TTI介质叠前逆时偏移成像研究综述
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摘要
逆时偏移是基于双程波波动方程进行波场逆时外推,再利用成像条件提取成像值,进而实现偏移成像的一种方法.目前,RTM已经由各向同性介质推广到了TI介质,包括VTI介质和TTI介质.考虑了各向异性因素的逆时偏移技术能更好地满足日益增长的勘探精度的要求,进一步提高和改善成像效果.在回顾各向异性介质逆时偏移发展历史的基础之上,本文针对于国内外TTI介质逆时偏移当前的研究现状进行了概述,并对目前TTI介质逆时偏移方法中所存在的特有的数值稳定性和qSV波人为干扰压制问题的解决方法进行了归纳总结.最后对逆时偏移未来的发展方向和研究重点进行了展望.
The reverse time migration is a method of migration that extropolate the wave field base on two-way wave equation,then getting the image using the imaging conditions.Now,RTM has been extended from isotropic media to transversely isotropic(TI) media including vertical TI(VTI) and Tilted TI(TTI) media.The reverse-time migration added to anistropy factors can meet the continually increasing needs of the exploration precision better,and further enhance and improve the quality of image.On the basis of reviewing the developing history of anistropic reverse-time migration,we introduce the current research situation of TTI reverse-time migration,meanwhile,summarize the problems which are owned by TTI reverse-time migration specially,including numerical instabilities and qSV-wave artifacts.Finally,we predict the future development trend and the key point of research.
The reverse time migration is a method of migration that extropolate the wave field base on two-way wave equation,then getting the image using the imaging conditions.Now,RTM has been extended from isotropic media to transversely isotropic(TI) media including vertical TI(VTI) and Tilted TI(TTI) media.The reverse-time migration added to anistropy factors can meet the continually increasing needs of the exploration precision better,and further enhance and improve the quality of image.On the basis of reviewing the developing history of anistropic reverse-time migration,we introduce the current research situation of TTI reverse-time migration,meanwhile,summarize the problems which are owned by TTI reverse-time migration specially,including numerical instabilities and qSV-wave artifacts.Finally,we predict the future development trend and the key point of research.
引文
[1]McMechan G A.Migration by extrapolation of time-dependentboundary values[J].Geophysical Prospecting,1983,31(3):413-420.
[2]Whitemore N D.Iterative depth migration by backward timepropagation[A].//53rd Annual International Meeting[C].SEG,Expanded Abstracts,1983:825-830.
[3]Baysal E,Kosloff D D,Sherwood J W C.Reverse timemigration[J].Geophysics,1983,48(11):1514-1524.
[4]Loewenthal D,Mulfti I R.Reversed time migration in spatialfrequency domain[J].Geophysics,1983,48(5):627-635.
[5]吴国忱.各向异性介质地震波传播与成像[M].东营:中国石油大学出版社,2006.Wu G C.Propagation and Imaging of Seismic Wave inAnisotropic Media[M](in Chinese).Dongying:ChinaUniversity of Petroleum Press,2006.
[6]Thomsen L.Weak elastic anisotropy[J].Geophysics,1986,51(10):1954-1996.
[7]Huang T,Zhang Y,Zhang H Z,et al.Subsalt imaging usingTTI reverse time migration[J].The Leading Edge,2009,28(4):448-452.
[8]韩令贺,何兵寿.VTI介质一阶准P波方程正演模拟及边界条件[J].石油地球物理勘探,2010,45(6):819-825.Han L H,He B S.One-order quasi-P wave equation forwardmodeling and boundary conditions in VTI media[J].OilGeophysical Prospecting(in Chinese),2010,45(6):819-825.
[9]Alkhalifah T.Acoustic approximations for processing in transverselyisotropic media[J].Geophysics,1998,63(2):623-631.
[10]Alkhalifah T.An acoustic wave equation for anisotropic media[J].Geophysics,2000,65(4):1239-1250.
[11]Kie H,Toro W.A new acoustic wave equation for modelingin anisotropic media[A].SEG Expanded Abstracts,2001:1171-1174.
[12]吴国忱,梁锴.VTI介质频率-空间域准P波正演模拟[J].石油地球物理勘探,2005,40(5):535-545.Wu G C,Liang K.Quasi P-wave forward modeling infrequency-space domain in VTI media[J].Oil GeophysicalProspecting(in Chinese),2005,40(5):535-545.
[13]吴国忱,梁锴.VTI介质qP波方程高精度有限差分算子[J].地球物理进展,2007,22(3):896-904.Wu G C,Liang K.High precision finite difference operatorsfor qP wave equation in VTI media[J].Progress inGeophysics(in Chinese),2007,22(3):896-904.
[14]黄翼坚,朱光明,刘池洋.一个近似的VTI介质声波方程[J].地球物理学报,2011,54(8):2177-2123.Huang Y J,Zhu G M,Liu C Y.An approximate acousticwave equation for VTI media[J].Chinese J.Geophys.(inChinese),2011,54(8):2177-2123.
