基于无分裂复频移卷积完全匹配层边界的黏弹介质勒夫波模拟

谢俊法, 孙成禹, 伍敦仕, 乔志浩

谢俊法, 孙成禹, 伍敦仕, 乔志浩. 2016: 基于无分裂复频移卷积完全匹配层边界的黏弹介质勒夫波模拟. 地震学报, 38(2): 244-258. DOI: 10.11939/jass.2016.02.009
引用本文: 谢俊法, 孙成禹, 伍敦仕, 乔志浩. 2016: 基于无分裂复频移卷积完全匹配层边界的黏弹介质勒夫波模拟. 地震学报, 38(2): 244-258. DOI: 10.11939/jass.2016.02.009
Xie Junfa, Sun Chengyu, Wu Dunshi, Qiao Zhihao. 2016: Love wave modeling in viscoelastic media with unsplit CFS-CPML conditions. Acta Seismologica Sinica, 38(2): 244-258. DOI: 10.11939/jass.2016.02.009
Citation: Xie Junfa, Sun Chengyu, Wu Dunshi, Qiao Zhihao. 2016: Love wave modeling in viscoelastic media with unsplit CFS-CPML conditions. Acta Seismologica Sinica, 38(2): 244-258. DOI: 10.11939/jass.2016.02.009

基于无分裂复频移卷积完全匹配层边界的黏弹介质勒夫波模拟

基金项目: 

国家自然科学基金 41374123

详细信息
    通讯作者:

    孙成禹, E-mail: suncy@upc.edu.cn

  • 中图分类号: P315.3+1

Love wave modeling in viscoelastic media with unsplit CFS-CPML conditions

  • 摘要: 本文建立了无分裂复频移卷积完全匹配层(CFS-CPML)吸收边界条件,利用交错网格下的高精度有限差分格式对黏弹性介质中的勒夫波场进行了数值模拟;分析了松弛机制个数对品质因子拟合精度的影响,验证了CFS-CPML边界条件对大角度掠射波的吸收效果.数值结果表明:本文方法所使用的5个松弛机制和空间4阶差分精度,即可在保证计算效率的前提下满足目前理论研究的需要;随着品质因子的减小,频散特征曲线的相速度逐渐向增高的方向偏离理论频散特征曲线的相速度,且各模式的高频能量也随之减弱.本文结果可为发展高精度的面波反演方法提供必要的理论依据.
    Abstract: Numerical simulation is an important way to study the characteristics of seismic wavefield. In this paper, we established the unsplit complex frequency shifted convolutional perfectly matched layer (CFS-CPML) absorbing boundary condition, and staggered grid and high precision finite difference were used to simulate Love wavefield in viscoelastic medium. And then we analyzed the influence of the number of relaxation mechanisms on the Q value fitting and verified the absorbing effect of CFS-CPML boundary conditions on the waves with large incident angles. The numerical results show that the requirements of the present theoretical wavefield study can be met with higher calculation efficiency if five relaxation mechanisms and finite difference with spatial four-order accuracy are selected for this method. At the same time, the phase velocity of dispersion curve gradually deviates from that of the theoretical curve with the decrease of quality factor, and the high frequency energy of each pattern also weakens. The study provided certain theoretical basis for high precision surface wave inversion method.
  • 图  1   不同物理参数在交错网格单元中的布局方式

    Figure  1.   Distribution of different physical parameters within the staggered-grid cells

    图  2   松弛机制个数与常Q拟合精度的关系

    Figure  2.   Relationship between relaxation mechanism number and constant Q fitting precision

    图  3   理论相速度与数值相速度的对比

    Figure  3.   Comparison of theoretical phase(open circles)velocities with numerical ones(dots)

    图  4   均匀各向同性线性黏弹性介质模型示意图

    Figure  4.   Schematic diagram of the homogeneous isotropic linear viscoelastic medium

    图  5   基于黏弹性介质模型采用Split-PML吸收边界所获取的0.14 s(上),0.3 s(中),0.54 s(下)时刻的垂直分量波场快照

    Figure  5.   Snapshots of the vertical component with Split-PML absorbing boundary at 0.14 s(upper),0.3 s(middle),and 0.54 s(lower)for homogeneous isotropic linear viscoelastic medium

    图  6   基于黏弹介质模型采用CFS-CPML吸收边界所获取的0.14 s(上),0.3 s(中),0.54 s(下)时刻的垂直分量波场快照

    Figure  6.   Snapshots of the vertical component with CFS-CPML absorbing boundary at 0.14 s(upper),0.3 s(middle),and 0.54 s(lower)for homogeneous isotropic linear viscoelastic medium

    图  7   炮记录的对比

    (a)采用Split-PML技术,箭头所指为顶部边界的反射;(b)采用CFS-CPML技术

    Figure  7.   Comparison of seismograms

    (a)Shot records with Split-PML technique implemented on the four sides,where the arrows point to the top boundary reflection;(b)Shot records with CFS-CPML technique implemented on the four sides

    图  8   单道波形的对比

    下图为上图虚线框的放大图.(a)炮检距为零的地震道;(b)炮检距为400 m的地震道

    Figure  8.   Waveform comparison of single trace

    Lower panels are amplification of the part delineated by dashed lines in upper panels (a)The seismic trace with offset zero;(b)The seismic trace with offset 400 m

    图  9   双层介质模型中的勒夫波记录(左)及其频散特征图(右)

    频散图中的白色曲线为根据矩阵传递算法(Haskell,1953)正演所得的理论勒夫波频散曲线(a)上层QS=200;(b)上层QS=40;(c)上层QS=20;(d)上层QS=10

    Figure  9.   Love wave records(left panels)and their frequency-phase velocity field dispersion characteristic diagram(right panels)simulated in two-layer medium model

    White curves in right panels are the theory Love wave dispersion curves based on the matrix transfer algorithm(Haskell,1953).(a)QS=200 for the first layer;(b)QS=40 for the first layer;(c)QS=20 for the first layer;(d)QS=10 for the first layer

    图  10   4层介质中勒夫波记录(左)及其频散特征图(右)

    频散图中的白色曲线为根据矩阵传递算法(Haskell,1953)正演所得的理论勒夫波频散曲线(a)速度递增模型;(b)夹高速层模型;(c)夹低速层模型

    Figure  10.   Love wave records(left panels)and their frequency-phase velocity field dispersion characteristic diagram(right panels)simulated in four-layer medium. White curves are the theory Love wave dispersion curves based on the matrix transfer algorithm(Haskell,1953).

    (a)Velocity increase model;(b)High velocity interlayer model;(c)Low velocity interlayer model

    表  1   两层介质模型参数

    Table  1   Parameters of a two-layer model

    层号层厚/m密度/(kg·m-3)vS/(m·s-1)QS
    1102000300200,40,20,10
    22000600200
    下载: 导出CSV

    表  2   4层介质模型参数

    Table  2   The parameters of the four-layer medium model

    层号层厚/mvS/(m·s-1)ρ/(kg·m-3)
    递增模型夹高速层模型夹低速层模型
    154004006002000
    256008004002000
    358006008002000
    41000100010002000
    下载: 导出CSV
  • 田坤.2014.黏性介质正演及逆时偏移成像方法研究[D].青岛: 中国石油大学(华东):35-39.

    Tian K.2014.Study on Method of Forward Modeling and Reverse Time Migration in Viscous Media[D].Qingdao: China University of Petroleum:35-39

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出版历程
  • 收稿日期:  2015-08-12
  • 修回日期:  2015-12-06
  • 发布日期:  2016-02-29

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