基于有理式近似的高精度波场传播算子
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摘要
以地震波单程波传播方程为基础,利用有理式展开方法,推导出一种新的高精度波场传播算子。该算子波场延拓满足分裂步框架,采用快速傅里叶变换(FFT)进行计算。频散曲线分析以及数值试验的对比研究表明:本文方法的波场成像能力明显优于裂步傅里叶法(SSF),可以达到与傅里叶有限差分法(FFD)类似的波场成像效果。计算效率方面,其波场延拓只需三次FFT计算和一次插值,仅比SSF多了一次FFT和插值,但比FFD(计算量相当于五次FFT)少了两次FFT。这种算子不仅精度高,稳定性好,而且计算效率高,具有重要的理论意义和实际应用价值。
Based on one-way wave equation,we propose a new wave-field extrapolation operator of high-accuracy using rational expansion method.This operator uses split-step framework and Fast Fourier Transforms(FFT) in wave-field continuation.Analysis results of dispersion curves and numerical experiments show that the imaging capability of this operator is significantly better than split-step Fourier method(SSF).Its imaging capability is nearly as good as Fourier Finite Difference method(FFD).In the aspect of computing efficiency,the operator only needs 3 FFTs and one interpolation,which is one more FFT and interpolation than conventional SSF(needs 2 FFTs) in computation,but two FFTs less than FFD(equivalent to 5 FFTs).It is not only highly accurate,unconditionally stable,but also highly efficient in migration imaging.This method is of important theoretical and practical significance.
Based on one-way wave equation,we propose a new wave-field extrapolation operator of high-accuracy using rational expansion method.This operator uses split-step framework and Fast Fourier Transforms(FFT) in wave-field continuation.Analysis results of dispersion curves and numerical experiments show that the imaging capability of this operator is significantly better than split-step Fourier method(SSF).Its imaging capability is nearly as good as Fourier Finite Difference method(FFD).In the aspect of computing efficiency,the operator only needs 3 FFTs and one interpolation,which is one more FFT and interpolation than conventional SSF(needs 2 FFTs) in computation,but two FFTs less than FFD(equivalent to 5 FFTs).It is not only highly accurate,unconditionally stable,but also highly efficient in migration imaging.This method is of important theoretical and practical significance.
引文
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[2]马在田.高阶有限差分偏移.石油地球物理勘探,1982,17(1):6～15Ma Zaitian.High order finite-difference migration.OGP,1982,17(1):6～15
[3]Gazdag J.Wave equation migration with the phase-shift method.Geophysics,1978,43(7):1342～1351
[4]贺振华.反射地震资料偏移处理与反演方法.重庆:重庆大学出版社,1989,56～74
[5]Stoffa P L et al.Split-step fourier migration.Geo-physics,1990,55(4):410～421
[6]Wu Rushan.Wide-angle elastic wave one-way propa-gation in heterogeneous media and an elastic wavecomplex-screen method.Journal of Geophysics Re-search,1994,99(B1):751～766
[7]Ristow D and Rühl T.Fourier finite-difference mi-gration.Geophysics,1994,59(12):1882～1893
[8]Fu Liyun.Comparison of different one-way propaga-tors for wave forward propagation in heterogeneouscrustal wave guides.Bulletin of the SeismologicalSociety of America,2006,96(3):1091～1113
[9]Fu Liyun.Broadband constant-coefficient propaga-tors.Geophysical Prospecting,2005,53(3):299～310
[10]Fu Liyun.Wavefield interpolation in the Fourierwavefield extrapolation.Geophysics,2004,69(1):257～264
[11]熊晓军.单程波动方程地震数值模拟新方法研究[博士学位论文].四川成都:成都理工大学,2007Xiong Xiaojun.Method Research of One-way Wave-equation Seismic Numerical Simulation.Chengdu:Chengdu University of Technology,2007
