黏弹性VTI介质频率空间域准P波正演模拟
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摘要
有限差分方法是波场数值模拟的一个重要方法,时间域有限差分计算方法因按时间片递推计算,每个时间片的舍入误差会累积到下一片中,当时间片较多,最终会导致累积误差太大.而频率域计算是按频率片对空间网格进行整体求解方程组,其计算误差分配到了每个网格点上,并且各个频率片之间是独立计算的,因此不存在累计误差,而且在频率-空间域更易于模拟黏弹各向异性介质的衰减,同时采用25点优化差分算子克服了常规差分算子的数值频散.本文首先推导了黏弹性VTI介质的频率-空间域准P波波动方程,在此基础上,利用25点优化差分算子构造了差分格式,实现了频率空间域的正演模拟.并以断层模型为例,模拟并对比分析了利用弹性VTI介质波动方程差分格式和利用黏弹性VTI介质波动方程差分格式模拟的井间地震准P波波场记录,得出黏弹性介质地震记录由于衰减振幅相对较小,主频相对较低的结论.
The finite difference is an important method of wavefield numerical simulation.It can calculate recursively by time slice,and the round-off errors of each time slice may accumulate to the next time slice in time domain,eventually,which will lead to too large accumulated error when the time slice is enough.However,solving all equation set in frequency domain is based on the frequency slice on the space grid,whose error is assigned to each grid point,it is without accumulated error and easier to simulate the attenuation of the viscoelastic anisotropic media in frequency-space domain.In order to overcome the numerical dispersion of routine finite-difference operators,25-point optimized finite-difference operators are applied.This paper derives firstly the formula of quasi-P wave in viscoelastic VTI media in frequency-space domain,and then constructs the difference format using 25-point optimized finite difference operators,so it implements forward modeling.A case study of fault model compares and analyzes the crosswell seismic quasi-P wavefield stimulated with the finite difference method for both elastic VTI media and viscoelastic VTI media.In the end,it comes to the conclusion that the amplitude of seismic wave is relatively smaller and the main frequency is decreased in viscoelastic media.
The finite difference is an important method of wavefield numerical simulation.It can calculate recursively by time slice,and the round-off errors of each time slice may accumulate to the next time slice in time domain,eventually,which will lead to too large accumulated error when the time slice is enough.However,solving all equation set in frequency domain is based on the frequency slice on the space grid,whose error is assigned to each grid point,it is without accumulated error and easier to simulate the attenuation of the viscoelastic anisotropic media in frequency-space domain.In order to overcome the numerical dispersion of routine finite-difference operators,25-point optimized finite-difference operators are applied.This paper derives firstly the formula of quasi-P wave in viscoelastic VTI media in frequency-space domain,and then constructs the difference format using 25-point optimized finite difference operators,so it implements forward modeling.A case study of fault model compares and analyzes the crosswell seismic quasi-P wavefield stimulated with the finite difference method for both elastic VTI media and viscoelastic VTI media.In the end,it comes to the conclusion that the amplitude of seismic wave is relatively smaller and the main frequency is decreased in viscoelastic media.
引文
[1] 宋常瑜,裴正林.井间地震黏弹性波场特征的数值模拟研究.石油物探,2006,45(5) :508～513 Song C Y,Pei Z L.Numerical simulation of viscoelastic wavefield for crosshole seismic exploration.Geophysical Prospecting for Petroleum(in Chinese) ,2006,45(5) :508～513
[2] 郭智奇,刘财,杨宝俊等.黏弹各向异性介质中地震波场模拟与特征.地球物理学进展,2007,22(3) :804～810 Guo Z Q,Liu CYang B J,et al.Seismic wave fields modeling and feature in viscoelastic anisotropic media.Progress in Geophysics(in Chinese),2007,22(3) :804～810
[3] 杜启振,刘莲莲,孙晶波.各向异性黏弹性空隙介质地震波场伪谱法正演模拟.物理学报,2007,56(10) :6143～6148 Du Q Z,Liu L L,Sun J B.Numerical modeling of seismic wavefield in anisotropic viscoelastic porous medium with the pseudo-spectral method.Acta Physica Sinica(in Chinese),2007,56(10) :6143～6148
[4] Lysmer,Drake.A finite-element method for seismology.In:Bolt B A Eds.Methods in Computational Physics,Volume 11:Seismology:Surface Waves and Earth Oscillations.Academic Press Inc.,1972． 181～216
[5] Marfurt K J.Accuracy of finite-difference and finite-element modeling of scalar and elastic wave equations.Geophysics,1984,49(5) :533～549
[6] Marfurt K J,Shin C S.The future of iterative modeling in geophysical exploration.In:Eisner E Ed.Handbook of Geophysical Exploration:I Seismic Exploration,Volume 21:Supercomputers in Seismic Exploration.Pergamon Press,1989． 203～228
[7] Pratt R G,Worhington M H.Inverse theory applied to multi-source crosshole tomography,Part Ⅰ.Acoustic wave-equation method.Geophys.Prosp.,1990,38:287～310
[8] Pratt R G.Inverse theory applied to multi-source crosshole tomography,part Ⅱ:Elastic wave-equation method.Geophys.Prosp.,1990,38:287～310