[15]Zhou H B,Zhang G Q,Bloor R.An anisotropic acoustic waveequation for modeling and migration in 2DTTI media[A].//76th Annual International Meeting[C].SEG,ExpandedAbstracts,2006:194-198.
[16]Hestholm S.Acoustic VTI modeling using high-order finite-differences[A].//77th Annual International Meeting[C].SEG,Expanded Abstracts,2007:139-143.
[17]Du X,Fletcher R,Fowler P J.A new pseudo-acoustic waveequation for VTI media[A].//Presented at the 70th AnnualInternational Conference and Exhibition,EAGE,2008.
[18]Zhou H Z,Zhang Y.Reverse time migration in 3DheterogeneousTTI media[A].//78th Annual International Meeting[C].SEG,Expanded Abstracts,2008,2196-2200.
[19]Fletcher R,Du X,Fowler P J.A new pseudo-acoustic waveequation for TI media[A].//78th Annual InternationalMeeting[C].SEG,Expanded Abstracts,2008:2082-2086.
[20]Fletcher R P,Du X,Fowler P J.Reverse time migration intilted transversely isotropic(TTI)media[J].Geophysics,2009,74(6)WCA179-WCA187,doi:10.1190/1.3269902.
[21]Duveneck E,Milik P,Bakker P M.Acoustic VTI waveequations and their application for anisotropic reverse-timemigration[A].//78th Annual International Meeting[C].SEG,Expanded Abstracts,2008:2186-2190.
[22]Yan J,Sava P.Elastic wavefield separation for VTI media[A].//78th Annual International Meeting[C].SEG,Expanded Abstracts,2008:2191-2195.
[23]Fowler P J,Du X,Fletcher R P.Coupled equations for reverse-time migration in transversely isotropic media[J].Geophysics,2010,75(1):S11-S22.
[24]Kang W,Cheng J B.Prestack scalar reverse time migrationof elastic seismic data in TI media[A].//81st AnnualInternational Meeting[C].SEG,Expanded Abstracts,2011:3367-3371.
[25]Zhang Y,Zhang H Z,Zhang G Q.A stable TTI reverse timemigration and its implementation[A].//79th AnnualInternational Meeting[C].SEG,Expanded Abstracts,2009:2794-2798.
[26]Liu W,Bube K P,Zhang L B,et al.Stable reverse-timemigration in varible-tilt TI media[A].//71st AnnualConference and Exhibition[C].EAGE,Expanded Abstracts,2009:064.
[27]Crawley S,Brandsberg-Dahl S,McClean J,et al.TTI reversetime migration using the pseudo-analytic method[J].TheLeading Edge,2010,29(11):1378-1384.
[28]Crawley S,Brandsberg-Dahl S,McClean J,et al.TTI reversetime migration using the pseudo-analytic method[A].//Presented at the 80th Annual International Conference andExhibition,EAGE,2010.
[29]Ekkehart T.Reverse-time migration in TTI media[A].//80th Annual International Meeting[C].SEG,ExpandedAbstracts,2010,29:3193-3197.
[30]Duveneck E,Bakker P M.Stable P-wave modeling forreverse-time migration in tilted TI media[A].//81st AnnualInternational Meeting[C].SEG,Expanded Abstracts,2011:S65-S75.
[31]Chu C L,Macy B,Anno P.An accurate and stable waveequation for pure acoustic TTI modeling[A].//81st AnnualInternational Meeting[C].SEG,Expanded Abstracts,2011:179-184.
[32]Pestana R C,Stoffa P L.Time evolution of the wave equationusing rapid expansion method REM[J].Geophysics,2010,75(4):T121-T131.
[33]Pestana R C,Ursin B,Stoffa P L.Separate P-and SV-waveequations for VTI media[J].Geophysics,2011,75(4):T163-T167.
[34]Zhan G,Pestana R C,Stoffa P L.An acoustic wave equationfor pure P wave in 2D TTI media[A].//81st AnnualInternational Meeting[C].SEG,Expanded Abstracts,2011:S168-S173.
[35]Du X,Bancroft J C,Lines L R.Reverse-time migration fortilted TI media[A].//SEG Expanded Abstracts[C],2005:1930-1933.
[36]Shan G J.Optimized implicit finite-difference and Fourierfinite-difference migration for VTI media[J].Geophysics,2009,74(6):WCA179-WCA197.
[37]Tian Y C,Xie G S.Acoustic wavefield simulation in TTI mediawith High-order stagger-grid finite-difference scheme[A].//Presented at the 81st Annual International Conference andExhibition,EAGE[C].2011.
[38]杨仁虎,常旭,刘伊克.叠前逆时偏移影响因素分析[J].地球物理学报,2010,53(8):1902-1913.Yang R H,Chang X,Liu Y K.The influence factorsanalysis of imaging precision in pre-stack reverse timemigration[J].Chinese J.Geophys.(in Chinese),2010,53(8):1902-1913.
