等价各向异性介质一阶拟声波 方程正演模拟及其效率分析

杨富森 李振春 王小丹 张凯 刘成斋

杨富森, 李振春, 王小丹, 张凯, 刘成斋. 2015: 等价各向异性介质一阶拟声波 方程正演模拟及其效率分析. 地震学报, 37(4): 648-660. doi: 10.11939/jass.2015.04.011
引用本文: 杨富森, 李振春, 王小丹, 张凯, 刘成斋. 2015: 等价各向异性介质一阶拟声波 方程正演模拟及其效率分析. 地震学报, 37(4): 648-660. doi: 10.11939/jass.2015.04.011
Yang Fusen, Li Zhenchun, Wang Xiaodan, Zhang Kai, Liu Chengzhai. 2015: Equivalent anisotropic first-order pseudo-acoustic wave equations modeling and its efficiency analysis. Acta Seismologica Sinica, 37(4): 648-660. doi: 10.11939/jass.2015.04.011
Citation: Yang Fusen, Li Zhenchun, Wang Xiaodan, Zhang Kai, Liu Chengzhai. 2015: Equivalent anisotropic first-order pseudo-acoustic wave equations modeling and its efficiency analysis. Acta Seismologica Sinica, 37(4): 648-660. doi: 10.11939/jass.2015.04.011

等价各向异性介质一阶拟声波 方程正演模拟及其效率分析

doi: 10.11939/jass.2015.04.011
基金项目: 国家自然科学基金(41204086,41374122)、国家高技术研究发展计划(863)课题(2011AA060301)和山东省自然科学基金(ZR2013DL012)联合资助.
详细信息
    通讯作者:

    杨富森, e-mail:sende12345@163.com

  • 中图分类号: P315.3+1

Equivalent anisotropic first-order pseudo-acoustic wave equations modeling and its efficiency analysis

  • 摘要: 为克服各向异性弹性波动方程正演模拟的局限,本文研究了各向异性介质拟声波方程的交错网格有限差分数值解法.首先,从VTI介质胡克定律和qP-qSV波频散关系两种思路出发,通过声假设近似,给出了两种不同形式的VTI介质一阶拟声波方程,并通过引入波场的伪速度分量,推导了一种新的VTI介质一阶应力-速度方程,并通过旋转坐标系将其推广到TTI介质中;其次,构造了一阶拟声波方程的交错网格高阶有限差分格式,并推导了相应的PML边界条件;最后,对本文方法中固有的qSV人为干扰波的产生机制和压制方法进行了简单讨论.数值结果表明:3种一阶拟声波方程在运动学和动力学上是等价的,相对于各向异性弹性波正演模拟,其节省了内存,提高了计算效率;各向异性因素会影响反射波旅行时和振幅等波场特征,在后续的处理、反演和解释中不可忽略;VTI介质HESS模型的逆时偏移结果也验证了本文方法的合理性.

     

  • 图  1  交错网格及波场分量位置示意图

    Figure  1.  Schematic diagram of staggered-grids and the location of wavefield

    图  2  波场快照对比(t=400 ms)

    (a)VTI介质弹性波方程正演得到的垂直应力分量波场;(b)用式(2)正演得到的波场q;(c)用式(6)正演得到的波场p;(d)用式(7)正演得到的波场p

    Figure  2.  Comparison of wavefield snapshots (t=400 ms)

    (a)Wavefield of vertical stress component modeled by elastic wave equation in VTI media;(b)Wavefield q modeled by equation(2);(c)Wavefield p modeled by equation(6);(d) Wavefield p modeled by equation(7)

    图  3  应用PML边界条件后的波场快照

    (a)qP波,t=600 ms;(b)qSV波,t=2 000 ms

    Figure  3.  Wavefield snapshots with PML boundary condition

    (a)qP wave,t=600 ms;(b)qSV wave, t=2 000 ms

    图  4  设置震源环前后各向异性介质拟声波正演的波场快照对比(t=400 ms)

    (a)VTI介质(设置震源环前);(b)VTI介质(设置震源环后);(c)TTI介质(设置震源环前,θ=45°);(d)TTI介质(设置震源环后,θ=45°)