[12]符力耘,孙伟家,李东平.退化的Fourier偏移算子及其在复杂断块成像中的应用.地球物理学报,2007,50(4):1241～1250Fu Liyun,Sun Weijia,Li Dongping.Degenerate mi-grators for imaging fault-related complex structures.Chinese Journal of Geophysics,2007,50(4):1241～1250
[13]符力耘.地震波探测地质构造复杂性的定量分析方法.中国科学D辑:地球科学,2009,39(9):1179～1190Fu Liyun.Quantitative assessment of the complexityof geological structures in terms of seismic propaga-tors.Sci China Ser D-Earth Sci,2009,39(9):1179～1190.1007/s11430-009-0167-z
[14]孙伟家,符力耘,姚振兴.基于耦合反射/透射系数单程波传播算子的地震波模拟研究.地球物理学报,2009,52(10):2558～2565Sun Weijia,Fu Liyun,Yao Zhenxing.One-waypropagators coupled with reflection/transmission co-efficients for seismogram synthesis in complex media.Chinese Journal of Geophysic,2009,52(10):2558～2565
[15]朱遂伟,张金海,姚振兴.高阶优化傅里叶有限差分算子偏移.石油地球物理勘探,2009,44(6):680～684Zhu Suiwei,Zhang Jinhai,Yao Zhenxing.High or-der optimization Fourier finite difference operator mi-gration method.OGP,2009,44(6):680～684
[16]Zhang Jinhai,Wang Weimin,Yao Zhenxing.Com-parison between the Fourier finite-difference methodand the generalized-screen method.GeophysicalProspecting,2009,57(3):355～365
[2]马在田.高阶有限差分偏移.石油地球物理勘探,1982,17(1):6～15Ma Zaitian.High order finite-difference migration.OGP,1982,17(1):6～15
[3]Gazdag J.Wave equation migration with the phase-shift method.Geophysics,1978,43(7):1342～1351
[4]贺振华.反射地震资料偏移处理与反演方法.重庆:重庆大学出版社,1989,56～74
[5]Stoffa P L et al.Split-step fourier migration.Geo-physics,1990,55(4):410～421
[6]Wu Rushan.Wide-angle elastic wave one-way propa-gation in heterogeneous media and an elastic wavecomplex-screen method.Journal of Geophysics Re-search,1994,99(B1):751～766
[7]Ristow D and Rühl T.Fourier finite-difference mi-gration.Geophysics,1994,59(12):1882～1893
[8]Fu Liyun.Comparison of different one-way propaga-tors for wave forward propagation in heterogeneouscrustal wave guides.Bulletin of the SeismologicalSociety of America,2006,96(3):1091～1113
[9]Fu Liyun.Broadband constant-coefficient propaga-tors.Geophysical Prospecting,2005,53(3):299～310
[10]Fu Liyun.Wavefield interpolation in the Fourierwavefield extrapolation.Geophysics,2004,69(1):257～264
[11]熊晓军.单程波动方程地震数值模拟新方法研究[博士学位论文].四川成都:成都理工大学,2007Xiong Xiaojun.Method Research of One-way Wave-equation Seismic Numerical Simulation.Chengdu:Chengdu University of Technology,2007
[12]符力耘,孙伟家,李东平.退化的Fourier偏移算子及其在复杂断块成像中的应用.地球物理学报,2007,50(4):1241～1250Fu Liyun,Sun Weijia,Li Dongping.Degenerate mi-grators for imaging fault-related complex structures.Chinese Journal of Geophysics,2007,50(4):1241～1250
[13]符力耘.地震波探测地质构造复杂性的定量分析方法.中国科学D辑:地球科学,2009,39(9):1179～1190Fu Liyun.Quantitative assessment of the complexityof geological structures in terms of seismic propaga-tors.Sci China Ser D-Earth Sci,2009,39(9):1179～1190.1007/s11430-009-0167-z
[14]孙伟家,符力耘,姚振兴.基于耦合反射/透射系数单程波传播算子的地震波模拟研究.地球物理学报,2009,52(10):2558～2565Sun Weijia,Fu Liyun,Yao Zhenxing.One-waypropagators coupled with reflection/transmission co-efficients for seismogram synthesis in complex media.Chinese Journal of Geophysic,2009,52(10):2558～2565
[15]朱遂伟,张金海,姚振兴.高阶优化傅里叶有限差分算子偏移.石油地球物理勘探,2009,44(6):680～684Zhu Suiwei,Zhang Jinhai,Yao Zhenxing.High or-der optimization Fourier finite difference operator mi-gration method.OGP,2009,44(6):680～684
[16]Zhang Jinhai,Wang Weimin,Yao Zhenxing.Com-parison between the Fourier finite-difference methodand the generalized-screen method.GeophysicalProspecting,2009,57(3):355～365
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