广义屏波场模拟和成像的网格离散方案研究
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摘要
设计合适的空间离散网格是频率域地震波模拟和成像的关键步骤之一.以基于Padé近似的广义屏算子为例,根据照明分析、波场模拟和偏移结果考察了时间步长、道间距和空间网格间距之间的关系.数值试算表明,该频率域算子存在稳定性条件,计算网格须满足此条件,否则偏移结果会存在不可预知的噪音甚至假像.此外,当处理稀疏空间采样的地震数据时,常规的道间插值或使用较细的计算网格均不能明显改善偏移成像效果.因此,偏移时合理的做法是在检点之间的网格点上赋零值地震道.这为其他频率域算法的计算网格设计提供了重要参考.
Defining an appropriate discrete grid is a crucial part of frequency-domain modelling and imaging.The results of the illumination analysis, modelling and migration were applied to investigate the relationship among time step,trace interval and spatial grid interval for the Padégeneralized screen propagator.Numerical tests indicate that the stability condition must be satisfied when defining grid discritization strategies,or the frequency-domain migration result could be mistakenly interpreted due to the existence of unexpected coherent noise.Besides,when migrating the insufficient spatial-sparsesampling data,the spatial grid doesn't have to be too fine.And the regular interpolations among traces can hardly improve the migration result.Therefore it's more reasonable to inject zero-value traces on grid points between adjacent receivers than using interpolation.This study provides an important reference for efficiently defining discrete grids for other frequency-domain methods.
Defining an appropriate discrete grid is a crucial part of frequency-domain modelling and imaging.The results of the illumination analysis, modelling and migration were applied to investigate the relationship among time step,trace interval and spatial grid interval for the Padégeneralized screen propagator.Numerical tests indicate that the stability condition must be satisfied when defining grid discritization strategies,or the frequency-domain migration result could be mistakenly interpreted due to the existence of unexpected coherent noise.Besides,when migrating the insufficient spatial-sparsesampling data,the spatial grid doesn't have to be too fine.And the regular interpolations among traces can hardly improve the migration result.Therefore it's more reasonable to inject zero-value traces on grid points between adjacent receivers than using interpolation.This study provides an important reference for efficiently defining discrete grids for other frequency-domain methods.
引文
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[5]Wu R,Wang Y,Luo M.Beamlet migration using local cosine basis[J].Geophysics,2008,73(5):S207-S217;doi:10.1190/1.2969776.
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[18]Krüger O S,Saenger E H,Shapiro S A.Scattering and diffraction by a single crack:An accuracy analysis of the rotated staggered grid[J].Geophysical Journal International,2005,162(1):25-31.
[19]Bansal R,Sen M K.Finite-difference modelling of Swave splitting in anisotropic media[J].Geophysical Prospecting,2008,56(3):293-312.
[20]Hustedt B,Operto S,Virieux J.Mixed-grid and staggered-grid finite-difference methods for frequency-domain acoustic wave modelling[J].Geophysical Journal International,2004,157(3):1 269-1 296.
[21]Moczo P.Finite-difference technique for SH-waves in2-D media using irregular grids-application to the seismic response problem[J].Geophysical Journal International,1989,99(2):321-329.
[22]Jastram C,Behle A.Acoustic modelling on a grid of vertically varying spacing[J].Geophysical Prospecting,1992,40(2):157-169.
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[24]Opral I,Zahradník J.Elastic finite-difference method for irregular grids[J].Geophysics,1999,64(1):240-250.
[25]Adriano S,Oliveira M.A fourth-order finitedifference method for the acoustic wave equation on irregular grids[J].Geophysics,2003,68(2):672-676.
[26]Wang Y,and Schuster G T.Finite-difference variable grid scheme for acoustic and elastic wave equation modelling[C]//Expanded Abstracts,66th Annual International Meeting,SEG.SEG,1996:674-677.
[27]Hayashi K,Burns D R.Variable grid finite-difference modelling including surface topography[C]//Expanded Abstracts,69th Annual International Meeting,SEG.SEG,1999:523-527.
[28]Aoi S,Fujiwara H.3DFinite-difference method using discontinuous grids[J].Bulletin of the Seismological Society of America,1999,89:918-930.
[29]Hu J,Jia X.Numerical modelling using frequencyadaptive meshes[C]//Expanded Abstract,82nd Annual International Meeting,SEG.SEG,2013:3 401-3 405.
[30]Mulder W A,Plessix R.E.How to choose a subset of frequencies in frequency domain finite-difference migration[J].Geophysical Journal International,2004,158(3):801-812.
[31]Claerbout J F.Toward a unified theory of reflector mapping[J].Geophysics,1971,36(3):467-481.
[32]Hou Song,Yin Junjie,Wang Yun.Effect of group interval on seismic migration[J].Petroleum Geology and Engineering,2009,23(4):32-34.侯嵩,尹军杰,王赟.道间距对地震偏移的影响[J].石油地质与工程,2009,23(4):32-34.
[2]Marfurt K J.Accuracy of finite-difference and finite-element modelling of the scalar and elastic wave-equations[J].Geophysics,1984,49(5):533-549.
[3]Alford R M,Kelly K R,Boore D M.Accuracy of finite-difference modelling of the acoustic wave equation[J].Geophysics,1974,39(6):834-842.
