起伏地表条件下基于复Pade逼近的叠前深度偏移
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摘要
叠前深度偏移是解决复杂地表和复杂构造地震成像的有效技术,而波场"直接下延"法实现了复杂地表条件下的地震成像.基于上述成果,结合高精度的波场延拓算子,本文提出了一种新的叠前深度偏移方法,这种方法是在波场延拓时,对声波方程中的平方根项进行复Pade逼近,通过推导得到基于复Pade逼近的傅里叶有限差分算子,结合波场"直接下延"法,实现了起伏地表条件下的叠前深度偏移,该算法减少了偏移噪音,从而得到准确、稳定的偏移成像结果.通过理论模型试算和实际资料试处理,验证了该方法的有效性.
Oil and gas exploration is turning to the areas with irregular topography and complex geologic structures.Prestack depth migration is a valid way to deal with irregular topography and complex geologic structures."Wave field downward continuation" based on accumulating step by step is a valid way to solve the problem of irregular surface migration.Based on these achievements,this paper shows a new prestack depth migration method combined with high-precision wave field continuation operator.A complex Pade approximation of the square root of the acoustic wave equation is used for wavefield extrapolation.We derive the Fourier finite difference operator based on complex Pade approximation.Based on this operator,we use the method of "wave field downward continuation" to achieve the prestack depth migration of irregular topography.It produces images with fewer noises and yields accurate and stable imaging results.Tests on the Marmousi model data set and the real seismic data show that the superiority of the proposed migration method.Compared to other migration methods,this method has better migration quality.
Oil and gas exploration is turning to the areas with irregular topography and complex geologic structures.Prestack depth migration is a valid way to deal with irregular topography and complex geologic structures."Wave field downward continuation" based on accumulating step by step is a valid way to solve the problem of irregular surface migration.Based on these achievements,this paper shows a new prestack depth migration method combined with high-precision wave field continuation operator.A complex Pade approximation of the square root of the acoustic wave equation is used for wavefield extrapolation.We derive the Fourier finite difference operator based on complex Pade approximation.Based on this operator,we use the method of "wave field downward continuation" to achieve the prestack depth migration of irregular topography.It produces images with fewer noises and yields accurate and stable imaging results.Tests on the Marmousi model data set and the real seismic data show that the superiority of the proposed migration method.Compared to other migration methods,this method has better migration quality.
引文
[1]Gazdag J,Sguazzero P.Migration of seismic data by phase shiftplus interpolation[J].Geophysics,1984,49(2):124-131.
[2]Stoffa P L,Fokkema J T,de Luna Freire R M,et al.Split-step Fourier migration[J].Geophysics,1990,55(4):410-421.
[3]Hale D.Stable explicit depth extrapolation of seismic wavefields[J].Geophysics,1991,56(11):1770-1777.
[4]Ristow D,Ruhl T.Fourier finite-difference migration[J].Geophysics,1994,59(12):1882-1893.
[5]刘定进,印兴耀.傅里叶有限差分法保幅叠前深度偏移方法[J].地球物理学报,2007,50(1):168-276.Liu D J;Yin X Y.A method of Fourier finite_differencepreserved_amplitude prestack depth migration[J].Chinese J.Geophys.(in Chinese),2007,50(1):168-276.
[6]M illinazzo F A,Zala C A,Brooke G H.Square-rootapproximations for parabolic equation algorithms[J].J.Acoust.Soc.Am.,1997,101(2):760-766.
[7]Biondi B.Stable wide-angle Fourier finite-difference downwardextrapolation of 3-D wavefields[J].Geophysics,2002,67(3):872-882.
[8]Zhang L,Rector J W,Hoversten G M.Split-step complexPade migration[J].Journal of Seismic Exploration,2003,12(2):229-236.
[9]Zhang L,Rector J W,Hoversten,et al.Split-step complexPade-Fourier depth migration[J].Expanded abstracts of 74thSEG Mtg,2004.989-992.
[10]Amazonas D,C.Costa J,Schleicher J,et al.Wide-angle FDand FFD migration using complex Pade approximations[J].Geophysics,2007,72(6):S215-S220.
[11]Reshef,M.Depth migration from irregular surface with thedepth extrapolation methods[J].Geophysics,1991,56(1):119-122.
[12]李振春.地震成像理论与方法[M].青岛:石油大学研究生院,2004.Li Z C.Seismic imaging theory and method[M].Qingdao:Graduate school of University of Petroleum,2004.
[13]Beasley,Lynn.The zero velocity layer:Migration fromirregular surfaces[J].Geophysics,1992,57(11):1435-1443.
[14]Beasley C J,Lynn W.The zero welocity layer:migration fromirregular surfaces[J].Expanded abstracts of 59th SEG Mtg,1989,1179-1183.
