吉林大学学报(地球科学版) ›› 2016, Vol. 46 ›› Issue (6): 1855-1864.doi: 10.13278/j.cnki.jjuese.201606304

• 地球探测与信息技术 • 上一篇    下一篇

Shearlet域稀疏约束地震数据重建

刘成明, 王德利, 胡斌, 王通   

  1. 吉林大学地球探测科学与技术学院, 长春 130026
  • 收稿日期:2016-03-04 出版日期:2016-11-26 发布日期:2016-11-26
  • 通讯作者: 王德利,男(1973),教授,博士生导师,主要从事各向异性介质波场正、反演理论和高精度地震勘探研究,E-mail:wangdeli@jlu.edu.cn E-mail:wangdeli@jlu.edu.cn
  • 作者简介:刘成明,男(1990),博士研究生,主要从事地震数据稀疏约束处理方法的研究,E-mail:liucm1991@qq.com
  • 基金资助:
    国家科技重大专项项目（2011ZX05023-005-008）；国家自然科学基金项目（41374108）

Seismic Data Interpolation Based on Sparse Constraint in Shearlet Domain

Liu Chengming, Wang Deli, Hu Bin, Wang Tong   

  1. College of GeoExploration Science and Technology, Jilin University, Changchun 130026, China
  • Received:2016-03-04 Online:2016-11-26 Published:2016-11-26
  • Supported by:
    Supported by National Science and Technology Major Project (2011ZX05023-005-008) and National Natural Science Foundation of China (41374108)

PDF (PC)

364

摘要： 在地震数据处理流程中，通常对不规则的、稀疏的或者缺失的地震数据进行插值处理，通过插值方法来避免多次波的预测错误和成像假频等现象，使地震数据处理更加精准。Shearlet变换是一种多尺度变换，具有最佳的稀疏性、方向性以及局部化特性。将Shearlet变换与基于Landweber加速下降迭代方法结合起来对地震数据进行插值，在保证求解精度的同时提高了计算效率。信号和噪声在Shearlet域具有不同的分布特点，通过阈值法压制随机噪声，可提高算法的抗噪性。此外，采用jitter采样的方式，更好地压制了假频信息。理论和实际地震数据验证了该方法的有效性。

关键词: Shearlet变换, 插值, 稀疏变换, 压缩感知, jitter采样

Abstract: Seismic data interpolation for the missing traces forms a crucial step in the seismic processing flow. Interpolation result will affect the subsequent migration imaging and the effect of multiple elimination directly. Shearlet transform is a new multi-scale transform with multi-directions, multi-resolutions, and optimal sparse approximation properties. We propose an accelerate iterative Landweber algorithm for seismic data interpolation based on Shearlet transform, ensuring the precision and improving the computational efficiency at the same time. According to the distribution characteristics of signals and noise, the signal-to-noise ratio could be improved by using a threshold method to suppress random noise, improving the anti-noise capability of our algorithm. Moreover, jittered undersampling is adopted to suppress aliasing. A stylized experiment on synthetic as well as field data show the method is effective and robust.

Key words: Shearlet transform, interpolation, sparse transform, compress sensing, jittered undersampling

中图分类号: 

