Kelvin-Voigt黏弹性介质地震波场数值模拟与衰减特征
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摘要
利用高阶交错网格有限差分模拟Kelvin-Voigt黏弹性介质中传播的地震波,同时将完全匹配层吸收边界条件引入到其边界处理中。数值模拟结果表明,完全匹配层吸收边界效果好,高阶有限差分能模拟得到的黏弹性介质波场精度较高。对模拟的黏弹性波场进行分析,表明介质的粘滞性使地震反射波的能量变弱,高频衰减明显,并比低频衰减得快,主频向低频方向移动,有效频带变窄,即降低了地震波的分辨率;并且反射转换波比反射纵波要衰减得快;而且还随着传播距离的增加,其峰值频率也逐渐降低。通过数值模拟分析具有不同的粘滞系数介质对地震波的吸收和衰减,结果表明随着粘滞系数的增大,地下介质对地震波的吸收衰减更明显。
This paper uses finite difference algorithm of high-order staggered-grid simulate Kelvin-Voigt viscoelastic media of seismic waves and meanwhile introduces the perfectly matched layer(PML) absorbing boundary condition into its boundary.Numerical simulation demonstrates that the effect of this algorithm of absorbing boundary is very good and the wavefield of viscoelastic media obtained from high-order finite difference is relatively accurate.An analysis of viscoelastic wavefield simulation shows that the energy of the reflected wave becomes weaker,the attenuation of the high frequency wave is much more apparent in comparison with that of the low frequency wave,the main frequency becomes closer to the low frequency,and the effective bandwidth is narrower,which all induce low resolution of seismic wave according to the simulation of viscoelastic wavefields.Besides,the attenuation of PS-wave is much more rapid in comparison with that of PP-wave and the peak frequency becomes lower gradually with the increase of the propagating distance.It is also shown that the absorption and attenuation are more apparent with the increase of viscosity coefficient by analysis of the absorption and attenuation of seismic wave in different viscosity coefficient media.
This paper uses finite difference algorithm of high-order staggered-grid simulate Kelvin-Voigt viscoelastic media of seismic waves and meanwhile introduces the perfectly matched layer(PML) absorbing boundary condition into its boundary.Numerical simulation demonstrates that the effect of this algorithm of absorbing boundary is very good and the wavefield of viscoelastic media obtained from high-order finite difference is relatively accurate.An analysis of viscoelastic wavefield simulation shows that the energy of the reflected wave becomes weaker,the attenuation of the high frequency wave is much more apparent in comparison with that of the low frequency wave,the main frequency becomes closer to the low frequency,and the effective bandwidth is narrower,which all induce low resolution of seismic wave according to the simulation of viscoelastic wavefields.Besides,the attenuation of PS-wave is much more rapid in comparison with that of PP-wave and the peak frequency becomes lower gradually with the increase of the propagating distance.It is also shown that the absorption and attenuation are more apparent with the increase of viscosity coefficient by analysis of the absorption and attenuation of seismic wave in different viscosity coefficient media.
引文
[1]牛滨华,孙春岩.半无限空间各向同性黏弹性介质与地震波传播[M].北京:地质出版社,2007.
[2]刘瑞珣,张秉良,张臣.描述岩石黏弹性固体性质的开尔文模型[J].地学前缘,2008,15(3):221-225.
[3]Carcione J M.Seismic modeling in viscoelastic media[J].Geo-physics,1993,58(1):110-120.
[4]Robertsson J O A,Blanch J O,Symes W W.Viscoelastic finite-difference modeling[J].Geophysics,1994,59(9):1444-1456.
[5]Xu T,George A.Efficient 3-D viscoelastic modeling with applica-tion to near-surface land seismic data[J].Geophysics,1998,63(2):601-612.
[6]刘财,张智,邵志刚,等.线性粘弹体中地震波场伪谱法模拟技术[J].地球物理学进展,2005,20(3):640-644.
[7]单启铜,乐友善.PML边界条件下二维黏弹性介质波场模拟[J].石油物探,2007,46(2):126-130.
[8]裴正林.任意起伏地表弹性波方程交错网格高阶有限差分法数值模拟[J].石油地球物理勘探,2004,39(6):629-634.
[9]Kindelan M,Kamel A,Sguazzero P.On the construction and ef?ciency of staggered numerical differentiators for the wave equation[J].Geophysics,1990,55(1):107-110.
[10]Chew W,Liu Q.Perfectly matched layers for elastodynamics:ANew absorbing boundary condition[J].Journal of ComputationalAcoustics,1996,4(4):341-359.
[11]Collino F,Tsogka C.Application of the PML absorbing layer modelto the linear elastodynamic problem in anisotropic heterogeneousmedia[J].Geophysics,2001,66(1):294-307.
[12]刘洋,魏修成.CMP道集反射波吸收方程和层Q值反演[J].石油天然气学报,2009,31(6):69-76.
[2]刘瑞珣,张秉良,张臣.描述岩石黏弹性固体性质的开尔文模型[J].地学前缘,2008,15(3):221-225.
[3]Carcione J M.Seismic modeling in viscoelastic media[J].Geo-physics,1993,58(1):110-120.
[4]Robertsson J O A,Blanch J O,Symes W W.Viscoelastic finite-difference modeling[J].Geophysics,1994,59(9):1444-1456.
[5]Xu T,George A.Efficient 3-D viscoelastic modeling with applica-tion to near-surface land seismic data[J].Geophysics,1998,63(2):601-612.
[6]刘财,张智,邵志刚,等.线性粘弹体中地震波场伪谱法模拟技术[J].地球物理学进展,2005,20(3):640-644.
[7]单启铜,乐友善.PML边界条件下二维黏弹性介质波场模拟[J].石油物探,2007,46(2):126-130.
[8]裴正林.任意起伏地表弹性波方程交错网格高阶有限差分法数值模拟[J].石油地球物理勘探,2004,39(6):629-634.
[9]Kindelan M,Kamel A,Sguazzero P.On the construction and ef?ciency of staggered numerical differentiators for the wave equation[J].Geophysics,1990,55(1):107-110.
[10]Chew W,Liu Q.Perfectly matched layers for elastodynamics:ANew absorbing boundary condition[J].Journal of ComputationalAcoustics,1996,4(4):341-359.
[11]Collino F,Tsogka C.Application of the PML absorbing layer modelto the linear elastodynamic problem in anisotropic heterogeneousmedia[J].Geophysics,2001,66(1):294-307.
[12]刘洋,魏修成.CMP道集反射波吸收方程和层Q值反演[J].石油天然气学报,2009,31(6):69-76.
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