[39]杜启振,秦童.横向各向同性介质弹性波多分量叠前逆时偏移[J].地球物理学报,2009,52(3):801-807.Du Q Z,Qin T.Multicomponent prestack reverse-timemigration of elastic waves in transverse isotropic medium[J].Chinese J.Geophys.(in Chinese),2009,52(3):801-807.
[40]底青云,王妙月.弹性波有限元逆时偏移技术研究[J].地球物理学报,1997,40(4):570-579.Di Q Y,Wang M Y.The study of finite element reverse-timemigration for elastic wave[J].Acta Geophysica Sinica(Chinese J.Geophys.)(in Chinese),1997,40(4):570-579.
[41]张美根,王妙月.各向异性弹性波有限元叠前逆时偏移[J].地球物理学报,2001,44(5):711-719.Zhang M G,Wang M Y.Pre-stack finite element reverse-time migration for anisotropic elastic wave[J].Chinese J.Geophys.(in Chinese),2001,44(5):711-719.
[42]何兵寿,张会星,魏修成,等.双程声波方程叠前逆时深度偏移的成像条件[J].石油地球物理勘探,2010,45(2):237-243.He B S,Zhang H X,Wei X C,et al.Imaging conditions fortwo-way acoustic wave equation pre-stack reverse-time depthmigration[J].Oil Geophysical Prospecting(in Chinese),2010,45(2):237-243.
[43]何兵寿,张会星,韩月.双程声波方程叠前逆时深度偏移及其并行算法[J].煤炭学报,2010,35(3):458-462.He B S,Zhang H X,Han Y.Reverse-time migration of twoway equations and its parallel algorithm[J].Journal of ChinaCoal Society(in Chinese),2010,35(3):458-462.
[44]王童奎,付兴深,朱德献,等.谱元法叠前逆时偏移研究[J].地球物理学进展,2008,23(3):681-685.Wang T K,Fu X S,Zhu D X,et al.Spectral-elementmethod for pre-stack reverse-time migration[J].Progress inGeophysics(in Chinese),2008,23(3):681-685.
[45]何兵寿,张会星,范国苗.双程声波方程逆时深度偏移[J].物探化探计算技术,2010,32(2):113-119.He B S,Zhang H X,Fan G M.Reverse-time depthmigration of two way acoustic wave equations[J].Computing Techniques for Geophysical and GeochemicalExploration(in Chinese),2010,32(2):113-119.
[46]丁仁伟,李振春,孙晓东,等.叠前逆时深度偏移中的激发时间成像条件[J].地球物理学进展,2008,23(6):1859-1865.Ding R W,Li Z C,Sun X D,et al.Prestack reverse-timedepth migration and the imaging condition[J].Progress inGeophysics(in Chinese),2008,23(6):1859-1865.
[47]陈克洋.基于高阶有限差分的波动方程叠前逆时偏移方法[J].石油物探,2009,48(5):475-478.Chen K Y.Wave equation pre-stack reverse-time migrationmethod based on high-order finite-difference approach[J].Geophysical Prospecting for Petroleum(in Chinese),2009,48(5):475-478.
[48]陈可洋.高阶交错网格有限差分法弹性波叠前逆时深度偏移[J].油气地球物理,2010,8(3):1-4.Chen K Y.Elastic wave pre-stack reverse time depthmigration with high-order staggered-grid finite differencescheme[J].Petroleum Geophysics(in Chinese),2010,8(3):1-4.
[49]刘红伟,李博,刘洪,等.地震叠前逆时偏移高阶有限差分算法及GPU实现[J].地球物理学报,2010,53(7):1725-1733.Liu H W,Liu B,Liu H,et al.The algorithm of high orderfinite difference pre-stack reverse time migration and GPUimplementation[J].Chinese J.Geophys.(in Chinese),2010,53(7):1725-1733.
[50]刘红伟,邹振,刘洪,等.地震叠前逆时偏移中的去噪与存储[J].地球物理学报,2010,53(9):2171-2180.Liu H W,Zou Z,Liu H,et al.The problem of denoise andstronge in seismic reverse time migration[J].Chinese J.Geophys.(in Chinese),2010,53(9):2171-2180.
[51]刘红伟,刘洪,李博,等.起伏地表叠前逆时偏移理论及GPU加速技术[J].地球物理学报,2011,54(7):1883-1892.Liu H W,Liu H,Li B,et al.Pre-stack reverse-timemigration for rugged topography and GPU accelerationtechnology[J].Chinese J.Geophys.(in Chinese),2011,54(7):1883-1892.
[52]李博,刘红伟,刘国锋,等.地震叠前逆时偏移算法的CPU与GPU实施对策[J].地球物理学报,2010,53(12):2938-2943.Liu B,Liu H W,Liu G F,et al.Computational strategy ofseismic pre-stack reverse time migration on CPU/GPU[J].Chinese J.Geophys.(in Chinese),2010,53(12):2938-2943.
