声波方程频率域高精度正演的17点格式及数值实现
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摘要
频率域正演计算是频率域全波形反演的基础.传统的最优9点格式只具有二阶精度,不能满足高精度地震成像的需要.本文考虑两个四阶精度的格式,即经典的四阶9点格式和优化的17点格式.17点格式可将最小波长内所需网格点数减小到2.56.通过在简单模型和Overthrust模型上的数值实验,比较分析了三种格式的正演效果;简单模型数值实验显示了17点格式克服频散误差的能力优于四阶9点格式和最优9点格式;复杂模型数值实验则进一步承认了算法的可行性.
Frequency-domain modeling is the basis of frequency-domain full waveform inversion.The classical optimal 9-point scheme is only of second-order accuracy,and does not meet the need of high-accuracy seismic imaging.This paper deals with two fourth-order schemes,namely fourth-order 9-point scheme and optimized 17-point scheme.The 17-point scheme reduces the number of grid points required by the shortest wavelength to 2.56.We also perform numerical tests on a simple model and the Overthrust model,and the modeling results with the three schemes are compared.The results demonstrate the superiority of the 17-point scheme over the fourth-order 9-point scheme and optimal 9-point scheme in terms of reducing dispersion errors.Numerical tests on complex model further confirm the feasibility of the 17-point scheme.
Frequency-domain modeling is the basis of frequency-domain full waveform inversion.The classical optimal 9-point scheme is only of second-order accuracy,and does not meet the need of high-accuracy seismic imaging.This paper deals with two fourth-order schemes,namely fourth-order 9-point scheme and optimized 17-point scheme.The 17-point scheme reduces the number of grid points required by the shortest wavelength to 2.56.We also perform numerical tests on a simple model and the Overthrust model,and the modeling results with the three schemes are compared.The results demonstrate the superiority of the 17-point scheme over the fourth-order 9-point scheme and optimal 9-point scheme in terms of reducing dispersion errors.Numerical tests on complex model further confirm the feasibility of the 17-point scheme.
引文
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[2]Virieux J,Operto S.An overview of full-waveform inversionin exploration geophysics.Geophysics,2009,74(6):WCC1-WCC26.
[3]Tarantola A.Inversion of seismic reflection data in the acoustic approximation.Geophysics,1984,49(8):1259-1266.
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[5]Pratt R G,Wothington M H.Inverse theory applied to multi-source cross-hole tomography,Part1:Acoustic wave equation method.Geophysical Prospecting,1990,38(3):287-310.
[6]Pratt R G.Inverse theory applied to multi-source cross-hole tomography,Part2:Elastic wave-equation method.Geophysical Prospecting,1990,38(3):311-329.
[7]Pratt R G.Guass-Newton and full Newton methods in frequency domain seismic waveform inversion.Geophysics,1998,173:922-931.
[8]Lysmer Drake.Methods in computational physics,Volume 11:Seismology:Surface waves and earth oscillations:A finite-element method for seismology.MA:Academic Press Inc.,1972:181-216.
[9]Marfurt K J.Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations.Geophysics,1984,49(5):533-549.
[10]Marfurt K J,Shin C S.The future of iterative modeling in geophysical exploration.∥Eisner E,ed.Handbook ofGeophysical Exploration:I Seismic Exploration,Volume21:Supercomputers in seismic exploration.New York:Pergamon Press,1989:203-228.
[11]Shin C S.Nonlinear Elastic wave Inversion by Blocky Parameterization.Tulsa:University of Tulsa,1988.
[12]Jo C H,Suh J H,Shin C S.An optimal nine-point finite difference frequency-space2-D acoustic wave extrapolator.Geophysics,1996,61(2):529-537.
[13]ˇStekl I.Frequency Domain Seismic Forward Modeling:A Tool for Waveform Inversion.London:Imperial College London,1997.
[14]ˇStekl I,Pratt R G.Accurate visco-elastic modeling by frequency-domain finite differences using rotated operators.Geophysics,1998,63(5):1779-1794.
