最小二乘傅立叶有限差分偏移
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摘要
一般偏移算法是用反演算子通过解析方法求解.最小二乘偏移方法采用另一种思路,即采用数值方法,通过解一个线性离散反问题来索求解.这样我们试着寻找一个模型匹配地震数据并能表现出其某些特点来得到偏移图像.最小二乘法能减少偏移赝像,得到更精确的偏移效果.Kirchhoff算子在最小二乘偏移方法中应用较广,但需要较多的迭代次数,而且具有Kirchhoff偏移的缺点.本文把最小二乘方法运用到基于波长延拓的波动方程偏移方法中,为提高最小二乘偏移的效率,可采用效率较高的正传播算子和反传播算子.我们利用效率较高,能适应剧烈横向变速的傅立叶有限差分正传播和反传播算子来做叠后最小二乘偏移.数值实例表明,通过少数的共轭梯度法迭代,就能得到与真实模型差别很微小的偏移效果.对于傅式变换我们采用了数值软件FFTW,其变换速度比常规FFT算法一般要快六倍以上,进一步提高了效率.本文算法很容易在并行机上实现,这些特点在处理大型数据时大有裨益.
Conventional migration algorithms utilize the inversion of a forward modeling operator by analytical means.Alternatively,least-squares migration method involves a numerical approach where the solution is retrieved by solving a linear discrete inverse problem.In this case,we intend to seek a model that fits the seismic data and exhibits some certain features.Least-squares migration reduces migration artifacts and generally produces very accurate seismic images.Kirchhoff operator is popularly used in the least-squares migration.However,many iterations are required and the methods have the drawbacks belong to the Kirchoff migration method.In this paper,we apply the least-squares technique to the wave equation migration methods based on wave extrapolation.An key to improve the efficiency of lease-squares migration is adopting efficient modeling and migrations operator.We perform least-squares migration using efficient Fourier finite-difference modeling and migration operators.Numerical examples show that the least-squares images can be efficiently retrieved in a few iterations of conjugate gradients method.In addition,we adopt the numerical software FFTW to perform Fourier transformation,which generally is more than six times quicker than conventional FFT programs,therefore the algorithm become more efficient.The algorithm can be easily implemented in parallel architecture.These features make the algorithm very attractive.
Conventional migration algorithms utilize the inversion of a forward modeling operator by analytical means.Alternatively,least-squares migration method involves a numerical approach where the solution is retrieved by solving a linear discrete inverse problem.In this case,we intend to seek a model that fits the seismic data and exhibits some certain features.Least-squares migration reduces migration artifacts and generally produces very accurate seismic images.Kirchhoff operator is popularly used in the least-squares migration.However,many iterations are required and the methods have the drawbacks belong to the Kirchoff migration method.In this paper,we apply the least-squares technique to the wave equation migration methods based on wave extrapolation.An key to improve the efficiency of lease-squares migration is adopting efficient modeling and migrations operator.We perform least-squares migration using efficient Fourier finite-difference modeling and migration operators.Numerical examples show that the least-squares images can be efficiently retrieved in a few iterations of conjugate gradients method.In addition,we adopt the numerical software FFTW to perform Fourier transformation,which generally is more than six times quicker than conventional FFT programs,therefore the algorithm become more efficient.The algorithm can be easily implemented in parallel architecture.These features make the algorithm very attractive.
引文
[1]刘伊克,常旭.地震层析成像反演中解的定量评价及其应用[J].地球物理学报,2000,43(2):251～256.
[2]宛新林,席道瑛,高尔根,沈兆武.用改进的光滑约束最小二乘正交分解法实现电阻率三维反演[J].地球物理学报,2005,48(2):439～444.
[3]LeBras R,Clayton R W.An iterative inversion of backscat-tered acoustic waves[J].Geophysics,1988,53:501～508.
[4]Lambare G,Virieux J,Mandariaga R,Jin S.Iterative asymp-totic inversion in the acoustic approximation[J].Geophysics,1992,57:1138～1154.
[5]Nemeth T,Wu C,Schuster G T.Least-squares migration of incomplete reflection data[J].Geophysics,1999,64:208～221.
[6]Duquet B,Marfurt J K,Dellinger J A.Kirchhoff modeling,inversion for reflectivity,and subsurfaceillumination[J].Geo-physics,2000,65:1195～1209.
[7]戴前伟,冯德山,何继善.KirchhOff偏移法在探地雷达正演图像处理中的应用[J].地球物理学进展,2005,20(3):849～853.
[8]吴庆举,李永华,张瑞青,张乃玲.接收函数的克希霍夫2D偏移方法[J].地球物理学报,2007,50(2):539～545.
[9]徐升,Gilles Lambaré.复杂介质下保真振幅Kirchhoff深度偏移[J].地球物理学报,2006,49(5):1431～1444.
[10]膝佃波,汪鹏程,王赟,等.利用叠前KirchhOff积分偏移识别小断裂与低幅度构造[J].地球物理学进展,2005,20(4):1035～1038.
[11]Jonathan Richard Shewchuk.An introduction to the conju-gate gradient method without the agonizing pain[J].School of Computer Science Camegie Mellon University,1994.
[12]胡祖志,胡祥云,何展翔.大地电磁非线性共轭梯度拟三维反演[J].地球物理学报,2006,49(4):1226～1234.
[13]Kuehl H,Sacchi MD.Split-step WKBJ least-squares migra-tion/inversion of incomplete data.5thSEGJ international Symposium-Imaging[J].Technology,2001.
[14]Claerbout J E.Imaging the earth′s interior[J].Blackwell Scientific Publications,1985.