[53]王保利,高静怀,陈文超,等.地震叠前逆时偏移的有效边界存储策略[J].地球物理学报,2012,55(7):2412-2421.Wang B L,Gao J H,Chen W C,et al.Efficient boundarystorage strategies for seismic reverse time migration[J].Chinese J.Geophys.(in Chinese),2012,55(7):2412-2421.
[54]Fletcher R F,Fowler P,Kitchenside P,et al.Suppressingartifacts in prestack reverse time migration[A].//75thAnn.Internat Mtg.,Soc.Expi.Geophys.ExpandedAbstracts[C].2005:2049-2052.
[55]Liu F Q,Zhang G Q,Morton S A,et al.Reverse-timeMigration Using One-way Wavefield Imaging Condition[A].//Expanded Abstracts of 77th Annual International SEGMeeting[C].2007:2170-2174.
[56]Guitton A,Kaelin B,Biondi B.Least-squares attenuation ofreverse-time migration artifacts[J].Geophysics,2007,72(1):S19-S23.
[57]Mulder W A,Plessix R E.A comparison between one-wayand two-way wave-equation migration[J].Geophysics,2004,69(6):1491-1504.
[58]Yoon K,Marfurt K J.Reverse-time migration using thePoynting vector[J].Exploration Geophysics,2006,37(1):102-107.
[59]Costa J C,Neto F A S,Alcantara M R M,et al.Obliquity-correction imaging condition for reverse time migration[J].Geophysics,2009,74(3):S57-S66.
[60]Chattopadhyay S,McMechan G A.Imaging conditions forprestack reverse-time migration[J].Geophysics,2008,73(3):S81-S89.
[61]Kaelin B,Guitton A.Imaging condition for reverse timemigration[A].//Expanded Abstracts of 76th AnnualInternational SEG Meeting[C].2006:2594-2598.
[62]Suh S Y.Reverse-time migration bu fan filtering plus wavefielddecomposition[A].//Expanded Abstracts of 79th AnnualInternational SEG Meeting[C].2009:2804-2807.
[63]Zhang Y,Sun J.Practical issues of reverse time migration:true amplitude gathers,noise removal and harmonic-sourceencoding[A].//CPS/SEG International GeophysicalConference&Exposition[C].2009,ID5.
[64]杨勤勇,段心标.逆时偏移技术发展现状与趋势[J].石油物探,2010,49(1):92-98.Yang Q Y,Duan X B.Development status and trend ofreverse time migration[J].Geophysical Prospecting forPetroleum(in Chinese),2010,49(1):92-98.
[65]陈可洋.地震波逆时偏移方法研究综述[J].勘探地球物理进展,2010,33(3):153-159.Chen K Y.Review of seismic reverse time migration methods[J].Progress in Exploration Geophysics(in Chinese),2010,33(3):153-159.
[66]张春燕,李振春,孙晓东.逆时偏移方法技术进展综述[J].勘探地球物理进展,2010,33(5):309-317.Zhang C Y,Li Z C,Sun X D.Review of reverse timemigration[J].Progress in Exploration Geophysics(inChinese),2010,33(3):309-317.
[67]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 L,Liu Y.Progress in reverse time migration imaging[J].Progress in Geophysics(in Chinese),2011,26(3):1085-1100.
[68]Yoon K,Marfurt K J,Starr W.Challenges in reverse-timemigration[A].//74th Annual International Meeting[C].SEG,Expanded Abstracts,2004:1057-1060.
[69]周瑞红,赵景霞.逆时偏移及其成像条件[J].内蒙古石油化工,2009,35(3):23-26.Zhou R H,Zhao J X.Reverse-time migration and its imagingconditions[J].Inner Mongulia Petrochemical Industry(inChinese),2009,35(3):23-26.
[70]徐琴,李振春,鮑伟.波动方程偏移中的成像条件研究进展[J].勘探地球物理进展,2008,31(4):247-252.Xu Q,Li Z C,Bao W.Progress in research of imagingcondition for wave equation migration[J].Progress inExploration Geophysics(in Chinese),2008,31(4):247-252.
[71]Sava P,Fomel S.Time-shift imaging condition[A].//Expanded Abstracts of 75th Annual International SEGMeeting[C].2005:1850-1854.
[72]Valenciano A A,Biondi B.Deconvolution imaging conditionfor reverse-time migration[R].Stanford Exploration Project,Report,2002,112:83-96.
[73]Bruno K,Guitton A.Imaging condition for reverse timemigration[A].//76th Annual International Meeting,SEG[C].Expanded Abstracts,2006:2594-2598.
[74]Daley P F,Horn F.Reflection and transmission coefficientsfor seismic waves in ellipsoidally anisotropic media[J].Geophysics,1979,44(1):27-38.
[75]Tsvankin I.P-wave signatures and notation for transverselyisotropic media:An overview[J].Geophysics,1996,61(2):467-483.