[15]Shin C,Sohn H.A frequency-space2-D scalar wave extrapolator using extended25-point finite-difference operator.Geophysics,1998,63(1):289-296.
[16]Hustedt B,Operto S,Virieux J.Mixed-grid and staggered-grid finite-difference methods for frequency-domain acoustic wave modeling.Geohpys.J.Int.,2004,157(3):1269-1296.
[17]Alford R M,Kelly K R,Boore D M.Accuracy of finite-difference modeling of the acoustic wave equation.Geophysics,1974,39(6):834-842.
[18]Chen J B.Lax-Wendroff and Nystrm methods for seismic modeling.Geophysical Prospecting,2009,57(6):931-941.
[19]Chen J B,Liu G F,Liu H.Seismic imaging based on spectral differentiation matrix and GPU implementation.Journal of Applied Geophysics,2012,79:1-5.
[2]Virieux J,Operto S.An overview of full-waveform inversionin exploration geophysics.Geophysics,2009,74(6):WCC1-WCC26.
[3]Tarantola A.Inversion of seismic reflection data in the acoustic approximation.Geophysics,1984,49(8):1259-1266.
[4]Pratt R G.Frequency-domain elastic wave modeling by finite differences:A tool for cross-hole seismic imaging.Geophysics,1990,55(5):626-632.
[5]Pratt R G,Wothington M H.Inverse theory applied to multi-source cross-hole tomography,Part1:Acoustic wave equation method.Geophysical Prospecting,1990,38(3):287-310.
[6]Pratt R G.Inverse theory applied to multi-source cross-hole tomography,Part2:Elastic wave-equation method.Geophysical Prospecting,1990,38(3):311-329.
[7]Pratt R G.Guass-Newton and full Newton methods in frequency domain seismic waveform inversion.Geophysics,1998,173:922-931.
[8]Lysmer Drake.Methods in computational physics,Volume 11:Seismology:Surface waves and earth oscillations:A finite-element method for seismology.MA:Academic Press Inc.,1972:181-216.
[9]Marfurt K J.Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations.Geophysics,1984,49(5):533-549.
[10]Marfurt K J,Shin C S.The future of iterative modeling in geophysical exploration.∥Eisner E,ed.Handbook ofGeophysical Exploration:I Seismic Exploration,Volume21:Supercomputers in seismic exploration.New York:Pergamon Press,1989:203-228.
[11]Shin C S.Nonlinear Elastic wave Inversion by Blocky Parameterization.Tulsa:University of Tulsa,1988.
[12]Jo C H,Suh J H,Shin C S.An optimal nine-point finite difference frequency-space2-D acoustic wave extrapolator.Geophysics,1996,61(2):529-537.
[13]ˇStekl I.Frequency Domain Seismic Forward Modeling:A Tool for Waveform Inversion.London:Imperial College London,1997.
[14]ˇStekl I,Pratt R G.Accurate visco-elastic modeling by frequency-domain finite differences using rotated operators.Geophysics,1998,63(5):1779-1794.
[15]Shin C,Sohn H.A frequency-space2-D scalar wave extrapolator using extended25-point finite-difference operator.Geophysics,1998,63(1):289-296.
[16]Hustedt B,Operto S,Virieux J.Mixed-grid and staggered-grid finite-difference methods for frequency-domain acoustic wave modeling.Geohpys.J.Int.,2004,157(3):1269-1296.
[17]Alford R M,Kelly K R,Boore D M.Accuracy of finite-difference modeling of the acoustic wave equation.Geophysics,1974,39(6):834-842.
[18]Chen J B.Lax-Wendroff and Nystrm methods for seismic modeling.Geophysical Prospecting,2009,57(6):931-941.
[19]Chen J B,Liu G F,Liu H.Seismic imaging based on spectral differentiation matrix and GPU implementation.Journal of Applied Geophysics,2012,79:1-5.
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