基于一阶速度应力方程的双相各向异性介质波场模拟及耗散系数分析
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摘要
为了解决在石油地震勘探中常常遇到的各向异性问题,利用双相各向异性介质的波动方程,导出双相各向异性PTL介质中的固相、流体相的一阶应力速度方程及差分方程。利用高阶二维交错网格差分方法,对双相PTL介质波长进行了模拟和分析,并讨论了耗散系数与双相PTL介质的波场问题。模拟结果表明:①双相PTL介质中存在快P波、慢P波和SV波,波场具有各向异性性质。②耗散系数对地震波传播的影响主要体现在对地震波能量的吸收和衰减上,耗散系数对慢P波产生较大的影响,大的耗散系数将使慢P波很快被衰减掉;在不同方位上,耗散系数存在较大差异时,慢P波能量并非只是在一个方向上衰减,而是整个慢P波的大部分能量在所有的方向上都要被衰减掉。该研究认识提高了计算效率,增强了计算的稳定性。
In order to solve the common problem of anisotropy in seismic exploration,we derived first-order stress velocity and difference equations of solid and fluid phases in a dual-phase anisotropic PTL medium by using the wave equation of dual-phase anisotropic medium.The higher 2-D cross grid difference method was applied to simulate and analyze the wavelength of dual-phase PTL medium and to study the dissipation coefficient and wave field of the dual-phase PTL medium.The following results were obtained through modeling.(1) Rapid P-,slow P-and SV-waves co-exist in the dual-phase PTL medium and their wave fields are anisotropic.(2) The influences of dissipation coefficient on the propagation of seismic waves are mainly represented by adsorption and attenuation of seismic wave energy.The influence of dissipation coefficient on the slow P-wave is significant,and the slow P-wave can be rapidly and completely attenuated when the dissipation coefficient is large.If the dissipation coefficients are significantly different in different directions,the attenuation of slow P-wave energy occurs in all directions rather than only in one direction.This study improves efficiency and enhances stability of computation,thus is of great significance to petroleum seismic exploration.
In order to solve the common problem of anisotropy in seismic exploration,we derived first-order stress velocity and difference equations of solid and fluid phases in a dual-phase anisotropic PTL medium by using the wave equation of dual-phase anisotropic medium.The higher 2-D cross grid difference method was applied to simulate and analyze the wavelength of dual-phase PTL medium and to study the dissipation coefficient and wave field of the dual-phase PTL medium.The following results were obtained through modeling.(1) Rapid P-,slow P-and SV-waves co-exist in the dual-phase PTL medium and their wave fields are anisotropic.(2) The influences of dissipation coefficient on the propagation of seismic waves are mainly represented by adsorption and attenuation of seismic wave energy.The influence of dissipation coefficient on the slow P-wave is significant,and the slow P-wave can be rapidly and completely attenuated when the dissipation coefficient is large.If the dissipation coefficients are significantly different in different directions,the attenuation of slow P-wave energy occurs in all directions rather than only in one direction.This study improves efficiency and enhances stability of computation,thus is of great significance to petroleum seismic exploration.
引文
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[8]肖思和,许多.基于Biot方程的纵波波场高阶有限差分法模拟及波场分析[J].矿物岩石,2010,30(1):116-120.
[2]刘洋,李承楚.双相各向异性介质中弹性波传播伪谱法数值模拟研究[J].地震学报,2000,22(2):132-138.
[3]杨顶辉,张中杰,滕吉文,等.双相各向异性研究、问题与应用前景[J].地球物理学进展,2000,15(2):7-21.
[4]杨顶辉.双相各向异性介质中弹性波方程的有限元解法及波场模拟[J].地球物理学报,2002,45(4):575-583.
[5]AMOS NUR.双相介质中波的传播[M].许云,译.北京:石油工业出版社,1986.
[6]牟永光,裴正林.三维复杂介质地震数值模拟[M].北京:石油工业出版社,2005.
[7]孙卫涛,杨慧珠.双相各向异性介质弹性波场有限差分正演模拟[J].固体力学学报,2004,25(1):21-28.
[8]肖思和,许多.基于Biot方程的纵波波场高阶有限差分法模拟及波场分析[J].矿物岩石,2010,30(1):116-120.
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