    Figure  4.  Wavefield snapshots comparison of anisotropic pseudo-acoustic wave modeling without and with source box (t=400 ms)

    (a)VTI media (without source box);(b)VTI media (with source box);(c)TTI media (without source box, θ=45°);(d)TTI media (with source box, θ=45°)

    图  5  二维TTI介质层状模型及其各向异性参数

    Figure  5.  2D TTI layered model and its anisotropic parameters

    图  6  单炮地震记录对比

    (a,d)用式(2)正演得到的炮记录;(b,e)用式(6)正演得到的炮记录;(c,f)用式(7)正演得到的炮记录;(g)TTI介质拟声波方程正演得到的炮记录;(h)VTI介质弹性波方程正演得到的炮记录;(i)各向同性声波方程正演得到的炮记录.其中,(a)-(c)为设置震源环前的结果;(d)-(f)为设置震源环后的结果

    Figure  6.  Comparison of single shot seismic records

    (a,d) Shot records modeled by equation (2);(b,e) Shot records modeled by equation (6);(c,f) Shot records modeled by equation (7);(g) Shot records modeled by TTI pseudo-acoustic wave equation;(h)Shot records modeled by VTI elastic wave equation;(i) Shot records modeled by isotropic acoustic wave equation. Figs.(a)-(c) are results without source box, and Figs.(d)-(f) are results with source box

    图  7  单道地震信号对比

    (a)从图6a,b,c中近偏移距(地面位置为1 200 m)处抽取的单道信号对比;(b,c)从图6d e,f中近偏移距(地面位置为1 200 m)和远偏移距(地面位置为200 m)处抽取的单道信号对比;(d,e)从图6f,h中近偏移距(地面位置为1 200 m)和远偏移距(地面位置为200 m)处抽取的单道信号对比;(f,g) 从图6f,g,i中近偏移距(地面位置为1 200 m)和远偏移距(地面位置为200 m)处抽取的单道信号对比

    Figure  7.  Comparison of single trace seismic signals

    Fig.(a) is single trace signals comparison of near offset (distance=1 200 m) extracted from Figs.6a,b,c; Fig.(b) and (c) are single trace signals comparison of near offset (distance=1 200 m) and far offset (distance=200 m) extracted from Figs.6d,e,f; Figs.(d) and (e) are single trace signals comparison between near offset (distance=1 200 m) and far offset (distance=200 m) extracted from Figs.6f, h; Figs.(f) and (g) are single trace signals comparison between near offset(distance=1 200 m) and far offset (distance=200 m) extracted from Figs.6f, g, i

    图  8  二维VTI介质HESS模型及其各向异性参数

    Figure  8.  2D VTI HESS model and its anisotropic parameters

    图  9  各向同性(a)和各向异性(b)介质逆时偏移剖面

    Figure  9.  Fig.9 Reverse-time migration sections for isotropic (a) and anisotropic (b) media

    表  1  几种波动方程的计算效率对比

    Table  1.   Computational efficiency comparison of the several wave equations

    方程类型计算量平均计算时间/s
    VTI一阶拟声波方程(2)∂p/∂x,∂q/∂z,∂u/∂x,∂w/∂z72
    VTI一阶拟声波方程(6)∂p/∂x,∂p/∂z,∂u/∂x,∂k/∂z,∂w/∂z,∂ζ/∂z105
    VTI一阶拟声波方程(7)∂p/∂x,∂p/∂z,∂q/∂x,∂q/∂z,∂up/∂x,∂wq/∂z103
    各向同性声波方程∂p/∂x,∂p/∂z,∂u/∂x,∂w/∂z70
    VTI弹性波方程∂τxx/∂x,∂τxz/∂z,∂τxz/∂x,∂τzz/∂z,∂vx/∂x,∂vx/∂z,
    ∂vz/∂x,∂vz/∂z
    130
    下载: 导出CSV
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    Duveneck E, Milcik P, Bakker P M. 2008. Acoustic VTI wave equations and their application for anisotropic reverse-time migration[C]//SEG Technical Program Expanded Abstracts. Las Vegas: Society of Exploration Geophysicists: 2186-2190.
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出版历程
  • 收稿日期:  2014-07-24
  • 修回日期:  2015-03-22
  • 刊出日期:  2015-07-01

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