基于优化算子边界存储策略的高效逆时偏移方法
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摘要
随着高性能计算技术的快速发展,逆时偏移在地震勘探中的应用越来越广泛,但一直受限于昂贵的计算成本和巨大的存储需求。为此,提出一种基于优化算子边界存储策略的高效逆时偏移方法:首先将一阶声波方程从笛卡尔坐标系下变换至曲线坐标系下,实现深度域速度场到垂直时间域速度场的转换,在垂直时间域的逆时偏移可降低纵向采样率,克服高速区域的过采样问题,提升计算效率;其次,借鉴震源波场近似的思路,由近似差分公式构造出优化算子,利用优化算子代替特定的差分项,推导了震源波场的近似重构方程,该策略仅需存储一层边界波场,可有效降低逆时偏移的存储量。数值算例结果表明,提出的基于优化算子边界存储策略的垂直时间域声波逆时偏移方法能够有效降低常规逆时偏移方法的存储量和计算时间,同时能够对复杂结构精确成像,具有良好的实用性。
The application of the reverse time migration(RTM)is still limited by its expensive computing costs and huge storage requirements although it has been more widely used in the seismic exploration with the rapid development of high-performance computing technology.In this paper,an efficient RTM method based on optimal operator boundary storage strategy is proposed.Firstly,the first-order equation is transformed into a curved coordinate system from Cartesian coordinate system to realize the conversion of velocity field from the depth domain to the vertical time domain.The RTM in the vertical time domain can reduce the vertical sampling rate,overcome the oversampling problem in high-velocity zones,and improve the computational efficiency.Secondly,based on the source wavefield approximation,an optimal operator is constructed by the approximate difference formula to replace the specific difference term,and the approximate reconstruction equation of the source wavefield is derived.This strategy only needs to store one layer of boundary wavefield,which can effectively reduce the storage of RTM.The numerical results show that the vertical time domain acoustic wave RTM method based on the optimal operator boundary storage strategy has good practicality,which can effectively reduce the storage capacity and calculation time,and accurately image complex structures.
The application of the reverse time migration(RTM)is still limited by its expensive computing costs and huge storage requirements although it has been more widely used in the seismic exploration with the rapid development of high-performance computing technology.In this paper,an efficient RTM method based on optimal operator boundary storage strategy is proposed.Firstly,the first-order equation is transformed into a curved coordinate system from Cartesian coordinate system to realize the conversion of velocity field from the depth domain to the vertical time domain.The RTM in the vertical time domain can reduce the vertical sampling rate,overcome the oversampling problem in high-velocity zones,and improve the computational efficiency.Secondly,based on the source wavefield approximation,an optimal operator is constructed by the approximate difference formula to replace the specific difference term,and the approximate reconstruction equation of the source wavefield is derived.This strategy only needs to store one layer of boundary wavefield,which can effectively reduce the storage of RTM.The numerical results show that the vertical time domain acoustic wave RTM method based on the optimal operator boundary storage strategy has good practicality,which can effectively reduce the storage capacity and calculation time,and accurately image complex structures.
引文
[1] Baysal E,Kosloff D D and Sherwood W C.Reverse time migration[J].Geophysics,1983,48(11):1514-1524.
[2] McMechan G A.Migration by extrapolation of time-dependent boundary values[J].Geophysical Prospecting,1983,31(3):413-420.
[3] Whitmore N D.Iterative depth migration by backward time propagation[C].SEG Technical Program Expanded Abstracts,1983,2:382-385.
[4] Biondi B and Shan G.Prestack imaging of overturned reflections by reverse time migration[C].SEG Technical Program Expanded Abstracts,2002,21:1284-1287.
[5] Yoon K,Marfurt K J,Starr W.Challenges in reverse-time migration[C].SEG Technical Program Expanded Abstracts,2004:23:1057-1060.
[6] 杨午阳,张厚柱,撒利明,等.RTM有关问题探讨[J].石油地球物理勘探,2016,51(6):1251-1262.YANG Wuyang,ZHANG Houzhu,SA Liming,et al.Some issues about reverse time migration[J].Oil Geo-physical Prospecting,2016,51 (6):1251-1262.