[15]Yang Kai,Wang Huazhong,Ma Zaitian.Wave equationdatuming from irregular surfaces using finite differencescheme[J].Expanded abstracts of 69th SEG Mtg,1999.1456-1459.
[16]何英,王华忠,马在田,等.复杂地形条件下波动方程叠前深度成像[J].勘探地球物理进展,2002,25(3):13-19.He Y,Wang H Z,Ma Z T,et al.Pre-stack wave equationdepth migration for irregular topography[J].Progress inExploration Geophysics(in Chinese),2002,25(3):13-19.
[17]田文辉,李振春,张辉.直接下延法波动方程叠前深度偏移[J].石油物探,2006,45(5):447-451.Tian W H,Li Z C,Zhang H.Direct continuation methodbased on wave equation for prestack depth Migration[J].Geophysical Prospecting for Petroleum.(in Chinese),2006,45(5):447-451.
[18]叶月明,李振春,仝兆岐,等.双复杂介质条件下频率空间域有限差分法保幅偏移[J].地球物理学报,2008,51(5):1511-1519.Ye Y M,Li Z C,Tong Z Q,et al.Xwfd preserved-amplitudemigration with dual-complexity[J].Chinese J.Geophys.(inChinese),2008,51(5):1511-1519.
[19]叶月明,李振春,仝兆岐,等.双复杂条件下带误差补偿的频率空间域有限差分法叠前深度偏移[J].地球物理学进展,2008,23(1):136-145.YeY M,Li Z C,Tong Z Q,et al.Xwfd pre-stack depthmigration based on dual-complexity with error compensationcorrection[J].Progress in Geophysics(in Chinese),2008,23(1):136-145.
[20]李振春,叶月明,仝兆岐.起伏地表条件下基于高阶广义屏算子的叠前深度偏移[J].勘探地球物理进展,2007,30(5):377-381.Li Z C,Ye Y M,Tong Z Q.High order generalized screenpropagator prestack depth migration for irregular Topography[J].Progress in Exploration Geophysics(in Chinese),2007,30(5):377-381.
[21]郭淑娟,李振春,仝兆岐,等.起伏地表条件下分块法插值叠前深度偏移[J].地球物理学进展,2011,26(1):214-219.Guo S J,Li Z C,Tong Z Q,et al.Pre-stack depth migrationunder complex surface using blocking interpolation algorithm[J].Progress in Geophysics(in Chinese),2011,26(1):214-219.
[22]刘庆敏,李振春,李留中,等.双复杂条件下的波动方程叠前深度偏移[J].地球物理学进展,2007,22(6):1884-1888.Liu Q M,Li Z C,Li L Z,et al.Wave equation pre-stackdepth migration with dual-complexity[J].Progress inGeophysics(in Chinese),2007,22(6):1884-1888.
[23]Gazdag J.Wave equation migration with the phase-shift method[J].Geophysics,1978,73(7):1342-1351.
[24]Bamberger A,Engquist B.Higher order paraxial wave equationapproximations in heterogeneous media[J].Journal ofApplied Mathematics,1988,48(1):129-154.
[25]张宇,徐升,张关泉,等.真振幅全倾角单程波方程偏移方法[J].石油物探,2007,46(6):582-587.Zhang Y,Xu S,Zhang G Q,et al.True amplitude turning-wave one-way wave equation migration[J].GeophysicalProspecting for Petroleum(in Chinese),2007,46(6):582-587.
[26]Zhang Y,Zhang G.Theory of true amplitude common-shotmigration[J].Expanded abstracts of 72th SEG Mtg,2002,2471-2473.
[2]Stoffa P L,Fokkema J T,de Luna Freire R M,et al.Split-step Fourier migration[J].Geophysics,1990,55(4):410-421.
[3]Hale D.Stable explicit depth extrapolation of seismic wavefields[J].Geophysics,1991,56(11):1770-1777.
[4]Ristow D,Ruhl T.Fourier finite-difference migration[J].Geophysics,1994,59(12):1882-1893.
[5]刘定进,印兴耀.傅里叶有限差分法保幅叠前深度偏移方法[J].地球物理学报,2007,50(1):168-276.Liu D J;Yin X Y.A method of Fourier finite_differencepreserved_amplitude prestack depth migration[J].Chinese J.Geophys.(in Chinese),2007,50(1):168-276.
[6]M illinazzo F A,Zala C A,Brooke G H.Square-rootapproximations for parabolic equation algorithms[J].J.Acoust.Soc.Am.,1997,101(2):760-766.
[7]Biondi B.Stable wide-angle Fourier finite-difference downwardextrapolation of 3-D wavefields[J].Geophysics,2002,67(3):872-882.
