagators for wave extrapolation using a thin-slab model. SEG Technical Program Expanded Abstracts, 1996, 15:419-422.
[55]
Wu R S, Huang L J, Xie X B. Backscattered wave accumulation using the de Wolf approximation and a phase-screen propagator. SEG Technical Program Expanded Abstracts, 1995, 14:1293-1296.
[56]
de Hoop M V, Le Rousseau J H, Wu R S. Generalization of the phase-screen approximation for the scattering of acoustic waves. Wave Motion,2000,31(3):285-296.
[57]
Zhang Y, Sun J, Gray S H et al. Towards accurate amplitudes for one-way wavefield extrapolation of 3-D common shot records. 7lst Annual International Meeting. SEG, 2001, Workshop.
[58]
Sava P, Biondi B, Fomel S.Amplitude-preserved common image gathers by wave-equation migration. SEG Technical Program Expanded Abstracts, 2001, 20:296-299.
[59]
Sun R and McMechan G A. Scalar reverse-time depth migration of prestack elastic seismic data. Geophy-sics, 2001, 66(5): 1519-1527.
[60]
Bleistein N and Gray S H. Amplitude calculations for 3-D Gaussian beam migration using complex-valued travel times. Inverse Problems, 2010, 26(8): 1-28.
[61]
Phadke S and Dhubia S. Reverse time migration of marine models with elastic wave equation and amplitude preservation. SEG Technical Program Expanded Abstracts,2012,31:1-5.
[62]
Qin Y L and McGarry R. True-amplitude common-shot acoustic reverse time migration. SEG Technical Program Expanded Abstracts, 2013, 32:3894-3898.
[63]
Hill N R. Prestack Gaussian-beam depth migration. Geophysics, 2001, 66(4): 1240-1250.
[64]
Popov M M, Semtchenok N M, Popov P M et al. Depth migration by the Gaussian beam summation method. Geophysics, 2010, 75(2): S81-S93.
[65]
Mulder W A and Plessix R E. A comparison between one-way and two-way wave-equation migration. Geophysics, 2004, 69(6): 1491-1504.
[66]
Yoon K, Marfurt K J and Starr W. Challenges in reverse-time migration. SEG Technical Program Expanded Abstracts, 2004,23:1057-1060.
[67]
Yoon K and Marfurt K. Reverse-time migration using the Poyntingvector. Exploration Geophysics, 2006, 37(1): 102-107.
[68]
Fletcher R, Fowler F P, Kitchenside P et al. Suppressing artifacts in prestack reverse time migration. SEG Technical Program Expanded Abstracts, 2005, 24:2049-2051.
[69]
Costa J C, Neto F A and Alcantara M R M et al.Obliquity-correction imaging condition for reverse time migration. Geophysics, 2009, 74(3): S57-S66.
[70]
Clapp R G. Reverse time migration with random boundaries. SEG Technical Program Expanded Abstracts, 2009, 28: 2809-2813.
[71]
Symes W W. Reverse time migration with optimal checkpointing. Geophysics, 2007, 72(5): SM213-SM221.
[72]
Sun R, McMechan G A and Lee C-S. Prestack scalar reverse-time depth migration of 3D elastic seismic data. Geophysics, 2006, 71(5): S199-S207.
[73]
Whitmore N D.Iterative depth migration by back-ward time propagation. SEG Technical Program Expanded Abstracts, 1983, 2: 382-385.
[74]
Chang W F, G and McMechan A. Reverse-time migration of offset vertical seismic profiling data using the excitation-time imaging condition. Geophysics, 1986, 51(1): 67-84.
Du Qizhen and Qing Tong. Multicomponent prestack reverse-time migration of elastic waves in transverse in isotropic medium. Chinese Journal of Geophysics,2009,52(3):801-807.
[76]
Dellinger J and Etgen J. Wave-field separation in two-dimensional anisotropic media.Geophysics,1990,55(7):914-919.