[76]Zhang L B,Rector J W III,Hoversten G M.An acousticwave equation for modeling in tilted TI media[A].//73rdAnnual International Meeting[C].SEG,ExpandedAbstracts,2003:153-156.
[77]Liu W,Bube K P,Zhang L B,et al.Stable reverse-timemigration in variable-title TTI media[A].//71st Conference&Exhibition[C].EAGE,Extended Abstracts,2009:64.
[78]Yoon K,Sang S,Jean J,et al.Stability and speedup issuesin TTI RTM implementation[A].//80th AnnualInternational Meeting[C].SEG,Expanded Abstracts,2010:3221-3225.
[79]Grechka V,Zhang L B,Rector J W.Shear waves in acousticanisotropic media[J].Geophysics,2004,69(2):576-582.
[80]Zhou H,Zhang G.Removing S-wave noise in TTI reversetime migration[A].//79th Annual International Meeting[C].SEG,Expanded Abstracts,2009:2849-2853.
[81]Liu F,Morton S A,Jiang S,et al.Decoupled wave equations forP-and Sv-waves in acoustic VTI media[A].//79th AnnualInternational Meeting[C].SEG,Expanded Abstracts,2009,28:2844-2848.
[2]Whitemore N D.Iterative depth migration by backward timepropagation[A].//53rd Annual International Meeting[C].SEG,Expanded Abstracts,1983:825-830.
[3]Baysal E,Kosloff D D,Sherwood J W C.Reverse timemigration[J].Geophysics,1983,48(11):1514-1524.
[4]Loewenthal D,Mulfti I R.Reversed time migration in spatialfrequency domain[J].Geophysics,1983,48(5):627-635.
[5]吴国忱.各向异性介质地震波传播与成像[M].东营:中国石油大学出版社,2006.Wu G C.Propagation and Imaging of Seismic Wave inAnisotropic Media[M](in Chinese).Dongying:ChinaUniversity of Petroleum Press,2006.
[6]Thomsen L.Weak elastic anisotropy[J].Geophysics,1986,51(10):1954-1996.
[7]Huang T,Zhang Y,Zhang H Z,et al.Subsalt imaging usingTTI reverse time migration[J].The Leading Edge,2009,28(4):448-452.
[8]韩令贺,何兵寿.VTI介质一阶准P波方程正演模拟及边界条件[J].石油地球物理勘探,2010,45(6):819-825.Han L H,He B S.One-order quasi-P wave equation forwardmodeling and boundary conditions in VTI media[J].OilGeophysical Prospecting(in Chinese),2010,45(6):819-825.
[9]Alkhalifah T.Acoustic approximations for processing in transverselyisotropic media[J].Geophysics,1998,63(2):623-631.
[10]Alkhalifah T.An acoustic wave equation for anisotropic media[J].Geophysics,2000,65(4):1239-1250.
[11]Kie H,Toro W.A new acoustic wave equation for modelingin anisotropic media[A].SEG Expanded Abstracts,2001:1171-1174.
[12]吴国忱,梁锴.VTI介质频率-空间域准P波正演模拟[J].石油地球物理勘探,2005,40(5):535-545.Wu G C,Liang K.Quasi P-wave forward modeling infrequency-space domain in VTI media[J].Oil GeophysicalProspecting(in Chinese),2005,40(5):535-545.
[13]吴国忱,梁锴.VTI介质qP波方程高精度有限差分算子[J].地球物理进展,2007,22(3):896-904.Wu G C,Liang K.High precision finite difference operatorsfor qP wave equation in VTI media[J].Progress inGeophysics(in Chinese),2007,22(3):896-904.
[14]黄翼坚,朱光明,刘池洋.一个近似的VTI介质声波方程[J].地球物理学报,2011,54(8):2177-2123.Huang Y J,Zhu G M,Liu C Y.An approximate acousticwave equation for VTI media[J].Chinese J.Geophys.(inChinese),2011,54(8):2177-2123.
[15]Zhou H B,Zhang G Q,Bloor R.An anisotropic acoustic waveequation for modeling and migration in 2DTTI media[A].//76th Annual International Meeting[C].SEG,ExpandedAbstracts,2006:194-198.
[16]Hestholm S.Acoustic VTI modeling using high-order finite-differences[A].//77th Annual International Meeting[C].SEG,Expanded Abstracts,2007:139-143.
[17]Du X,Fletcher R,Fowler P J.A new pseudo-acoustic waveequation for VTI media[A].//Presented at the 70th AnnualInternational Conference and Exhibition,EAGE,2008.
[18]Zhou H Z,Zhang Y.Reverse time migration in 3DheterogeneousTTI media[A].//78th Annual International Meeting[C].SEG,Expanded Abstracts,2008,2196-2200.
[19]Fletcher R,Du X,Fowler P J.A new pseudo-acoustic waveequation for TI media[A].//78th Annual InternationalMeeting[C].SEG,Expanded Abstracts,2008:2082-2086.