[8]Zhang L,Rector J W,Hoversten G M.Split-step complexPade migration[J].Journal of Seismic Exploration,2003,12(2):229-236.
[9]Zhang L,Rector J W,Hoversten,et al.Split-step complexPade-Fourier depth migration[J].Expanded abstracts of 74thSEG Mtg,2004.989-992.
[10]Amazonas D,C.Costa J,Schleicher J,et al.Wide-angle FDand FFD migration using complex Pade approximations[J].Geophysics,2007,72(6):S215-S220.
[11]Reshef,M.Depth migration from irregular surface with thedepth extrapolation methods[J].Geophysics,1991,56(1):119-122.
[12]李振春.地震成像理论与方法[M].青岛:石油大学研究生院,2004.Li Z C.Seismic imaging theory and method[M].Qingdao:Graduate school of University of Petroleum,2004.
[13]Beasley,Lynn.The zero velocity layer:Migration fromirregular surfaces[J].Geophysics,1992,57(11):1435-1443.
[14]Beasley C J,Lynn W.The zero welocity layer:migration fromirregular surfaces[J].Expanded abstracts of 59th SEG Mtg,1989,1179-1183.
[15]Yang Kai,Wang Huazhong,Ma Zaitian.Wave equationdatuming from irregular surfaces using finite differencescheme[J].Expanded abstracts of 69th SEG Mtg,1999.1456-1459.
[16]何英,王华忠,马在田,等.复杂地形条件下波动方程叠前深度成像[J].勘探地球物理进展,2002,25(3):13-19.He Y,Wang H Z,Ma Z T,et al.Pre-stack wave equationdepth migration for irregular topography[J].Progress inExploration Geophysics(in Chinese),2002,25(3):13-19.
[17]田文辉,李振春,张辉.直接下延法波动方程叠前深度偏移[J].石油物探,2006,45(5):447-451.Tian W H,Li Z C,Zhang H.Direct continuation methodbased on wave equation for prestack depth Migration[J].Geophysical Prospecting for Petroleum.(in Chinese),2006,45(5):447-451.
[18]叶月明,李振春,仝兆岐,等.双复杂介质条件下频率空间域有限差分法保幅偏移[J].地球物理学报,2008,51(5):1511-1519.Ye Y M,Li Z C,Tong Z Q,et al.Xwfd preserved-amplitudemigration with dual-complexity[J].Chinese J.Geophys.(inChinese),2008,51(5):1511-1519.
[19]叶月明,李振春,仝兆岐,等.双复杂条件下带误差补偿的频率空间域有限差分法叠前深度偏移[J].地球物理学进展,2008,23(1):136-145.YeY M,Li Z C,Tong Z Q,et al.Xwfd pre-stack depthmigration based on dual-complexity with error compensationcorrection[J].Progress in Geophysics(in Chinese),2008,23(1):136-145.
[20]李振春,叶月明,仝兆岐.起伏地表条件下基于高阶广义屏算子的叠前深度偏移[J].勘探地球物理进展,2007,30(5):377-381.Li Z C,Ye Y M,Tong Z Q.High order generalized screenpropagator prestack depth migration for irregular Topography[J].Progress in Exploration Geophysics(in Chinese),2007,30(5):377-381.
[21]郭淑娟,李振春,仝兆岐,等.起伏地表条件下分块法插值叠前深度偏移[J].地球物理学进展,2011,26(1):214-219.Guo S J,Li Z C,Tong Z Q,et al.Pre-stack depth migrationunder complex surface using blocking interpolation algorithm[J].Progress in Geophysics(in Chinese),2011,26(1):214-219.
[22]刘庆敏,李振春,李留中,等.双复杂条件下的波动方程叠前深度偏移[J].地球物理学进展,2007,22(6):1884-1888.Liu Q M,Li Z C,Li L Z,et al.Wave equation pre-stackdepth migration with dual-complexity[J].Progress inGeophysics(in Chinese),2007,22(6):1884-1888.
[23]Gazdag J.Wave equation migration with the phase-shift method[J].Geophysics,1978,73(7):1342-1351.
[24]Bamberger A,Engquist B.Higher order paraxial wave equationapproximations in heterogeneous media[J].Journal ofApplied Mathematics,1988,48(1):129-154.
[25]张宇,徐升,张关泉,等.真振幅全倾角单程波方程偏移方法[J].石油物探,2007,46(6):582-587.Zhang Y,Xu S,Zhang G Q,et al.True amplitude turning-wave one-way wave equation migration[J].GeophysicalProspecting for Petroleum(in Chinese),2007,46(6):582-587.
[26]Zhang Y,Zhang G.Theory of true amplitude common-shotmigration[J].Expanded abstracts of 72th SEG Mtg,2002,2471-2473.
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