[9] Pratt R G.Frequency-domain elastic wave modeling by finite differences :A tool for crosshole seismic imaging.Geophysics,1990,55(5) :626～632
[10] Jo C H,Shin C,Suh J H.An optimal 9-point finite-difference frequency space 2-D scalar wave extrapolator.Geophysics,1996,61(2) :529～537
[11] Shin C,Sohn H.A frequency-space 2-D scalar wave extrapolator using extended 25-point finite-difference operators.Geophysics,1998,63(1) :289～296
[12] Min D J,Shin C,Kwon B D,et al.Improved frequency domain elastic wave modeling using weighted-averaging difference operators.Geophysics,2000,65(3) :884～895
[13] 吴国忱,梁锴.VTI介质频率-空间域准P波正演模拟.石油地球物理勘探.2005,40(5) :535～545 Wu G C,Liang K.Quasi P-wave forward modeling in frequency-space domain in VTI media.Oil Geophysical Prospecting (in Chinese) ,2005 ,40(5) :535～545
[14] 吴国忱,梁锴.VTI介质准P波频率空间域组合边界条件研究.石油物探,2005,44(4) :301～307 Wu G C,Liang K.Combined boundary conditions of quasi-P wave within frequency-space domain in VTI media.Geophysical Prospecting For Petrole (in Chinese) ,2005 ,44 (4) :301～307
[15] 吴国忱.各向异性介质地震波传播和成像.山东东营:中国石油大学出版社,2006 Wu G C.Seismic Wave Propagation and Imaging in Anisotropy Media (in Chinese).Dongying:China University of Petroleum Press,2006
[16] 吴国忱,梁锴.VTI介质qP波方程高精度有限差分算子.地球物理学进展,2007,22(3) :896～904 Wu G C,Liang K.High precision finite difference operators for qP wave equation in VTI media.Progress in Geophysics (in Chinese),2007 ,22(3) :896～904
[17] 殷文,印兴耀,吴国忱等.高精度频率域弹性波方程有限差分方法及波场模拟.地球物理学报,2006,49(2) :561～568 Yin W,Yin X Y,Wu G C,et al.The method of finite difference of high precision elastic wave equations in the frequency domain and wave-field simulation.Chinese J.Geophys.(in Chinese) ,2006,49(2) :561～568
[2] 郭智奇,刘财,杨宝俊等.黏弹各向异性介质中地震波场模拟与特征.地球物理学进展,2007,22(3) :804～810 Guo Z Q,Liu CYang B J,et al.Seismic wave fields modeling and feature in viscoelastic anisotropic media.Progress in Geophysics(in Chinese),2007,22(3) :804～810
[3] 杜启振,刘莲莲,孙晶波.各向异性黏弹性空隙介质地震波场伪谱法正演模拟.物理学报,2007,56(10) :6143～6148 Du Q Z,Liu L L,Sun J B.Numerical modeling of seismic wavefield in anisotropic viscoelastic porous medium with the pseudo-spectral method.Acta Physica Sinica(in Chinese),2007,56(10) :6143～6148
[4] Lysmer,Drake.A finite-element method for seismology.In:Bolt B A Eds.Methods in Computational Physics,Volume 11:Seismology:Surface Waves and Earth Oscillations.Academic Press Inc.,1972． 181～216
[5] Marfurt K J.Accuracy of finite-difference and finite-element modeling of scalar and elastic wave equations.Geophysics,1984,49(5) :533～549
[6] Marfurt K J,Shin C S.The future of iterative modeling in geophysical exploration.In:Eisner E Ed.Handbook of Geophysical Exploration:I Seismic Exploration,Volume 21:Supercomputers in Seismic Exploration.Pergamon Press,1989． 203～228
[7] Pratt R G,Worhington M H.Inverse theory applied to multi-source crosshole tomography,Part Ⅰ.Acoustic wave-equation method.Geophys.Prosp.,1990,38:287～310
[8] Pratt R G.Inverse theory applied to multi-source crosshole tomography,part Ⅱ:Elastic wave-equation method.Geophys.Prosp.,1990,38:287～310
[9] Pratt R G.Frequency-domain elastic wave modeling by finite differences :A tool for crosshole seismic imaging.Geophysics,1990,55(5) :626～632
[10] Jo C H,Shin C,Suh J H.An optimal 9-point finite-difference frequency space 2-D scalar wave extrapolator.Geophysics,1996,61(2) :529～537
[11] Shin C,Sohn H.A frequency-space 2-D scalar wave extrapolator using extended 25-point finite-difference operators.Geophysics,1998,63(1) :289～296
[12] Min D J,Shin C,Kwon B D,et al.Improved frequency domain elastic wave modeling using weighted-averaging difference operators.Geophysics,2000,65(3) :884～895
[13] 吴国忱,梁锴.VTI介质频率-空间域准P波正演模拟.石油地球物理勘探.2005,40(5) :535～545 Wu G C,Liang K.Quasi P-wave forward modeling in frequency-space domain in VTI media.Oil Geophysical Prospecting (in Chinese) ,2005 ,40(5) :535～545
[14] 吴国忱,梁锴.VTI介质准P波频率空间域组合边界条件研究.石油物探,2005,44(4) :301～307 Wu G C,Liang K.Combined boundary conditions of quasi-P wave within frequency-space domain in VTI media.Geophysical Prospecting For Petrole (in Chinese) ,2005 ,44 (4) :301～307
[15] 吴国忱.各向异性介质地震波传播和成像.山东东营:中国石油大学出版社,2006 Wu G C.Seismic Wave Propagation and Imaging in Anisotropy Media (in Chinese).Dongying:China University of Petroleum Press,2006
[16] 吴国忱,梁锴.VTI介质qP波方程高精度有限差分算子.地球物理学进展,2007,22(3) :896～904 Wu G C,Liang K.High precision finite difference operators for qP wave equation in VTI media.Progress in Geophysics (in Chinese),2007 ,22(3) :896～904
[17] 殷文,印兴耀,吴国忱等.高精度频率域弹性波方程有限差分方法及波场模拟.地球物理学报,2006,49(2) :561～568 Yin W,Yin X Y,Wu G C,et al.The method of finite difference of high precision elastic wave equations in the frequency domain and wave-field simulation.Chinese J.Geophys.(in Chinese) ,2006,49(2) :561～568
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