[20]Fletcher R P,Du X,Fowler P J.Reverse time migration intilted transversely isotropic(TTI)media[J].Geophysics,2009,74(6)WCA179-WCA187,doi:10.1190/1.3269902.
[21]Duveneck E,Milik P,Bakker P M.Acoustic VTI waveequations and their application for anisotropic reverse-timemigration[A].//78th Annual International Meeting[C].SEG,Expanded Abstracts,2008:2186-2190.
[22]Yan J,Sava P.Elastic wavefield separation for VTI media[A].//78th Annual International Meeting[C].SEG,Expanded Abstracts,2008:2191-2195.
[23]Fowler P J,Du X,Fletcher R P.Coupled equations for reverse-time migration in transversely isotropic media[J].Geophysics,2010,75(1):S11-S22.
[24]Kang W,Cheng J B.Prestack scalar reverse time migrationof elastic seismic data in TI media[A].//81st AnnualInternational Meeting[C].SEG,Expanded Abstracts,2011:3367-3371.
[25]Zhang Y,Zhang H Z,Zhang G Q.A stable TTI reverse timemigration and its implementation[A].//79th AnnualInternational Meeting[C].SEG,Expanded Abstracts,2009:2794-2798.
[26]Liu W,Bube K P,Zhang L B,et al.Stable reverse-timemigration in varible-tilt TI media[A].//71st AnnualConference and Exhibition[C].EAGE,Expanded Abstracts,2009:064.
[27]Crawley S,Brandsberg-Dahl S,McClean J,et al.TTI reversetime migration using the pseudo-analytic method[J].TheLeading Edge,2010,29(11):1378-1384.
[28]Crawley S,Brandsberg-Dahl S,McClean J,et al.TTI reversetime migration using the pseudo-analytic method[A].//Presented at the 80th Annual International Conference andExhibition,EAGE,2010.
[29]Ekkehart T.Reverse-time migration in TTI media[A].//80th Annual International Meeting[C].SEG,ExpandedAbstracts,2010,29:3193-3197.
[30]Duveneck E,Bakker P M.Stable P-wave modeling forreverse-time migration in tilted TI media[A].//81st AnnualInternational Meeting[C].SEG,Expanded Abstracts,2011:S65-S75.
[31]Chu C L,Macy B,Anno P.An accurate and stable waveequation for pure acoustic TTI modeling[A].//81st AnnualInternational Meeting[C].SEG,Expanded Abstracts,2011:179-184.
[32]Pestana R C,Stoffa P L.Time evolution of the wave equationusing rapid expansion method REM[J].Geophysics,2010,75(4):T121-T131.
[33]Pestana R C,Ursin B,Stoffa P L.Separate P-and SV-waveequations for VTI media[J].Geophysics,2011,75(4):T163-T167.
[34]Zhan G,Pestana R C,Stoffa P L.An acoustic wave equationfor pure P wave in 2D TTI media[A].//81st AnnualInternational Meeting[C].SEG,Expanded Abstracts,2011:S168-S173.
[35]Du X,Bancroft J C,Lines L R.Reverse-time migration fortilted TI media[A].//SEG Expanded Abstracts[C],2005:1930-1933.
[36]Shan G J.Optimized implicit finite-difference and Fourierfinite-difference migration for VTI media[J].Geophysics,2009,74(6):WCA179-WCA197.
[37]Tian Y C,Xie G S.Acoustic wavefield simulation in TTI mediawith High-order stagger-grid finite-difference scheme[A].//Presented at the 81st Annual International Conference andExhibition,EAGE[C].2011.
[38]杨仁虎,常旭,刘伊克.叠前逆时偏移影响因素分析[J].地球物理学报,2010,53(8):1902-1913.Yang R H,Chang X,Liu Y K.The influence factorsanalysis of imaging precision in pre-stack reverse timemigration[J].Chinese J.Geophys.(in Chinese),2010,53(8):1902-1913.
[39]杜启振,秦童.横向各向同性介质弹性波多分量叠前逆时偏移[J].地球物理学报,2009,52(3):801-807.Du Q Z,Qin T.Multicomponent prestack reverse-timemigration of elastic waves in transverse isotropic medium[J].Chinese J.Geophys.(in Chinese),2009,52(3):801-807.
[40]底青云,王妙月.弹性波有限元逆时偏移技术研究[J].地球物理学报,1997,40(4):570-579.Di Q Y,Wang M Y.The study of finite element reverse-timemigration for elastic wave[J].Acta Geophysica Sinica(Chinese J.Geophys.)(in Chinese),1997,40(4):570-579.
[41]张美根,王妙月.各向异性弹性波有限元叠前逆时偏移[J].地球物理学报,2001,44(5):711-719.Zhang M G,Wang M Y.Pre-stack finite element reverse-time migration for anisotropic elastic wave[J].Chinese J.Geophys.(in Chinese),2001,44(5):711-719.
