地球物理学报 ›› 2012, Vol. 55 ›› Issue (09): 3105–3114.doi: 10.6038/j.issn.0001-5733.2012.09.028

• 应用地球物理 • 上一篇    下一篇

时-空局域化地震波传播方法:Dreamlet叠前深度偏移

吴帮玉1,2, 吴如山2, 高静怀1   

  1. 1. 西安交通大学电子与信息工程学院波动与信息研究所, 西安 710049;
    2. Modeling and Imaging Laboratory, University of California, Santa Cruz, U.S.A. 95064
  • 收稿日期:2011-05-12 修回日期:2012-07-19 出版日期:2012-09-20 发布日期:2012-09-20
  • 通讯作者: 高静怀,男,教授,博士生导师,主要从事复杂介质中地震波传播及地震资料处理的理论与方法等研究. E-mail:jhgao@mail.xjtu.edu.cn E-mail:jhgao@mail.xjtu.edu.cn
  • 基金资助:
    国家自然科学基金重点项目(40730424);国家科技重大专项(2011ZX05023-005);WTOPI(Wavelet Transform on Propagation and Imaging for seismic exploration) Projectat University of California,Santa Cruz,United States,国家建设高水平大学公派研究生项目资助.

Time-space localized seismic wave propagation: Dreamlet prestack depth migration

WU Bang-Yu1,2, WU Ru-Shan2, GAO Jing-Huai1   

  1. 1. Institute of Wave and Information, School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, China;
    2. Modeling and Imaging Laboratory, University of California, Santa Cruz, CA, U.S.A. 95064
  • Received:2011-05-12 Revised:2012-07-19 Online:2012-09-20 Published:2012-09-20

摘要: 提出了一种在时间和空间上完全局域化的波场分解和传播算法─dreamlet偏移方法.Dreamlet是一种脉冲-小波束形式的波场分解原子,它利用多维局部分解变换,把时空域波场映射到局部时间-频率-空间-波数相空间,并用局部相空间的传播算子(dreamlet算子)沿深度延拓.本文利用多维局部余弦变换实现dreamlet算法,分解后的波场系数和传播算子不仅有很好的稀疏性,且均为实数,也即波的传播和成像过程完全在实数域实现.文中推导了局部余弦基dreamlet波场分解和传播算子理论公式并将其应用于叠前深度偏移.在dreamlet相空间波的传播过程为稀疏矩阵相乘,而且延拓后的地表数据波场的有效时间长度随深度的增加不断减小,从而可以减少需要传播的波场系数.二维SEG/EAGE盐丘和SIGSBEE模型算例验证了理论推导的正确性,成像结果显示该方法在横向速度变化剧烈情况下有很好的精度.

关键词: Dreamlet, 时空局域化, 多维局部余弦变换, 单程波动方程, 叠前深度偏移

Abstract: We propose a complete time-space localized seismic wavefield decomposition and propagation method─dreamlet migration. The time-space wavefield is projected to the time-frequency-space-wavenumber domain by the local cosine transform, and the wavefield is extrapolated to next depth by the local phase space dreamlet one-way propagator. The wavefield and propagator after decomposition are very sparse and most importantly, they stay in the real data domain, which means the process of propagation and imaging complete in the real data domain. In this paper, we derive the formulas of the wavefield decomposition and phase-space dreamlet one-way propagator. The dreamlet domain wave propagation is sparse matrix multiplication, and the valid time length of the receiver wavefield is shrinking as the depth increasing. Numerical examples and tests on the synthetic two dimensional SEG/EAGE salt model and SIGSBEE model demonstrate the validity of this method. Migration results show that this method has good imaging quality in laterally high contrast heterogeneous media.

Key words: Dreamlet, Time-space localization, Multi-dimensional local cosine transform, One-way wave equation, Prestack depth migration

中图分类号: 