[77]
Rosales D and Rickett J. PS-wave polarity reversal in angle domain common-image gathers. SEG Technical Program Expanded Abstracts, 2001, 20:1843-1846.
[78]
Rosales D, Fomel S and Biondi B L et al. Wave-equation angle-domain common-image gathers for converted waves. Geophysics, 2008,73(1): S17-S26.
[79]
Lu R, Yan J and Traynin P et al. Elastic RTM: Anisotropic wave-mode separation and converted-wave polarization correction. SEG Technical Program Expanded Abstracts, 2010,29: 3171-3175.
[80]
Yan R and Xie X B. An angle-domain imaging condition for elastic reverse time migration and its application to angle gather extraction. Geophysics, 2012,77(5): S105-S115.
[81]
Du Q Z, Zhu Y T and Ba J. Polarity reversal correction for elastic reverse time migration. Geophysics, 2012, 77(2): S31-S41.
[82]
Du Q Z, Gong X F and Zhang M Q et al. 3D PS-wave imaging with elastic reverse-time migration. Geophysics, 2014, 79(5): S173-S184.
[83]
Duan Y T and Save P. Converted-waves imaging condition for elastic reverse-time migration. SEG Technical Program Expanded Abstracts,2014,33:1904-1908.
[84]
Kuo J T and Dai T. Kirchhoff elastic wave migration for case of the noncoincident source and receiver.Geo-physics, 1984, 49(8):223-1238.
[85]
Dai T F and Kuo J. Real data results of Kirchhoff elastic wave migration. Geophysics, 1986, 51(4): 1006-1011.
[86]
Keho T H and Wu R S. Elastic Kirchhoff migration for vertical seismic profiles. SEG Technical Program Expanded Abstracts, 1987,6: 774-776.
[87]
Sena A G, Toksöz M N. Kirchhoff migration and velocity analysis for converted and nonconverted waves in anisotropic media. Geophysics, 1993,58(2): 265-276.
[88]
Hokstad K. Multicomponent Kirchhoff migration.Geophysics, 2000, 65(3): 861-873.
[89]
岳玉波. 复杂介质高斯束偏移成像方法研究[学位论文]. 山东青岛:中国石油大学(华东),2011.
[90]
Yue Y B, Qian Z P and Qian J F. PS-wave Kirchhoff depth migration and its application to imaging gas clouds. SEG Technical Program Expanded Abstracts, 2013, 32:1699-1703.
[91]
牟永光等.地震数据处理方法北京:石油工业出版社,2007.
[92]
李振春. 地震偏移成像技术研究现状与发展趋势.石油地球物理勘探,2014, 49(1):1-21.
Li Zhenchun. Research status and developmenttrends for seismic migration technology.OGP,2014, 49(1):1-21 .
[93]
Meadows M and Coen S. Exact inversion of plane-layered isotropic and anisotropic elastic media by the state-spaceapproach. Geophysics, 1986, 51(11): 2031-2050.
[94]
Meadows M and Abriel W L. 3-D poststack phase-shift migration in transversely isotropic media. SEG Technical Program Expanded Abstracts, 1994, 13:1205-1208.
[95]
Alkhalifah T. Gaussian beam depth migration for anisotropic media. Geophysics, 1995, 60(5): 1474-1484.
[96]
Zhu T, Gray S H, Wang D. Prestack Gaussian-beam depth migration in anisotropic media. Geophysics, 2007, 72(3): S133-S138.
[97]
Alkhalifah T and Tsvankin I. Velocity analysis for transversely isotropic media. Geophysics, 1995,60(5): 1550-1566.
[98]
Alkhalifah T. Acoustic approximations for processing in transversely isotropic media. Geophysics, 1998, 63(2): 623-631.
[99]
Alkhalifah T. An acoustic wave equation for aniso-tropic media. Geophysics, 2000,65(4):1239-1250.