[7] 姜国博,曾庆芹,李虹,等.RTM技术在土库曼斯坦地区的应用[J].石油地球物理勘探,2017,52(增刊2):81-83,103.JIANG Guobo,ZENG Qingqin,LI Hong,et al.Reverse time migration for the Block X in Turkmenistan[J].Oil Geophysical Prospecting,2017,52 (S2):81-85,103.
[8] 李海强,杨国权,李振春,等.基于局部平面波分解的逆时偏移角道集提取方法[J].石油地球物理勘探,2017,52(6):1177-1183.LI Haiqiang,YANG Guoquan,LI Zhenchun,et al.A method for extracting angle-domain common image gathers based on local plane wave decomposition[J].Oil Geophysical Prospecting,2017,52(6):1177-1183.
[9] Kreiss H O,Oliger J.Comparison of accurate methods for the integration of hyperbolic equations[J].Tellus,1972,24(3):199-215.
[10] 王伟国,熊水金,徐华宁,等.TTI 介质各向异性伪谱法RTM[J].石油地球物理勘探,2012,47(4):566-572.WANG Weiguo,XIONG Shuijin,XU Huaning,et al.Reverse time migration using pseudo-spectral method for tilted TI media[J].Oil Geophysical Prospecting,2012,47(4):566-572.
[11] Jastram C,Tessmer E.Elastic modelling on a grid with vertically varying spacing[J].Geophysical Prospecting,1994,42(4):357-370.
[12] 黄建平,黄金强,李振春,等.TTI介质一阶qP波方程交错网格伪谱法正演模拟[J].石油地球物理勘探,2016,51(3):487-496.HUANG Jianping,HUANG Jinqiang,LI Zhenchun,et al.Staggered grid pseudo-spectral numerical simulation of first-order quasi P-wave equation for TTI media[J].Oil Geophysical Prospecting,2016,51 (3):487-496.
[13] Fomel S,Ying L,Song X.Seismic wave extrapolation using low rank symbol approximation[J].Geophysical Prospecting,2013,61(3):526-536.
[14] 刘红伟,李博,刘洪,等.地震叠前RTM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 Hongwei,LI Bo,LIU Hong,et al.The reverse time algorithm of high order finite difference pre-stack migration and GPU implementation[J].Chinese Journal of Geophysics,2010,53(7):1725-1733.
[15] Nunes V,Minkoff S E.Imaging via subgrid upscaling and reverse time migration[C].SEG Technical Program Expanded Abstracts,2014,33:4008-4013.
[16] Liu Y,Sen M K.A new time-space domain high-order finite-difference method for the acoustic wave equa-tion[J].Journal of Computational Physics,2009,228(23):8779-8806.
[17] 张剑锋.弹性波数值模拟的非规则网格差分法[J].地球物理学报,1998,41(增刊1):357-366.ZHANG Jianfeng.Non-orthogonal grid finite difference method for numerical simulation of elastic wave propagation[J].Chinese Journal of Geophysics,1998,41(S1):357-366.
[18] Moczo P.Finite-difference technique for SH-waves in 2-D media using irregular grids:application to the seismic response problem[J].Geophysical Journal International,1989,99(2):321-329.
[19] 黄超,董良国.可变网格与局部时间步长的交错网格高阶差分弹性波模拟[J].地球物理学报,2009,52(11):2870-2878.HUANG Chao,DONG Liangguo.Staggered-grid high-order finite-difference method in elastic wave simulation with variable grids and local time-steps[J].Chinese Journal of Geophysics,2009,52(11):2870-2878.
[20] 宓铁良,孙兵兵,杨慧珠.基于第二代小波自适应网格的二维声波方程波传模拟[J].地球物理学报,2009,52(11):2862-2869.MI Tieliang,SUN Bingbing,YANG Huizhu.Adaptive mesh based on second generation wavelet simulation wave propagation for 2D acoustic wave equation[J].Chinese Journal of Geophysics,2009,52(11):2862-2869.
[21] Tessmer E.Seismic finite-difference modeling with spatially varying time steps[J].Geophysics,2000,65(4):1290-1293.
