基于分数阶时间导数常Q黏弹本构关系的含黏滞流体双相VTI介质中波场数值模拟

刘财, 胡宁, 郭智奇, 罗玉钦. 2018. 基于分数阶时间导数常Q黏弹本构关系的含黏滞流体双相VTI介质中波场数值模拟. 地球物理学报, 61(6): 2446-2458, doi: 10.6038/cjg2018M0063
引用本文: 刘财, 胡宁, 郭智奇, 罗玉钦. 2018. 基于分数阶时间导数常Q黏弹本构关系的含黏滞流体双相VTI介质中波场数值模拟. 地球物理学报, 61(6): 2446-2458, doi: 10.6038/cjg2018M0063
LIU Cai, HU Ning, GUO ZhiQi, LUO YuQin. 2018. Numerical simulation of the wavefield in a viscous fluid-saturated two-phase VTI medium based on the constant-Q viscoelastic constitutive relation with a fractional temporal derivative. Chinese Journal of Geophysics (in Chinese), 61(6): 2446-2458, doi: 10.6038/cjg2018M0063
Citation: LIU Cai, HU Ning, GUO ZhiQi, LUO YuQin. 2018. Numerical simulation of the wavefield in a viscous fluid-saturated two-phase VTI medium based on the constant-Q viscoelastic constitutive relation with a fractional temporal derivative. Chinese Journal of Geophysics (in Chinese), 61(6): 2446-2458, doi: 10.6038/cjg2018M0063

基于分数阶时间导数常Q黏弹本构关系的含黏滞流体双相VTI介质中波场数值模拟

  • 基金项目:

    国家自然科学基金重点项目(41430322,41430322)、中央高校基本科研业务费专项资金和吉林大学高层次科技创新团队建设项目联合资助

详细信息
    作者简介:

    刘财, 男, 1963年生, 教授, 博士生导师, 主要从事地震波场正反演理论和综合地球物理等研究.E-mail:liucai@jlu.edu.cn

    通讯作者: 胡宁, 男, 1987年生, 博士研究生, 主要研究方向为复杂介质弹性波传播机理.E-mail:jluhooning@163.com
  • 中图分类号: P631

Numerical simulation of the wavefield in a viscous fluid-saturated two-phase VTI medium based on the constant-Q viscoelastic constitutive relation with a fractional temporal derivative

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  • 分数阶微分算子具有描述历史依赖性和全域相关性的特质,本文利用这种特质描述双相介质固体骨架的黏弹性特征.基于Kjartansson常Q理论将含有分数阶时间导数的黏弹固体骨架各向异性本构关系与双相介质理论有机地结合起来,并引入流变学本构关系描述孔隙流体的黏滞性力学行为,提出一种新的基于分数阶时间导数常Q黏弹本构关系的含黏滞流体双相VTI模型.推导了相应的时间域波传播方程,然后对该方程进行了数值模拟.对整数阶导数采用高阶交错网格有限差分算法,对分数阶时间导数采用短时记忆中心差分算法,进行了不同相界、不同品质因子组及双层地质结构情况下该类介质中波场的数值模拟与特征分析.模拟结果表明:将含有分数阶时间导数的常Q黏弹固体骨架各向异性本构关系及孔隙流体的黏滞性本构关系引入双相介质理论是可行的,二者的结合能更好地反映地下介质的黏弹性特征,对于进一步认识波在黏弹各向异性孔隙介质中的传播机理具有重要意义,为反演和重构地下油气储层和结构奠定正演理论基础.

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  • 图 1 

    近似理想相界t=0.15 s时波场快照

    Figure 1. 

    Snapshots of wave-field with approximate ideal phase boundary at t=0.15 s.

    图 2 

    四种不同流体黏滞系数固相垂直速度分量t=0.15 s时波场快照

    Figure 2. 

    Snapshots of solid phase vertical velocity components of wave-field with four different fluid viscous coefficients at t=0.15 s

    图 3 

    不同流体黏滞系数的固相质点垂直速度分量时间记录对比

    Figure 3. 

    Comparison of vertical velocity components of solid-phase particles with four different fluid viscous coefficients

    图 4 

    四组不同品质因子固相垂直速度分量t=0.15 s时波场快照

    Figure 4. 

    Wavefield snapshots of solid-phase vertical velocity components with four different groups of quality factors at t=0.15 s

    图 5 

    不同品质因子组的固相质点水平速度分量时间记录对比

    Figure 5. 

    Comparison of vertical velocity components of solid-phase particles with four different groups of quality factors

    图 6 

    双层介质t=0.3 s时波场快照(左)和合成地震记录(右)

    Figure 6. 

    Wavefield snapshots (left) and seismic synthetic records (right) in tow-layer medium at t=0.15 s.

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出版历程
收稿日期:  2018-02-01
修回日期:  2018-04-12
上线日期:  2018-06-05

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