[100]
Du X, Bancroft J C and Lines L R. Reverse-time migration for tilted TI media. SEG Technical Program Expanded Abstracts, 2005, 24:1930.
[101]
Zhou H, Zhang G, Bloor R. An anisotropic acoustic wave equation for VTI media. 68th EAGE Conference & Exhibition, 2006.
[102]
Zhou H,Zhang G and Bloor R.An anisotropic acoustic wave equation for modeling and migration in 2D TTI media. SEG Technical Program Expanded Abstracts,2006, 25:194-198.
[103]
Duveneck E, Milcik P, Bakker P M et al. Acoustic VTI wave equations and their application for anisotropic reverse-time migration. SEG Technical Program Expanded Abstracts,2008,27: 2186-2190.
[104]
Duveneck E and Bakker P M. Stable P-wave modeling for reverse-timemigrationintilted TI media. Geophysics, 2011, 76(2): S65-S75.
[105]
Thomesen L. Weak elastic anisotropy. Geoghysics,1986,51(10):1954-1966.
[106]
Cohen J. Analytic study of the effective parameters for determination of the NMO velocity function in transversely isotropic media. Center for Wave Phenomena, Colorado School of Mines, 1996, CWP-191.
[107]
Helbig K. Elliptical anisotropy-Its significance and meaning. Geophysics, 1983,48(7):825-832.
[108]
Dellinger J and Muir F. Imaging reflections in elliptically anisotropic media. Geophysics, 1988,53(12):1616-1618.
[109]
Grechka V, Zhang L, Rector III J W. Shear waves in acoustic anisotropic media. Geophysics, 2004,69(2):576-582.
[110]
Etgen J T and Brandsberg-Dahl S. The pseudo-analytical method: Application of pseudo-Laplacians to acoustic and acoustic anisotropic wave propagation. SEG Technical Program Expanded Abstracts, 2009, 28:2552-2556.
[111]
Liu F, Morton S A, Jiang S et al. Decoupled wave equations for P and SV waves in an acoustic VTI media. SEG Technical Program Expanded Abstracts, 2009, 28:2844-2848.
[112]
Crawley S, Brandsberg-Dahl S, McClean J et al.TTI reverse time migration using the pseudo-analy-tic method. The Leading Edge, 2010, 29(11): 1378-1384.
[113]
Pestana R C, Ursin B, Stoffa P L. Separate P-and SV-wave equations for VTI media. 12th International Congress of the Brazilian Geophysical Society, 2011.
[114]
Zhan G, Pestana R C, Stoffa P L. An acoustic wave equation for pure P wave in 2D TTI media. 12thInternational Congress of the Brazilian Geophysical Society, 2011.
[115]
Pestana R C and Stoffa P L. Time evolution of the wave equation using rapid expansion method. Geophysics, 2010, 75(4): T121-T131.
[116]
Zhan G, Pestana R C and Stoffa P L. An efficient hybrid pseudo-spectral/finite-difference scheme for solving the TTI pure P-wave equation. Journal of Geophysics and Engineering, 2013, 10(2):025004.
Cheng Jiubing, Kang Wei, Wang Tengfei. Description of qP-wave propagation in anisotropic media, Part I:Pseudo-pure-mode wave equations. Chinese Journal of Geophysics, 2013, 56(10):3474-3486.
Huang Lianjie and Yang Wencai. Approxima method of inversion of the acoustic wave equation by inverse scattering. Chinese Journal of Geophysics,1991,34(5):626-634.
Luan Wengui. On the continuous dependence of the solution for several improperly posed problems in geophysics. Chinese Journal of Geophysics,1982,25(4):626-634.
[122]
徐基祥,王平,林蓓. 地震波逆散射成像技术潜力展望. 中国石油勘探,2006,(4):61-66.
Xü Jixiang, Wang Ping, Lin Bei. Expecatation for technology potantial of seismic wave reverse scattering image. China Petroleum Exploration,2006,(4):61-66.