[22] Alkhalifah T,Fomel S and Biondi B.The space-time domain:Theory and modelling for anisotropic media[J].Geophysical Journal International,2001,144(1):105-113.
[23] 李庆洋,黄建平,李振春,等.伪深度域声波数值模拟方法及应用[J].石油地球物理勘探,2015,50(2):283-289.LI Qingyang,HUANG Jianping,LI Zhenchun,et al.Acoustic wave numerical simulation in pseudo-depth domain[J].Oil Geophysical Prospecting,2015,50(2):283-289.
[24] Plessix R E,Milcik P,Corcoran C,et al.Full wave-form inversion with a pseudo-time approach[C].Extended Abstracts of 74th EAGE Conference & Exhibition,2012,W012.
[25] Li Q Y,Li Z C,Huang J P,et al.Least-squares reverse time migration in pseudo-time domain[C].Extended Abstracts of 78th EAGE Conference & Exhibition,2016,P105.
[26] Claerbout J F.Toward a unified theory of reflector mapping[J].Geophysics,1971,36(3):467-481.
[27] Gauthier O,Virieux J and Tarantola A.Two-dimensional nonlinear inversion of seismic waveforms:Numerical results[J].Geophysics,1986,51(7):1387-1403.
[28] Dussaud E,Symes W W,Williamson P,et al.Computational strategies for reverse time migration[C].SEG Technical Program Expanded Abstracts,2008,27:2267-2271.
[29] 杨仁虎,凌云,瞿立建,等.基于边界存储的地震波场重构及RTM成像应用研究[J].地球物理学进展,2017,32(3):1286-1289.YANG Renhu,LING Yun,QU Lijian,et al.Seismic wavefield reconstruction based on boundary storage and application of reverse time migration[J].Progress in Geophysics,2017,32(3):1286-1289.
[30] Symes W W.Reverse time migration with optimal checkpointing[J].Geophysics,2007,72(5):SM213-SM221.
[31] 宋利伟,石颖,柯璇,等.基于检查点方法的各向异性介质逆时偏移[J].石油物探,2018,57(2):274-282.SONG Liwei,SHI Ying,KE Xuan,et al.Reverse time migration of anisotropic media using the checkpoint method[J].Geophysical Prospecting for Petroleum,2018,57(2):274-282.
[32] Clapp R.Reverse time migration with random bound-aries[C].SEG Technical Program Expanded Abstracts,2009,28:2809-2813.
[33] 王保利,高静怀,陈文超,等.地震叠前RTM的有效边界存储策略[J].地球物理学报,2012,55(7):2412-2421.WANG Baoli,GAO Jinghuai,CHEN Wenchao,et al.Efficient boundary storage strategies for seismic reverse time migration[J]. Chinese Journal of Geophy-sics,2012,55(7):2412-2421.
[34] Feng B,Wang H Z.Reverse time migration with source wavefield reconstruction strategy[J].Journal of Geophysics and Engineering,2012,9(1):69-74.
[35] Sun W and Fu L Y.Two effective approaches to reduce data storage in reverse time migration[J].Computers & Geosciences,2013,56:69-75.
[36] Nguyen B D,McMechan G A.Five ways to avoid storing source wavefield snapshots in 2D elastic prestack reverse time migration[J].Geophysics,2015,80(1):S1-S18.
[37] Liu S,Li X,Wang W,et al.Source wavefield reconstruction using a linear combination of the boundary wavefield in reverse time migration[J].Geophysics,2015,80(6):S203-S212.
[38] Vasmel M,Robertsson J O A.Exact wavefield reconstruction on finite-difference grids with minimal me-mory requirements[J].Geophysics,2016,81(6):T303-T309.
[2] McMechan G A.Migration by extrapolation of time-dependent boundary values[J].Geophysical Prospecting,1983,31(3):413-420.
[3] Whitmore N D.Iterative depth migration by backward time propagation[C].SEG Technical Program Expanded Abstracts,1983,2:382-385.
[4] Biondi B and Shan G.Prestack imaging of overturned reflections by reverse time migration[C].SEG Technical Program Expanded Abstracts,2002,21:1284-1287.
