逆时偏移计算中的边界处理分析及应用
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摘要
在地震资料的处理中,逆时偏移方法可以实现复杂构造高精度成像,但计算量和存储量两大问题影响了该方法的实际应用.逆时偏移算法中的边界处理方式的优化可以大大减少存储量,本文讨论了记录波场边界信息的吸收边界和随机边界这两种方法的计算效率和成像效果,提出了吸收边界中只记录边界范围内未衰减单层波场的方法并通过数值实验验证了其可行性,选择了不同的边界策略应用于模型数据和实际资料的处理.结果表明:记录单层波场边界信息的吸收边界的成像效果同传统存储波场历史的方式几乎无差别,但要额外存储每个时刻的波场边界信息;随机边界不需要额外存储波场信息,但会带来边界漫反射影响和计算区域的增加;记录单层波场边界可以明显减少存储量,并且不影响成像效果.
In seismic data processing, reverse time migration (RTM) can achieve high resolution imaging for the complex structure, but the problem caused by large amount of computation and storage hinders the practical application of this method. The boundary treatment for the computation of reverse-time migration can greatly reduce the amount of storage, and in this paper, we discuss the computational efficiency and imaging effect of taking absorbing boundary and random boundary, present a new method that only records one unabsorbed layer of wavefield boundary and verify it by numerical experiment, and take different strategies in processing the modeling data and field data. The result shows:RTM imaging by absorbing boundary recording one layer of wavefield boundaries has almost no difference compared to traditional RTM by storing the history of wave propagation, but recording wavefield boundaries costs additional memory; taking random boundary doesn′t need extra memory for storing while leading to an increase in computation and the impact of diffuse by boundary; recording one layer of boundary can reduce the memory dramatically without impacting the imaging.
In seismic data processing, reverse time migration (RTM) can achieve high resolution imaging for the complex structure, but the problem caused by large amount of computation and storage hinders the practical application of this method. The boundary treatment for the computation of reverse-time migration can greatly reduce the amount of storage, and in this paper, we discuss the computational efficiency and imaging effect of taking absorbing boundary and random boundary, present a new method that only records one unabsorbed layer of wavefield boundary and verify it by numerical experiment, and take different strategies in processing the modeling data and field data. The result shows:RTM imaging by absorbing boundary recording one layer of wavefield boundaries has almost no difference compared to traditional RTM by storing the history of wave propagation, but recording wavefield boundaries costs additional memory; taking random boundary doesn′t need extra memory for storing while leading to an increase in computation and the impact of diffuse by boundary; recording one layer of boundary can reduce the memory dramatically without impacting the imaging.
引文
[1]Baysal E,Kosloff D D,Sherwood J W C.Reverse timemigration.Geophysics,1983,48(11):1514-1524.
[2]Whitmore N D.Iterative depth migration by backward timepropagation.53rd Annual International Meeting.SEG,Expanded Abstracts,1983:382-385.
[3]Claerbou J F.Toward a unified theory of reflector mapping.Geophysics,1971,36(3):467-481.
[4]Zhu J M,Lines L R.Comparison of Kirchhoff and reverse-time migration methods with applications to prestack depthimaging of complex structures.Geophysics,1998,63(4):1166-1176.
[5]Biondi B,Shan G.Prestack imaging of overturned reflectionsby reverse time migration.72nd Annual InternationalMeeting.SEG,Expanded Abstracts,2002.
[6]Yoon K,Marfurt K J,Starr W.Challenges in reverse-timemigration.74th Annual International Meeting.SEG,ExpandedAbstracts,2004:1057-1060.
[7]Fricke J R.Reverse-time migration in parallel:a tutorial.Geophysics,1988,53(9):1143-1150.
[8]Zhang J H,Wang S Q,Yao Z X.Accelerating 3DFouriermigration with Graphics Processing Units.Geophysics,2009,74(6):129-139.
