粘弹性介质地震波传播的褶积微分算子法数值模拟研究
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摘要
早期的褶积微分算子法都是基于正反傅立叶变换而实现的,其精度比四阶有限差分稍高。本文将计算数学中的Forsyte广义正交多项式微分算子与褶积算子相结合,构建了一个新的快速、高精度褶积微分算子,其计算结果非常接近实验函数微分的精确值,精度与l6阶有限差分相当。粘弹性波动方程更真实地描述了实际地下介质中弹性波的传播规律及其波场特征。本文以二维粘弹性波动方程为例,推导了粘弹性介质波动方程的离散格式,用迭积微分算子法实现了粘弹性介质的地震波场正演模拟,并对其波传播特征进行了分析。计算结果表明该算法能正确模拟粘弹性介质中的地震波,正确地反映粘弹性介质中波场的传播规律。
Early convolutional differentiators are all based on the Fourier transformation,their precision is a little higher than that of four-order finite difference.For improving the precision and efficiency of seismic modeling,a new modeling approach(Convolutional Forsyte Polynomial Differentiator Method,CFPD)is developed in this paper by using optimized convolutional operators for spatial differentiation and staggered-grid finite-difference for time differentiation in wave equation computation.The solution of this new method is much close to the exact value,and the precision is nearly equal to that of 16-order finite difference.Viscous-elastic wave equation can better explain wave phenomena of the true earth media.This paper applies the CFPD method to model 2-D viscous-elastic seismic wave field for the first time,and further derives the first-order velocity-stress discreate equations for viscous-elastic media.The numerical results show that the algorithm can bring reliable outcomes with high precision and fast speed,and viscous-elastic modeling is much efficient.
Early convolutional differentiators are all based on the Fourier transformation,their precision is a little higher than that of four-order finite difference.For improving the precision and efficiency of seismic modeling,a new modeling approach(Convolutional Forsyte Polynomial Differentiator Method,CFPD)is developed in this paper by using optimized convolutional operators for spatial differentiation and staggered-grid finite-difference for time differentiation in wave equation computation.The solution of this new method is much close to the exact value,and the precision is nearly equal to that of 16-order finite difference.Viscous-elastic wave equation can better explain wave phenomena of the true earth media.This paper applies the CFPD method to model 2-D viscous-elastic seismic wave field for the first time,and further derives the first-order velocity-stress discreate equations for viscous-elastic media.The numerical results show that the algorithm can bring reliable outcomes with high precision and fast speed,and viscous-elastic modeling is much efficient.
引文
[1][美]N H瑞克,著.许云,译.粘弹性介质中的地震波[M].北京:地质出版社,1981.
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[7]杜启振,杨慧珠.方位各向异性黏弹性介质波场有限元模拟[J].物理学报,2003,52(8):2010-201.
[8]张智,刘财,邵志刚,等.伪谱法在常Q粘弹介质地震波场模拟中的应用效果[J].地球物理学进展,2005,20(4):945-949.
[9]王德利,雍运动,韩立国,等.三维粘弹介质地震波场有限差分并行模拟[J].西北地震学报,2007,29(1):30-34.
[10]唐启军,韩立国,王恩利,等.基于随机各向同性背景的粘弹性单斜介质二维三分量正演模拟[J].西北地震学报,2009,31(1):35-39.
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[12]郑洪伟,李廷栋,高锐,等.数值模拟在地球动力学中的研究进展[J].地球物理学进展,2006,21(2):360-369.
[13]刘鲁波,陈晓非,王彦宾.切比雪夫伪谱法模拟地震波场[J].西北地震学报,2007,29(1):18-25.
[14]Zhou B,Greenhalgh S A.Seismic scalar wave equation model-ing by a convolutional diffentiator[J].Bulletin of Seismologi-cal Society of America,1992,82(1):289-303.
[15]Zhou B,Greenhalgh S A.Numerical seismogram computa-tions for inhomogeneous media using a short,variable lengthconvolutional differentiator[J].Geophysical Prospecting,1993,41:751-766.
[16]张中杰,滕吉文,杨顶辉.声波与弹性波场数值模拟中的迭积微分算子法[J].地震学报,1996,18(1):63-69.
[17]戴志阳,孙建国,查显杰.地震波场模拟中的褶积微分算子法[J].吉林大学学报(地球科学版),2005,35(4):520-524.
[18]戴志阳,孙建国,查显杰.地震波混合阶迭积算法模拟[J].物探化探计算技术,2005 27(2):111-114.
[19]谢靖.物探数据处理的数学方法[M].北京:地质出版社,1981:97-104.
[20]程冰洁,李小凡,龙桂华.基于广义正交多项式褶积微分算子的地震波场数值模拟方法[J].地球物理学报,2008,51(2):531-537.
[21]刘红艳,李小凡,张美根.非均匀介质中地震波传播的数值模拟[J].物探化探计算技术,2008,30(3):173-177.