[5] Yoon K,Marfurt K J,Starr W.Challenges in reverse-time migration[C].SEG Technical Program Expanded Abstracts,2004:23:1057-1060.
[6] 杨午阳,张厚柱,撒利明,等.RTM有关问题探讨[J].石油地球物理勘探,2016,51(6):1251-1262.YANG Wuyang,ZHANG Houzhu,SA Liming,et al.Some issues about reverse time migration[J].Oil Geo-physical Prospecting,2016,51 (6):1251-1262.
[7] 姜国博,曾庆芹,李虹,等.RTM技术在土库曼斯坦地区的应用[J].石油地球物理勘探,2017,52(增刊2):81-83,103.JIANG Guobo,ZENG Qingqin,LI Hong,et al.Reverse time migration for the Block X in Turkmenistan[J].Oil Geophysical Prospecting,2017,52 (S2):81-85,103.
[8] 李海强,杨国权,李振春,等.基于局部平面波分解的逆时偏移角道集提取方法[J].石油地球物理勘探,2017,52(6):1177-1183.LI Haiqiang,YANG Guoquan,LI Zhenchun,et al.A method for extracting angle-domain common image gathers based on local plane wave decomposition[J].Oil Geophysical Prospecting,2017,52(6):1177-1183.
[9] Kreiss H O,Oliger J.Comparison of accurate methods for the integration of hyperbolic equations[J].Tellus,1972,24(3):199-215.
[10] 王伟国,熊水金,徐华宁,等.TTI 介质各向异性伪谱法RTM[J].石油地球物理勘探,2012,47(4):566-572.WANG Weiguo,XIONG Shuijin,XU Huaning,et al.Reverse time migration using pseudo-spectral method for tilted TI media[J].Oil Geophysical Prospecting,2012,47(4):566-572.
[11] Jastram C,Tessmer E.Elastic modelling on a grid with vertically varying spacing[J].Geophysical Prospecting,1994,42(4):357-370.
[12] 黄建平,黄金强,李振春,等.TTI介质一阶qP波方程交错网格伪谱法正演模拟[J].石油地球物理勘探,2016,51(3):487-496.HUANG Jianping,HUANG Jinqiang,LI Zhenchun,et al.Staggered grid pseudo-spectral numerical simulation of first-order quasi P-wave equation for TTI media[J].Oil Geophysical Prospecting,2016,51 (3):487-496.
[13] Fomel S,Ying L,Song X.Seismic wave extrapolation using low rank symbol approximation[J].Geophysical Prospecting,2013,61(3):526-536.
[14] 刘红伟,李博,刘洪,等.地震叠前RTM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 Hongwei,LI Bo,LIU Hong,et al.The reverse time algorithm of high order finite difference pre-stack migration and GPU implementation[J].Chinese Journal of Geophysics,2010,53(7):1725-1733.
[15] Nunes V,Minkoff S E.Imaging via subgrid upscaling and reverse time migration[C].SEG Technical Program Expanded Abstracts,2014,33:4008-4013.
[16] Liu Y,Sen M K.A new time-space domain high-order finite-difference method for the acoustic wave equa-tion[J].Journal of Computational Physics,2009,228(23):8779-8806.
[17] 张剑锋.弹性波数值模拟的非规则网格差分法[J].地球物理学报,1998,41(增刊1):357-366.ZHANG Jianfeng.Non-orthogonal grid finite difference method for numerical simulation of elastic wave propagation[J].Chinese Journal of Geophysics,1998,41(S1):357-366.
[18] Moczo P.Finite-difference technique for SH-waves in 2-D media using irregular grids:application to the seismic response problem[J].Geophysical Journal International,1989,99(2):321-329.
[19] 黄超,董良国.可变网格与局部时间步长的交错网格高阶差分弹性波模拟[J].地球物理学报,2009,52(11):2870-2878.HUANG Chao,DONG Liangguo.Staggered-grid high-order finite-difference method in elastic wave simulation with variable grids and local time-steps[J].Chinese Journal of Geophysics,2009,52(11):2870-2878.