  • P631
[1] Steinberg B Z. Evolution of local spectra in smoothly varying nonhomogeneous environments local canonization and marching algorithms. J. Acoust. Soc. Am., 1993, 93(5): 2566-2580.
[2] Steinberg B Z, Birman R. Phase-space marching algorithm in the presence of a planar wave velocity discontinuity-A qualitative study. J. Acoust. Soc. Am., 1995, 98(1): 484-494.
[3] Wu R S, Wang Y Z, Gao J H. Beamlet migration based on local perturbation theory. // 70th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 2000: 1008-1011.
[4] Wu R S, Chen L. Wave propagation and imaging using Gabor-Daubechies beamlets. // Theory and Computational Acoustics, World Scientific, New Jersey, 2002: 661-670.
[5] Chen L, Wu R S, Chen Y. Target-oriented beamlet migration based on Gabor-Daubechies frame decomposition. Geophysics, 2006, 71(2): s37-s52.
[6] Wu R S, Wang Y Z, Luo M Q. Beamlet migration using local cosine basis. Geophysics, 2008, 73(5): 207-217.
[7] 毛剑, 吴如山, 高静怀. 利用局部谐和基小波束的高精度叠前深度域偏移成像方法研究. 地球物理学报, 2010, 53(10): 2442-2451. Mao J, Wu R S, Gao J H. High-accuracy prestack depth migration and imaging using local harmonic basis beamlet. Chinese J. Geophys. (in Chinese), 2010, 53(10): 2442-2451.
[8] 高静怀, 周艳辉, 毛剑等. 局部角度域波传播步进算法研究. 地球物理学报, 2007, 50(1): 248-259. Gao J H, Zhou Y H, Mao J, et al. A wave propagation method in local angle domain. Chinese J. Geophys. (in Chinese), 2007, 50(1): 248-259.
[9] Ma Y W, Margrave G F. Seismic depth migration with the Gabor transform. Geophysics, 2008, 73(3): s91-s97.
[10] Pedersen Ø, Brandsberg-Dahl S, Ursin B. Seismic imaging using lateral adaptive windows. Geophysics, 2010, 75(2): s73-s79.
[11] Candès E J, Demanet L, Donoho D, Li Y. Fast discrete curvelet transforms. SIAM Multiscale Modeling and Simulation, 2006, 5(3): 861-899.
[12] Herrmann F. Optimal seismic imaging with curvelets. // 73th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 2003: 997-1000.
[13] Candès E J, Demanet L. The curvelet representation of wave propagators is optimally sparse. Communications on Pure and Applied Mathematics, 2004, 58: 1472-1528.
[14] Douma H, de Hoop M V. Leading-order seismic imaging using curvelets. Geophysics, 2007, 72(6): s231-s248.
[15] Wu R S, Wu B Y, Geng Y. Seismic wave propagation and imaging using time-space wavelets. // 78th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 2008: 2983-2987.
[16] Wu R S, Wu B Y, Geng Y. Imaging in compressed domain using dreamlets. // CPS/SEG Beijing' 2009, International Geophysical Conference, Expanded Abstracts, ID: 57.
[17] Mao J, Wu R S, Gao J H. Directional illumination analysis using the local exponential frame. Geophysics, 2010, 75(4): s163-s174.
[18] Püschel M, Moura J. The algebraic approach to the discrete cosine and sine transform and their fast algorithms. SIAM Journal of Computing, 2003, 32(5): 1280-1316.
[19] Coifman R R, Meyer Y. Remaxques sur 1'analyse de Fourier a fengtre. Comptes Rendus de l' Acad6mie des Sciences, 1991, 312: 259-261.
[1] 吴帮玉;吴如山;高静怀;徐宗本. 基于时空局域化dreamlet单程波算子的观测系统沉降法偏移[J]. 地球物理学报, 2017, 60(9): 3505-3517.
[2] 王华忠;冯波;刘少勇;胡江涛;王雄文;李辉. 叠前地震数据特征波场分解、偏移成像与层析反演[J]. 地球物理学报, 2015, 58(6): 2024-2034.
[3] 高成;孙建国;齐鹏;孙辉;刘志强;刘明忱. 2D共炮时间域高斯波束偏移[J]. 地球物理学报, 2015, 58(4): 1333-1340.
[4] 杨继东;黄建平;王欣;李振春;段心意. 复杂地表条件下叠前菲涅尔束偏移方法[J]. 地球物理学报, 2015, 58(10): 3758-3770.
[5] 李添才;谢玉洪;李列;王华忠;王新领;但志伟;胡江涛. 黏声介质平面波有限差分叠前深度偏移及在莺歌海盆地的应用[J]. 地球物理学报, 2014, 57(5): 1612-1622.
[6] 吴帮玉;吴如山;高静怀. 基于局部余弦基小波束的观测系统沉降法叠前深度偏移[J]. 地球物理学报, 2013, 56(2): 635-643.
[7] 段鹏飞;程玖兵;陈爱萍;何光明. TI介质局部角度域高斯束叠前深度偏移成像[J]. 地球物理学报, 2013, 56(12): 4206-4214.
[8] 段鹏飞;程玖兵;陈三平;何光明. TI介质局部角度域射线追踪与叠前深度偏移成像[J]. 地球物理学报, 2013, 56(1): 269-279.
[9] 耿瑜;吴如山;高静怀. 基于Dreamlet变换的地震数据压缩理论与方法[J]. 地球物理学报, 2012, 55(08): 2705-2715.
[10] 刘定进;杨瑞娟;罗申玥;王鹏燕;郑小鹏;宋林. 稳定的保幅高阶广义屏地震偏移成像方法研究[J]. 地球物理学报, 2012, 55(07): 2402-2411.
浏览
全文


摘要

被引

  分享   
  讨论   
No Suggested Reading articles found!