基于Poynting矢量行波分离的最小二乘逆时偏移

王晓毅, 张江杰, 许宏桥, 田宝卿. 2021. 基于Poynting矢量行波分离的最小二乘逆时偏移. 地球物理学报, 64(2): 645-655, doi: 10.6038/cjg2021O0120
引用本文: 王晓毅, 张江杰, 许宏桥, 田宝卿. 2021. 基于Poynting矢量行波分离的最小二乘逆时偏移. 地球物理学报, 64(2): 645-655, doi: 10.6038/cjg2021O0120
WANG XiaoYi, ZHANG JiangJie, XU HongQiao, TIAN BaoQing. 2021. Least-squares reverse time migration with wavefield decomposition based on the Poynting vector. Chinese Journal of Geophysics (in Chinese), 64(2): 645-655, doi: 10.6038/cjg2021O0120
Citation: WANG XiaoYi, ZHANG JiangJie, XU HongQiao, TIAN BaoQing. 2021. Least-squares reverse time migration with wavefield decomposition based on the Poynting vector. Chinese Journal of Geophysics (in Chinese), 64(2): 645-655, doi: 10.6038/cjg2021O0120

基于Poynting矢量行波分离的最小二乘逆时偏移

  • 基金项目:

    国家自然科学基金(41604120)和国家科技重大专项(2017ZX05008-007)资助

详细信息
    作者简介:

    王晓毅, 男, 1992年生, 博士, 研究方向为地震波正演模拟与偏移成像.E-mail:wangxy@mail.iggcas.ac.cn

    通讯作者: 张江杰, 男, 1981年生, 副研究员, 研究方向为地震数据成像与速度分析等.E-mail:zhangjj@mail.iggcas.ac.cn
  • 中图分类号: P631

Least-squares reverse time migration with wavefield decomposition based on the Poynting vector

More Information
  • 因为在逆时偏移中基于双程波动方程构建震源波场和检波器波场,所以在波场延拓过程中地震波遇到波阻抗界面时,背向发育的反射波会与正常传播的波场互相关产生较强振幅的低频噪声.这一特点使得以逆时偏移为基础的最小二乘偏移方法在梯度计算时同样存在着低频噪声的干扰,从而导致反演收敛的速度减慢.考虑到计算量和存储成本的因素,本文借助Poynting矢量良好的方向指示性实现波场的上下行波分离,并在早期迭代的梯度计算中只保留震源波场和检波器波场沿不同垂直方向传播的组分之间的互相关,有效避免了成像噪声的干扰,提高了算法收敛的速率.数值算例验证了方案的有效性.

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  • 图 1 

    波的传播路径

    Figure 1. 

    Wave propagation paths

    图 2 

    偏移假象产生示意图

    Figure 2. 

    Schematic of the generation of migration artifacts

    图 3 

    均匀介质中声波Poynting矢量的求取及上下行波分离

    Figure 3. 

    Calculation of Poynting vector for acoustic waves and the up/down wavefield decomposition in the homogeneous medium

    图 4 

    复杂介质中声波Poynting矢量的求取及上下行波分离

    Figure 4. 

    Calculation of Poynting vector for acoustic waves and the up/down wavefield decomposition in a complex medium

    图 5 

    双层介质中重构的震源波场(a)和经AGC处理后的检波器波场(b)

    Figure 5. 

    Reconstructed source wavefield (a) and receiver wavefield processed by AGC (b) in a two-layer model.

    图 6 

    不同成像条件单炮数据的成像结果

    Figure 6. 

    Imaging results of single-shot data under different imaging conditions

    图 7 

    (a) 真实反射率模型;(b)基于全波成像条件的RTM偏移结果;(c)常规LSRTM迭代10次的反演结果;(d)基于Poynting矢量行波分离的LSRTM方法迭代10次的反演结果

    Figure 7. 

    (a) True reflectivity model; (b) Result of RTM with the full-wave imaging condition; (c) Inversion result after 10 iterations using the conventional LSRTM; (d) Inversion result after 10 iterations using LSRTM with the wavefield decomposition based on Poynting vector

    图 8 

    对于双层介质,常规LSRTM和基于Poynting矢量行波分离的LSRTM收敛性的对比(显然,我们方法的收敛速率更高,残差也更小)

    Figure 8. 

    Comparison of convergence between conventional LSRTM and LSRTM with the wavefield decomposition based on the Poynting vector for the two-layer model(Note that our scheme has a higher convergence rate and a minor residual)

    图 9 

    Marmousi模型

    Figure 9. 

    Marmousi model

    图 10 

    Marmousi模型中的波场快照

    Figure 10. 

    Snapshots of wavefield in the Marmousi model

    图 11 

    Marmousi模型的偏移成像结果

    Figure 11. 

    Migration results of the Mamousi model

    图 12 

    对于Marmousi模型,常规LSRTM和基于Poynting矢量行波分离的LSRTM的收敛曲线

    Figure 12. 

    Comparison of convergence between conventional LSRTM and LSRTM with the wavefield decomposition based on the Poynting vector for the Marmousi model

    图 13 

    常规LSRTM和基于Poynting矢量行波分离的LSRTM达到指定误差阈值所需时间

    Figure 13. 

    Time required for conventional LSRTM and LSRTM based on the Poynting-vector wavefield separation to reach the specified error threshold

    表 1 

    双层介质点积测试结果

    Table 1. 

    Dot product test result for a two-layer model

    Lm, Lm m, LTLm LTLm, LTLm Lm, LLTLm
    偏移算子
    (4)式
    11.4027 11.4027 222.5698 220.2105
    偏移算子
    (9)式
    11.4027 11.4817 35.3858 37.7962
    偏移算子
    (10)式
    11.4027 11.4817 28.2973 29.2468
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出版历程
收稿日期:  2020-04-01
修回日期:  2020-10-19
上线日期:  2021-02-10

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