[9]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.地球物理学报,2010,53(7):1725-1733.Liu H W,Li B,Liu H,et al.The algorithm of high orderfinite difference pre-stack reverse time migration and GPUimplementation.Chinese J.Geophys.(in Chinese),2010,53(7):1725-1733.
[10]Baysal E,Kosloff D D,Sherwood J W C.A 2-waynonreflecting wave equation.Geophysics,1984,49(2):132-141.
[11]Loewenthal D,Mufti I R.Reversed time migration in spatialfrequency domain.Geophysics,1983,48(5):627-635.
[12]Loewenthal D,Stoffa P L,Faria E L.Suppressing theunwanted reflections of the full wave equation.Geophysics,1987,52(7):1007-1012.
[13]Liu F Q,Zhang G Q,Morton S A,et al.Reverse-timemigration using one-way wavefield imaging condition.77thAnnual International Meeting.SEG,Expanded Abstracts,2007:2170-2174.
[14]Liu F Q,Zhang G Q,Morton S A,et al.An effectiveimaging condition for reverse-time migration using wavefielddecomposition.Geophysics,2011,76(1):S29-S39.
[15]Zhang Y,Sun J.Practical issues of reverse time migration:true amplitude gathers,noise removal and harmonic-sourceencoding.70th EAGE Conference&Exhibition,Rome,2008.
[16]杨仁虎,常旭,刘伊克.叠前逆时偏移影响因素分析.地球物理学报,2010,53(8):1902-1913.Yang R H,Chang X,Liu Y K.The influence factorsanalyses of imaging precision in pre-stack reverse timemigration.Chinses J.Geophys.(in Chinese),2010,53(8):1902-1913.
[17]杨仁虎.复杂介质地震波传播与逆时偏移成像方法研究[博士学位论文].北京:中国科学院研究生院,2010.Yang R H.The study on seismic wave propagation andreverse time migration in complex media[Ph.D.thesis](inChinese).Beijing:Graduate School of Chinese Academy ofSciences,2010.
[18]Symes W W.Reverse time migration with optimalcheckpointing.Geophysics,2007,72(5):SM213-SM221.
[19]Dussaud E,Symes W W,Williamson P,et al.Computationalstrategies for reverse-time migration.78th Annual InternationalMeeting.SEG,Expanded Abstracts,2008,27(1):2267-2271.
[20]Clapp R G.Reverse time migration with random boundaries.79th Annual International Meeting.SEG,Expanded Abstracts,2009:2809-2813.
[21]Graves R W.Simulating seismic wave propagation in 3Delastic media using staggered-grid finite differences.Bulletinof the Seismological Society of America,1996,86(4):1091-1106.
[22]Liu Y,Sen M K.An implicit staggered-grid finite-differencemethod for seismic modelling.Geophysical Journal International,2009,179(1):459-474.
[23]Kindelan M,Aamel A,Sguazzero P.On the construction andefficiency of staggered numerical differentiators for the waveequation.Geophysics,1990,55(1):107-110.
[24]Collino F,Tsogka C.Application of the perfectly matchedabsorbing layer model to the linear elastodynamic problem inanisotropic heterogeneous media.Geophysics,2001,66(1):294-307.
[25]Liu Y K,Chang X,Jin D G,et al.Reverse time migration ofmultiples for subsalt imaging.Geophysics,2011,76(5):WB209-WB216.
[2]Whitmore N D.Iterative depth migration by backward timepropagation.53rd Annual International Meeting.SEG,Expanded Abstracts,1983:382-385.
[3]Claerbou J F.Toward a unified theory of reflector mapping.Geophysics,1971,36(3):467-481.
[4]Zhu J M,Lines L R.Comparison of Kirchhoff and reverse-time migration methods with applications to prestack depthimaging of complex structures.Geophysics,1998,63(4):1166-1176.
[5]Biondi B,Shan G.Prestack imaging of overturned reflectionsby reverse time migration.72nd Annual InternationalMeeting.SEG,Expanded Abstracts,2002.