[4]Liu Y,Sen M k.A new time-space domain high-order finite-difference method for the acoustic wave equation[J].Journal of Computational Physics,2009,222(23):8 779-8 806.
[5]Wu R,Wang Y,Luo M.Beamlet migration using local cosine basis[J].Geophysics,2008,73(5):S207-S217;doi:10.1190/1.2969776.
[6]Xie X,Wu R S.Improve the wide angle accuracy of screen method under large contrast[C]//Expanded Abstracts,68th Annual International Meeting,SEG.SEG,1998:1811-1814;doi:10.1190/1.1820283.
[7]Wu R S.Wide-angle elastic wave one-way propagation in heterogeneous media and an elastic wave complex screen method[J].Journal of Geophysical Research,1994,99:751-766.
[8]Collino F,Joly P.Splitting of operators,alternate directions,and paraxial approximations for the threedimensional wave equation[J].SIAM Journal on Scientific Computing,1995,16:1 019-1 048.
[9]Biondi B,Palacharla G.3-D prestack migration of common azimuth data[J].Geophysics,1996,61(6):1 822-1 832.
[10]Ristow D,Ruhl T.3-D implicit finite-difference migration by multiway splitting[J].Geophysics,1997,62(2):554-567.
[11]Mulder W A,Plessix R E.A comparison between oneway and two-way wave-equation migration[J].Geophysics,2004,69(6):1 491-1 504.
[12]Madariaga R.Dynamics of an expanding circular fault[J].Bulletin of the Seismological Society of America,1976,66(3):639-666.
[13]Virieux J.P-SV wave propagation in heterogeneous media:Velocity stress finite difference method[J].Geophysics,1986,51(4):889-901.
[14]Graves R W.Simulating seismic wave propagation in3Delastic media using staggered-grid finite differences[J].Bulletin of the Seismological Society of America,1996,86(4):1 091-1 106.
[15]Robertsson J O A.A numerical free-surface condition for elastic/viscoelastic finite-difference modelling in the presence of topography[J].Geophysics,1996,61(6):1 921-1 934.
[16]Bohlen T,Saenger E H.Accuracy of heterogeneous staggered-grid finite-difference modelling of Rayleigh waves[J].Geophysics,2006,71(4):T109-T115;doi:10.1190/1.2213051.
[17]Saenger E H,Gold N,Shapiro S A.Modelling the propagation of elastic waves using a modified finite-difference grid[J].Wave Motion,2000,31:77-92.
[18]Krüger O S,Saenger E H,Shapiro S A.Scattering and diffraction by a single crack:An accuracy analysis of the rotated staggered grid[J].Geophysical Journal International,2005,162(1):25-31.
[19]Bansal R,Sen M K.Finite-difference modelling of Swave splitting in anisotropic media[J].Geophysical Prospecting,2008,56(3):293-312.
[20]Hustedt B,Operto S,Virieux J.Mixed-grid and staggered-grid finite-difference methods for frequency-domain acoustic wave modelling[J].Geophysical Journal International,2004,157(3):1 269-1 296.
[21]Moczo P.Finite-difference technique for SH-waves in2-D media using irregular grids-application to the seismic response problem[J].Geophysical Journal International,1989,99(2):321-329.
[22]Jastram C,Behle A.Acoustic modelling on a grid of vertically varying spacing[J].Geophysical Prospecting,1992,40(2):157-169.
[23]Jastram C,Tessmer E.Elastic modelling on a grid with vertically varying spacing[J].Geophysical Prospecting,1994,42(4):357-370.
[24]Opral I,Zahradník J.Elastic finite-difference method for irregular grids[J].Geophysics,1999,64(1):240-250.
[25]Adriano S,Oliveira M.A fourth-order finitedifference method for the acoustic wave equation on irregular grids[J].Geophysics,2003,68(2):672-676.
[26]Wang Y,and Schuster G T.Finite-difference variable grid scheme for acoustic and elastic wave equation modelling[C]//Expanded Abstracts,66th Annual International Meeting,SEG.SEG,1996:674-677.
[27]Hayashi K,Burns D R.Variable grid finite-difference modelling including surface topography[C]//Expanded Abstracts,69th Annual International Meeting,SEG.SEG,1999:523-527.
[28]Aoi S,Fujiwara H.3DFinite-difference method using discontinuous grids[J].Bulletin of the Seismological Society of America,1999,89:918-930.
[29]Hu J,Jia X.Numerical modelling using frequencyadaptive meshes[C]//Expanded Abstract,82nd Annual International Meeting,SEG.SEG,2013:3 401-3 405.
[30]Mulder W A,Plessix R.E.How to choose a subset of frequencies in frequency domain finite-difference migration[J].Geophysical Journal International,2004,158(3):801-812.
[31]Claerbout J F.Toward a unified theory of reflector mapping[J].Geophysics,1971,36(3):467-481.
[32]Hou Song,Yin Junjie,Wang Yun.Effect of group interval on seismic migration[J].Petroleum Geology and Engineering,2009,23(4):32-34.侯嵩,尹军杰,王赟.道间距对地震偏移的影响[J].石油地质与工程,2009,23(4):32-34.
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