[123]
Kolsky H. The propagation of stress pulses in viscoelastic solids. Philosophical magazine, 1956,1(8): 693-710.
[124]
Futterman. Dispersive body waves. Journal of Geophysics Research. 1962, 67(13):5279-5291.
[125]
Kjartansson E. Constant-Q wave propagation and attenuation. Journal of Geophysical Research, 1979, 84(B9):4737-4738.
[126]
Hargreaves N D, Calvert A J. Inverse Q filtering by Fourier transform. Geophysics, 1991, 56(4): 519-527.
[127]
Ribodetti A, Virieux J. Asymptotic theory for imaging the attenuation factor Q. Geophysics, 1998, 63(5): 1767-1778.
[128]
Dai Nanxun and West G F. Inverse Q migration. SEG Technical Program Expanded Abstracts, 1994,23: 1418-1421.
[129]
Mittet R, Sollie R and Hokstad K. Prestack depth migration with compensation for absorption and dispersion. Geophysics, 1995, 60(5):1485-1494.
[130]
Wang J, Zhou H, Tian Y K. A new scheme for elastic full waveform inversion based on velocity-stress wave equations in time domain. SEG Technical Program Expanded Abstracts 2012:1-5.
[131]
Wang Yanghua.Quantifying the effectiveness of stabilized inverse Q filtering. Geophysics, 2003,68(1):337-345.
[132]
Wang Yanghua. Inverse Q-filter for seismic resolution enhancement. Geophysics, 2006, 71(3):SV51-SV60.
[133]
杨午阳. 粘弹性波动方程保幅偏移技术研究[学位论文]. 北京:中国地质科学院, 2004.
Yang Wuyang. Amplitude-preserved migration with viscoelastic wave equations[D].Beijing: Chinese Academy of Geological Sciences, 2004.
Yang Wuyang, Yang Wencai, Liu Quanxin et al. Migration with viscoelastic wave equations. Lithlogic Reservoirs,2007, 19(1): 86-91.
[135]
Zhang Y, Zhang P and Zhang H. Compensating for visco-acoustic effects in reverse-time migration. SEG Technical Program Expanded Abstracts, 2010, 19:3160-3164.
[136]
Zhu T, Harris J M and Biondi B. Q-compensated reverse time migration. Geophysics, 2014, 79(3):S77-S87.
[137]
Al-Yahya K. Velocity analysis by iterative profile migration. Geophysics, 1989, 54(6): 718-729.
[138]
Doherty S M,Claerbout J F. Structure independent velocity estimation. Geophysics, 1976, 41(5): 850-881.
[139]
Lafond C F, Levander A R. Migration moveout analysis and depth focusing. Geophysics, 1993,58(1):91-100.
[140]
Lee W, Zhang L. Residual shot profile migration. Geophysics, 1992, 57(6): 815-822.
[141]
Liu Z, Bleistein N. Migration velocity analysis:Theory and an iterative algorithm. Geophysics, 1995, 60(1): 142-153.
[142]
Rickett J E, Sava P C. Offset and angle-domain common image-point gathers forshot-profile migration. Geophysics, 2002, 67(3): 883-889.
[143]
Sava P,Fomel S. Angle-domain common-image gathers by wavefield continuation methods. Geophysics, 2003, 68(3): 1065-1074.
[144]
Jeannot J P, Faye J P, Denelle E. Prestack migration velocities from depth focusing analysis. SEG Technical Program Expanded Abstracts, 1986, 15:438-440.
[145]
Berkhout A J, Rietveld W E. Determination of macro models for prestack migration: Part1, Estimation of macro velocities. SEG Technical Program Expanded Abstracts, 1994, 13:1330-1333.
[146]
Deregowski S M. Common-offset migrations and velocity analysis. First Break, 1990, 8(6):225-234.
[147]
Landa E, Thore P, Sorin V et al. Interpretation of velocity estimates from coherency inversion. Geophysics, 1991, 56(9): 1377-1383.