[42]何兵寿,张会星,魏修成,等.双程声波方程叠前逆时深度偏移的成像条件[J].石油地球物理勘探,2010,45(2):237-243.He B S,Zhang H X,Wei X C,et al.Imaging conditions fortwo-way acoustic wave equation pre-stack reverse-time depthmigration[J].Oil Geophysical Prospecting(in Chinese),2010,45(2):237-243.
[43]何兵寿,张会星,韩月.双程声波方程叠前逆时深度偏移及其并行算法[J].煤炭学报,2010,35(3):458-462.He B S,Zhang H X,Han Y.Reverse-time migration of twoway equations and its parallel algorithm[J].Journal of ChinaCoal Society(in Chinese),2010,35(3):458-462.
[44]王童奎,付兴深,朱德献,等.谱元法叠前逆时偏移研究[J].地球物理学进展,2008,23(3):681-685.Wang T K,Fu X S,Zhu D X,et al.Spectral-elementmethod for pre-stack reverse-time migration[J].Progress inGeophysics(in Chinese),2008,23(3):681-685.
[45]何兵寿,张会星,范国苗.双程声波方程逆时深度偏移[J].物探化探计算技术,2010,32(2):113-119.He B S,Zhang H X,Fan G M.Reverse-time depthmigration of two way acoustic wave equations[J].Computing Techniques for Geophysical and GeochemicalExploration(in Chinese),2010,32(2):113-119.
[46]丁仁伟,李振春,孙晓东,等.叠前逆时深度偏移中的激发时间成像条件[J].地球物理学进展,2008,23(6):1859-1865.Ding R W,Li Z C,Sun X D,et al.Prestack reverse-timedepth migration and the imaging condition[J].Progress inGeophysics(in Chinese),2008,23(6):1859-1865.
[47]陈克洋.基于高阶有限差分的波动方程叠前逆时偏移方法[J].石油物探,2009,48(5):475-478.Chen K Y.Wave equation pre-stack reverse-time migrationmethod based on high-order finite-difference approach[J].Geophysical Prospecting for Petroleum(in Chinese),2009,48(5):475-478.
[48]陈可洋.高阶交错网格有限差分法弹性波叠前逆时深度偏移[J].油气地球物理,2010,8(3):1-4.Chen K Y.Elastic wave pre-stack reverse time depthmigration with high-order staggered-grid finite differencescheme[J].Petroleum Geophysics(in Chinese),2010,8(3):1-4.
[49]刘红伟,李博,刘洪,等.地震叠前逆时偏移高阶有限差分算法及GPU实现[J].地球物理学报,2010,53(7):1725-1733.Liu H W,Liu B,Liu H,et al.The algorithm of high orderfinite difference pre-stack reverse time migration and GPUimplementation[J].Chinese J.Geophys.(in Chinese),2010,53(7):1725-1733.
[50]刘红伟,邹振,刘洪,等.地震叠前逆时偏移中的去噪与存储[J].地球物理学报,2010,53(9):2171-2180.Liu H W,Zou Z,Liu H,et al.The problem of denoise andstronge in seismic reverse time migration[J].Chinese J.Geophys.(in Chinese),2010,53(9):2171-2180.
[51]刘红伟,刘洪,李博,等.起伏地表叠前逆时偏移理论及GPU加速技术[J].地球物理学报,2011,54(7):1883-1892.Liu H W,Liu H,Li B,et al.Pre-stack reverse-timemigration for rugged topography and GPU accelerationtechnology[J].Chinese J.Geophys.(in Chinese),2011,54(7):1883-1892.
[52]李博,刘红伟,刘国锋,等.地震叠前逆时偏移算法的CPU与GPU实施对策[J].地球物理学报,2010,53(12):2938-2943.Liu B,Liu H W,Liu G F,et al.Computational strategy ofseismic pre-stack reverse time migration on CPU/GPU[J].Chinese J.Geophys.(in Chinese),2010,53(12):2938-2943.
[53]王保利,高静怀,陈文超,等.地震叠前逆时偏移的有效边界存储策略[J].地球物理学报,2012,55(7):2412-2421.Wang B L,Gao J H,Chen W C,et al.Efficient boundarystorage strategies for seismic reverse time migration[J].Chinese J.Geophys.(in Chinese),2012,55(7):2412-2421.
[54]Fletcher R F,Fowler P,Kitchenside P,et al.Suppressingartifacts in prestack reverse time migration[A].//75thAnn.Internat Mtg.,Soc.Expi.Geophys.ExpandedAbstracts[C].2005:2049-2052.
[55]Liu F Q,Zhang G Q,Morton S A,et al.Reverse-timeMigration Using One-way Wavefield Imaging Condition[A].//Expanded Abstracts of 77th Annual International SEGMeeting[C].2007:2170-2174.
[56]Guitton A,Kaelin B,Biondi B.Least-squares attenuation ofreverse-time migration artifacts[J].Geophysics,2007,72(1):S19-S23.
[57]Mulder W A,Plessix R E.A comparison between one-wayand two-way wave-equation migration[J].Geophysics,2004,69(6):1491-1504.