[6]Yoon K,Marfurt K J,Starr W.Challenges in reverse-timemigration.74th Annual International Meeting.SEG,ExpandedAbstracts,2004:1057-1060.
[7]Fricke J R.Reverse-time migration in parallel:a tutorial.Geophysics,1988,53(9):1143-1150.
[8]Zhang J H,Wang S Q,Yao Z X.Accelerating 3DFouriermigration with Graphics Processing Units.Geophysics,2009,74(6):129-139.
[9]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.地球物理学报,2010,53(7):1725-1733.Liu H W,Li B,Liu H,et al.The algorithm of high orderfinite difference pre-stack reverse time migration and GPUimplementation.Chinese J.Geophys.(in Chinese),2010,53(7):1725-1733.
[10]Baysal E,Kosloff D D,Sherwood J W C.A 2-waynonreflecting wave equation.Geophysics,1984,49(2):132-141.
[11]Loewenthal D,Mufti I R.Reversed time migration in spatialfrequency domain.Geophysics,1983,48(5):627-635.
[12]Loewenthal D,Stoffa P L,Faria E L.Suppressing theunwanted reflections of the full wave equation.Geophysics,1987,52(7):1007-1012.
[13]Liu F Q,Zhang G Q,Morton S A,et al.Reverse-timemigration using one-way wavefield imaging condition.77thAnnual International Meeting.SEG,Expanded Abstracts,2007:2170-2174.
[14]Liu F Q,Zhang G Q,Morton S A,et al.An effectiveimaging condition for reverse-time migration using wavefielddecomposition.Geophysics,2011,76(1):S29-S39.
[15]Zhang Y,Sun J.Practical issues of reverse time migration:true amplitude gathers,noise removal and harmonic-sourceencoding.70th EAGE Conference&Exhibition,Rome,2008.
[16]杨仁虎,常旭,刘伊克.叠前逆时偏移影响因素分析.地球物理学报,2010,53(8):1902-1913.Yang R H,Chang X,Liu Y K.The influence factorsanalyses of imaging precision in pre-stack reverse timemigration.Chinses J.Geophys.(in Chinese),2010,53(8):1902-1913.
[17]杨仁虎.复杂介质地震波传播与逆时偏移成像方法研究[博士学位论文].北京:中国科学院研究生院,2010.Yang R H.The study on seismic wave propagation andreverse time migration in complex media[Ph.D.thesis](inChinese).Beijing:Graduate School of Chinese Academy ofSciences,2010.
[18]Symes W W.Reverse time migration with optimalcheckpointing.Geophysics,2007,72(5):SM213-SM221.
[19]Dussaud E,Symes W W,Williamson P,et al.Computationalstrategies for reverse-time migration.78th Annual InternationalMeeting.SEG,Expanded Abstracts,2008,27(1):2267-2271.
[20]Clapp R G.Reverse time migration with random boundaries.79th Annual International Meeting.SEG,Expanded Abstracts,2009:2809-2813.
[21]Graves R W.Simulating seismic wave propagation in 3Delastic media using staggered-grid finite differences.Bulletinof the Seismological Society of America,1996,86(4):1091-1106.
[22]Liu Y,Sen M K.An implicit staggered-grid finite-differencemethod for seismic modelling.Geophysical Journal International,2009,179(1):459-474.
[23]Kindelan M,Aamel A,Sguazzero P.On the construction andefficiency of staggered numerical differentiators for the waveequation.Geophysics,1990,55(1):107-110.
[24]Collino F,Tsogka C.Application of the perfectly matchedabsorbing layer model to the linear elastodynamic problem inanisotropic heterogeneous media.Geophysics,2001,66(1):294-307.
[25]Liu Y K,Chang X,Jin D G,et al.Reverse time migration ofmultiples for subsalt imaging.Geophysics,2011,76(5):WB209-WB216.
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