[20] 宓铁良,孙兵兵,杨慧珠.基于第二代小波自适应网格的二维声波方程波传模拟[J].地球物理学报,2009,52(11):2862-2869.MI Tieliang,SUN Bingbing,YANG Huizhu.Adaptive mesh based on second generation wavelet simulation wave propagation for 2D acoustic wave equation[J].Chinese Journal of Geophysics,2009,52(11):2862-2869.
[21] Tessmer E.Seismic finite-difference modeling with spatially varying time steps[J].Geophysics,2000,65(4):1290-1293.
[22] Alkhalifah T,Fomel S and Biondi B.The space-time domain:Theory and modelling for anisotropic media[J].Geophysical Journal International,2001,144(1):105-113.
[23] 李庆洋,黄建平,李振春,等.伪深度域声波数值模拟方法及应用[J].石油地球物理勘探,2015,50(2):283-289.LI Qingyang,HUANG Jianping,LI Zhenchun,et al.Acoustic wave numerical simulation in pseudo-depth domain[J].Oil Geophysical Prospecting,2015,50(2):283-289.
[24] Plessix R E,Milcik P,Corcoran C,et al.Full wave-form inversion with a pseudo-time approach[C].Extended Abstracts of 74th EAGE Conference & Exhibition,2012,W012.
[25] Li Q Y,Li Z C,Huang J P,et al.Least-squares reverse time migration in pseudo-time domain[C].Extended Abstracts of 78th EAGE Conference & Exhibition,2016,P105.
[26] Claerbout J F.Toward a unified theory of reflector mapping[J].Geophysics,1971,36(3):467-481.
[27] Gauthier O,Virieux J and Tarantola A.Two-dimensional nonlinear inversion of seismic waveforms:Numerical results[J].Geophysics,1986,51(7):1387-1403.
[28] Dussaud E,Symes W W,Williamson P,et al.Computational strategies for reverse time migration[C].SEG Technical Program Expanded Abstracts,2008,27:2267-2271.
[29] 杨仁虎,凌云,瞿立建,等.基于边界存储的地震波场重构及RTM成像应用研究[J].地球物理学进展,2017,32(3):1286-1289.YANG Renhu,LING Yun,QU Lijian,et al.Seismic wavefield reconstruction based on boundary storage and application of reverse time migration[J].Progress in Geophysics,2017,32(3):1286-1289.
[30] Symes W W.Reverse time migration with optimal checkpointing[J].Geophysics,2007,72(5):SM213-SM221.
[31] 宋利伟,石颖,柯璇,等.基于检查点方法的各向异性介质逆时偏移[J].石油物探,2018,57(2):274-282.SONG Liwei,SHI Ying,KE Xuan,et al.Reverse time migration of anisotropic media using the checkpoint method[J].Geophysical Prospecting for Petroleum,2018,57(2):274-282.
[32] Clapp R.Reverse time migration with random bound-aries[C].SEG Technical Program Expanded Abstracts,2009,28:2809-2813.
[33] 王保利,高静怀,陈文超,等.地震叠前RTM的有效边界存储策略[J].地球物理学报,2012,55(7):2412-2421.WANG Baoli,GAO Jinghuai,CHEN Wenchao,et al.Efficient boundary storage strategies for seismic reverse time migration[J]. Chinese Journal of Geophy-sics,2012,55(7):2412-2421.
[34] Feng B,Wang H Z.Reverse time migration with source wavefield reconstruction strategy[J].Journal of Geophysics and Engineering,2012,9(1):69-74.
[35] Sun W and Fu L Y.Two effective approaches to reduce data storage in reverse time migration[J].Computers & Geosciences,2013,56:69-75.
[36] Nguyen B D,McMechan G A.Five ways to avoid storing source wavefield snapshots in 2D elastic prestack reverse time migration[J].Geophysics,2015,80(1):S1-S18.
[37] Liu S,Li X,Wang W,et al.Source wavefield reconstruction using a linear combination of the boundary wavefield in reverse time migration[J].Geophysics,2015,80(6):S203-S212.
[38] Vasmel M,Robertsson J O A.Exact wavefield reconstruction on finite-difference grids with minimal me-mory requirements[J].Geophysics,2016,81(6):T303-T309.