[22]刘红艳.复杂介质中地震波场数值模拟研究——基于广义正交多项式迭积微分算子法[D].北京:中国科学院地质与地球物理研究所,2008.
[23]程冰洁,李小凡.2.5维地震波场褶积微分算子法数值模拟[J].地球物理学进展,2008,23(4):1099-1105.
[24]李信富,李小凡.复杂介质地震波传播的褶积微分算子数值模拟[J].地震学报,2008,30(4):377-382.
[25]Gazdag J.Modelling of the acoustic wave equation withtransform method[J].Geophysics,1981,46:854.
[26]Cerjan C,Kosloff D,et al..A non-reflection boundary condi-tion for discrete acoustic and elastic wave equation[J].Geo-physics,1985,50:705-708.
[27]Kosloff R.Absorbing boundaries for wave propagation prob-lems[J].J.Comput.Phys.,1986,63:363-376.
[2]Carcione J M,D Kosloff,R Kosloff.Wave propagation simu-lation in a linear viscoacoustic medium[J].Geophys.J.Roy.Astr.Soc.,1988,193:393-407.
[3]Carcione J M,D Kosloff,R Kosloff.Wave propagation simu-lation in a linear viscoelastic medium[J].Geophys.J.Roy.As-tr.Soc.,1988,95:597-611.
[4]Carcione J M.Wave propagation in anisotropic linear viscoe-lastic media[J].Geophys.J.Int.,1990,101:739-950.
[5]Carcione J M.Seismic modeling in viscoelastic media[J].Geo-physics,1993,58(1):110-120.
[6]Carcione J M.Constitutive model and wave equations for line-ar,viscoelastic,anisotropic media[J].Geophysics,1995,60(2):537-548.
[7]杜启振,杨慧珠.方位各向异性黏弹性介质波场有限元模拟[J].物理学报,2003,52(8):2010-201.
[8]张智,刘财,邵志刚,等.伪谱法在常Q粘弹介质地震波场模拟中的应用效果[J].地球物理学进展,2005,20(4):945-949.
[9]王德利,雍运动,韩立国,等.三维粘弹介质地震波场有限差分并行模拟[J].西北地震学报,2007,29(1):30-34.
[10]唐启军,韩立国,王恩利,等.基于随机各向同性背景的粘弹性单斜介质二维三分量正演模拟[J].西北地震学报,2009,31(1):35-39.
[11]Jose M,Carcione,Gerard C,Herman,et al..Review Article:Seismic modeling[J].Geophysics,2002,67(4):1304-1325.
[12]郑洪伟,李廷栋,高锐,等.数值模拟在地球动力学中的研究进展[J].地球物理学进展,2006,21(2):360-369.
[13]刘鲁波,陈晓非,王彦宾.切比雪夫伪谱法模拟地震波场[J].西北地震学报,2007,29(1):18-25.
[14]Zhou B,Greenhalgh S A.Seismic scalar wave equation model-ing by a convolutional diffentiator[J].Bulletin of Seismologi-cal Society of America,1992,82(1):289-303.
[15]Zhou B,Greenhalgh S A.Numerical seismogram computa-tions for inhomogeneous media using a short,variable lengthconvolutional differentiator[J].Geophysical Prospecting,1993,41:751-766.
[16]张中杰,滕吉文,杨顶辉.声波与弹性波场数值模拟中的迭积微分算子法[J].地震学报,1996,18(1):63-69.
[17]戴志阳,孙建国,查显杰.地震波场模拟中的褶积微分算子法[J].吉林大学学报(地球科学版),2005,35(4):520-524.
[18]戴志阳,孙建国,查显杰.地震波混合阶迭积算法模拟[J].物探化探计算技术,2005 27(2):111-114.
[19]谢靖.物探数据处理的数学方法[M].北京:地质出版社,1981:97-104.
[20]程冰洁,李小凡,龙桂华.基于广义正交多项式褶积微分算子的地震波场数值模拟方法[J].地球物理学报,2008,51(2):531-537.
[21]刘红艳,李小凡,张美根.非均匀介质中地震波传播的数值模拟[J].物探化探计算技术,2008,30(3):173-177.
[22]刘红艳.复杂介质中地震波场数值模拟研究——基于广义正交多项式迭积微分算子法[D].北京:中国科学院地质与地球物理研究所,2008.
[23]程冰洁,李小凡.2.5维地震波场褶积微分算子法数值模拟[J].地球物理学进展,2008,23(4):1099-1105.
[24]李信富,李小凡.复杂介质地震波传播的褶积微分算子数值模拟[J].地震学报,2008,30(4):377-382.
[25]Gazdag J.Modelling of the acoustic wave equation withtransform method[J].Geophysics,1981,46:854.
[26]Cerjan C,Kosloff D,et al..A non-reflection boundary condi-tion for discrete acoustic and elastic wave equation[J].Geo-physics,1985,50:705-708.
[27]Kosloff R.Absorbing boundaries for wave propagation prob-lems[J].J.Comput.Phys.,1986,63:363-376.
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