[15]贾晓峰,胡天跃,王润秋.无单元法用于地震波波动方程模拟与成像[J].地球物理学进展,2006,21(1):11～17.
[16]刘礼农,高红伟,刘洪,张剑锋.三维VTI介质中波动方程深度偏移的最优分裂Fourier方法[J].地球物理学报,2005,48(2):406～414.
[17]王红落,常旭,陈传仁.基于波动方程有限差分算法的接收函数正演与偏移[J].地球物理学报,2005,48(2):415～422.
[18]贾晓峰,胡天跃.滑动最小二乘法求解地震波波动方程[J].地球物理学进展,2005,20(4):920～924.
[19]Dietrich Ristow,Thomas Ruhl.Fourier finite-difference mi-gration[J].Geophysics,1994,59:1882～1893.
[20]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):268～276.
[21]赵景霞,张叔伦,孙沛勇,倪逸.三维并行合成震源记录叠前深度偏移[J].地球物理学报,2006,49(1):205～233.
[22]王昌龙,张叔伦,赵景霞,杨其强.基于控制照明的合成震源记录交互剩余偏移速度分析[J].地球物理学报,2007,50(3):860～867.
[23]Duijindam A J W.Bayesian estimation in seismic inversion Part I-principles[J].Geophys.Prosp.,1988,36(8):878～898.
[24]Menke W.Geophysical data analysis:Discreter Inverse The-ory:Academic Press,Inc,1984.
[25]陈建江,印兴耀.基于贝叶斯理论的AVO三参数波形反演[J].地球物理学报,2007,50(4):1251～1260.
[26]Claerbout J F.Earth soundings analysis:processing versus inversion.Blackwell Scientific Publications,2004.
[2]宛新林,席道瑛,高尔根,沈兆武.用改进的光滑约束最小二乘正交分解法实现电阻率三维反演[J].地球物理学报,2005,48(2):439～444.
[3]LeBras R,Clayton R W.An iterative inversion of backscat-tered acoustic waves[J].Geophysics,1988,53:501～508.
[4]Lambare G,Virieux J,Mandariaga R,Jin S.Iterative asymp-totic inversion in the acoustic approximation[J].Geophysics,1992,57:1138～1154.
[5]Nemeth T,Wu C,Schuster G T.Least-squares migration of incomplete reflection data[J].Geophysics,1999,64:208～221.
[6]Duquet B,Marfurt J K,Dellinger J A.Kirchhoff modeling,inversion for reflectivity,and subsurfaceillumination[J].Geo-physics,2000,65:1195～1209.
[7]戴前伟,冯德山,何继善.KirchhOff偏移法在探地雷达正演图像处理中的应用[J].地球物理学进展,2005,20(3):849～853.
[8]吴庆举,李永华,张瑞青,张乃玲.接收函数的克希霍夫2D偏移方法[J].地球物理学报,2007,50(2):539～545.
[9]徐升,Gilles Lambaré.复杂介质下保真振幅Kirchhoff深度偏移[J].地球物理学报,2006,49(5):1431～1444.
[10]膝佃波,汪鹏程,王赟,等.利用叠前KirchhOff积分偏移识别小断裂与低幅度构造[J].地球物理学进展,2005,20(4):1035～1038.
[11]Jonathan Richard Shewchuk.An introduction to the conju-gate gradient method without the agonizing pain[J].School of Computer Science Camegie Mellon University,1994.
[12]胡祖志,胡祥云,何展翔.大地电磁非线性共轭梯度拟三维反演[J].地球物理学报,2006,49(4):1226～1234.
[13]Kuehl H,Sacchi MD.Split-step WKBJ least-squares migra-tion/inversion of incomplete data.5thSEGJ international Symposium-Imaging[J].Technology,2001.
[14]Claerbout J E.Imaging the earth′s interior[J].Blackwell Scientific Publications,1985.
[15]贾晓峰,胡天跃,王润秋.无单元法用于地震波波动方程模拟与成像[J].地球物理学进展,2006,21(1):11～17.
[16]刘礼农,高红伟,刘洪,张剑锋.三维VTI介质中波动方程深度偏移的最优分裂Fourier方法[J].地球物理学报,2005,48(2):406～414.
[17]王红落,常旭,陈传仁.基于波动方程有限差分算法的接收函数正演与偏移[J].地球物理学报,2005,48(2):415～422.
[18]贾晓峰,胡天跃.滑动最小二乘法求解地震波波动方程[J].地球物理学进展,2005,20(4):920～924.
[19]Dietrich Ristow,Thomas Ruhl.Fourier finite-difference mi-gration[J].Geophysics,1994,59:1882～1893.
[20]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):268～276.
[21]赵景霞,张叔伦,孙沛勇,倪逸.三维并行合成震源记录叠前深度偏移[J].地球物理学报,2006,49(1):205～233.
[22]王昌龙,张叔伦,赵景霞,杨其强.基于控制照明的合成震源记录交互剩余偏移速度分析[J].地球物理学报,2007,50(3):860～867.
[23]Duijindam A J W.Bayesian estimation in seismic inversion Part I-principles[J].Geophys.Prosp.,1988,36(8):878～898.
[24]Menke W.Geophysical data analysis:Discreter Inverse The-ory:Academic Press,Inc,1984.
[25]陈建江,印兴耀.基于贝叶斯理论的AVO三参数波形反演[J].地球物理学报,2007,50(4):1251～1260.
[26]Claerbout J F.Earth soundings analysis:processing versus inversion.Blackwell Scientific Publications,2004.
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