[58]Yoon K,Marfurt K J.Reverse-time migration using thePoynting vector[J].Exploration Geophysics,2006,37(1):102-107.
[59]Costa J C,Neto F A S,Alcantara M R M,et al.Obliquity-correction imaging condition for reverse time migration[J].Geophysics,2009,74(3):S57-S66.
[60]Chattopadhyay S,McMechan G A.Imaging conditions forprestack reverse-time migration[J].Geophysics,2008,73(3):S81-S89.
[61]Kaelin B,Guitton A.Imaging condition for reverse timemigration[A].//Expanded Abstracts of 76th AnnualInternational SEG Meeting[C].2006:2594-2598.
[62]Suh S Y.Reverse-time migration bu fan filtering plus wavefielddecomposition[A].//Expanded Abstracts of 79th AnnualInternational SEG Meeting[C].2009:2804-2807.
[63]Zhang Y,Sun J.Practical issues of reverse time migration:true amplitude gathers,noise removal and harmonic-sourceencoding[A].//CPS/SEG International GeophysicalConference&Exposition[C].2009,ID5.
[64]杨勤勇,段心标.逆时偏移技术发展现状与趋势[J].石油物探,2010,49(1):92-98.Yang Q Y,Duan X B.Development status and trend ofreverse time migration[J].Geophysical Prospecting forPetroleum(in Chinese),2010,49(1):92-98.
[65]陈可洋.地震波逆时偏移方法研究综述[J].勘探地球物理进展,2010,33(3):153-159.Chen K Y.Review of seismic reverse time migration methods[J].Progress in Exploration Geophysics(in Chinese),2010,33(3):153-159.
[66]张春燕,李振春,孙晓东.逆时偏移方法技术进展综述[J].勘探地球物理进展,2010,33(5):309-317.Zhang C Y,Li Z C,Sun X D.Review of reverse timemigration[J].Progress in Exploration Geophysics(inChinese),2010,33(3):309-317.
[67]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 L,Liu Y.Progress in reverse time migration imaging[J].Progress in Geophysics(in Chinese),2011,26(3):1085-1100.
[68]Yoon K,Marfurt K J,Starr W.Challenges in reverse-timemigration[A].//74th Annual International Meeting[C].SEG,Expanded Abstracts,2004:1057-1060.
[69]周瑞红,赵景霞.逆时偏移及其成像条件[J].内蒙古石油化工,2009,35(3):23-26.Zhou R H,Zhao J X.Reverse-time migration and its imagingconditions[J].Inner Mongulia Petrochemical Industry(inChinese),2009,35(3):23-26.
[70]徐琴,李振春,鮑伟.波动方程偏移中的成像条件研究进展[J].勘探地球物理进展,2008,31(4):247-252.Xu Q,Li Z C,Bao W.Progress in research of imagingcondition for wave equation migration[J].Progress inExploration Geophysics(in Chinese),2008,31(4):247-252.
[71]Sava P,Fomel S.Time-shift imaging condition[A].//Expanded Abstracts of 75th Annual International SEGMeeting[C].2005:1850-1854.
[72]Valenciano A A,Biondi B.Deconvolution imaging conditionfor reverse-time migration[R].Stanford Exploration Project,Report,2002,112:83-96.
[73]Bruno K,Guitton A.Imaging condition for reverse timemigration[A].//76th Annual International Meeting,SEG[C].Expanded Abstracts,2006:2594-2598.
[74]Daley P F,Horn F.Reflection and transmission coefficientsfor seismic waves in ellipsoidally anisotropic media[J].Geophysics,1979,44(1):27-38.
[75]Tsvankin I.P-wave signatures and notation for transverselyisotropic media:An overview[J].Geophysics,1996,61(2):467-483.
[76]Zhang L B,Rector J W III,Hoversten G M.An acousticwave equation for modeling in tilted TI media[A].//73rdAnnual International Meeting[C].SEG,ExpandedAbstracts,2003:153-156.
[77]Liu W,Bube K P,Zhang L B,et al.Stable reverse-timemigration in variable-title TTI media[A].//71st Conference&Exhibition[C].EAGE,Extended Abstracts,2009:64.
[78]Yoon K,Sang S,Jean J,et al.Stability and speedup issuesin TTI RTM implementation[A].//80th AnnualInternational Meeting[C].SEG,Expanded Abstracts,2010:3221-3225.
[79]Grechka V,Zhang L B,Rector J W.Shear waves in acousticanisotropic media[J].Geophysics,2004,69(2):576-582.
[80]Zhou H,Zhang G.Removing S-wave noise in TTI reversetime migration[A].//79th Annual International Meeting[C].SEG,Expanded Abstracts,2009:2849-2853.
[81]Liu F,Morton S A,Jiang S,et al.Decoupled wave equations forP-and Sv-waves in acoustic VTI media[A].//79th AnnualInternational Meeting[C].SEG,Expanded Abstracts,2009,28:2844-2848.