  • P631.4
[1] Canning A, Gardner G H F. Regularizing 3-D Data Sets with DMO[J]. Geophysics, 2012, 61(4):1103-1114.
[2] Chemingui N, Chemingui N. Handling the Irregular Geometry in Wide-Azimuth Surveys[J]. Seg Technical Program Expanded Abstracts, 1999, 15(1):2106.
[3] Spitz S. Seismic Trace Interpolation in the F-X Do-main[J]. Geophysics, 2012, 56(6):785.
[4] Gulunay N. Unaliased f-k Domain Trace Interpo-lation (UFKI)[J]. Seg Technical Program Expanded Abstracts, 1996, 15(1):2106.
[5] Herrmann F J, Gilles H. Non‐Parametric Seismic Data Recovery with Curvelet Frames[J]. Geophysical Journal International, 2008, 173(1):233-248.
[6] Wang D, Bao W, Xu S,et al. Seismic Data Inter-polation with Curvelet Domain Sparse Constrained Inversion[J]. Journal of Seismic Exploration, 2014, 23(1): 89-102.
[7] 路交通, 曹思远, 董建华. 基于稀疏变换的地震数据重构方法[J]. 物探与化探, 2013, 37(1): 175-179. Lu Jiaotong, Cao Siyuan, Dong Jianhua. A Study of Seismic Data Recovery Based on Sparse Transform[J]. Geophysical & Geochemical Exploration, 2013, 37(1): 175-179.
[8] Wang D L, Tong Z F, Tang C, et al. An Iterative Curvelet Thresholding Algorithm for Seismic Random Noise Attenuation[J]. Applied Geophysics, 2010, 7(4): 315-324.
[9] 刘财,崔芳姿,刘洋,等.基于低信噪比条件下新型Seislet变换的阈值去噪方法[J].吉林大学学报(地球科学版),2015,45(1):293-301. Liu Cai, Cui Fangzi, Liu Yang, et al. Threshold Denoising Method Based on New Seislet Transform in the Condition of Low SNR[J]. Journal of Jilin University (Earth Science Edition),2015,45(1):293-301.
[10] Candè E J, Wakin M B. An Introduction to Compre-ssive Sampling[J]. IEEE Signal Processing Magazine, 2008, 25(2):21-30.
[11] Hennenfent G, Herrmann F J. Simply Denoise: Wa-vefield Reconstruction via Jittered Undersampling[J]. Geophysics, 2008, 73(3): V19-V28.
[12] Herrmann F J, Wang D, Hennenfent G, et al. Cur-velet-Based Seismic Data Processing: A Multiscale and Nonlinear Approach[J]. Geophysics, 2008, 73(1):2220.
[13] Kutyniok G, Lim W Q. Compactly Supported Shear-lets Are Optimally Sparse[J]. Journal of Approximation Theory, 2011, 163(11): 1564-1589.
[14] Kittipoom P, Kutyniok G, Lim W Q. Construction of Compactly Supported Shearlet Frames[J]. Constructive Approximation, 2012, 35(1): 21-72.
[15] Daubechies I, Fornasier M, Loris I. Accelerated Pro-jected Gradient Method for Linear Inverse Problems with Sparsity Constraints[J]. Journal of Fourier Analysis and Applications, 2008, 14(5/6): 746-792.
[16] Guo K, Kutyniok G, Labate D. Sparse Multidimen-sional Representations Using Anisotropic Dilation and Shear Operators[C]//International Conference on the Interaction. Athens: Wavelets and Splines, 2005:189-201.
[17] Labate D, Kutyniok G. Sparse Multidimensional Re-presentation Using Shearlets[C]//Proceedings of SPIE.[S. l.]: The International Society for Optical Engineering, 2005, 5914(1):254-262.
[18] Kutyniok G, Shahram M, Zhuang X. ShearLab: A Rational Design of a Digital Parabolic Scaling Algorithm[J]. Siam Journal on Imaging Sciences, 2011, 5(4):1291-1332.
[19] Kittipoom P, Kutyniok G, Lim W Q. Construction of Compactly Supported Shearlet Frames[J]. Constructive Approximation, 2012, 35(1): 21-72.
[20] Vogel C R. Computational Methods for Inverse Pro-blems[M]. Philadelphia: Society for Industrial and Applied Mathematics, 2002.
[21] Daubechies I, Defrise M, Mol C D. An Iterative Th-resholding Algorithm for Linear Inverse Problems with a Sparsity Constrains[J]. Communications on Pure and Applied Mathematics, 2004, 57(11): 1413-1457.
[1] 王宪楠, 刘四新, 程浩. Shearlet变换在GPR数据随机噪声压制中的应用[J]. 吉林大学学报(地球科学版), 2017, 47(6): 1855-1864.
[2] 刘祚冬, 王红军, 马锋, 吴珍珍, 杜商, 汪永华. 基于空间网格插值的重油油藏资源量计算方法——以扎格罗斯白垩系重油层资源评价为例[J]. 吉林大学学报(地球科学版), 2017, 47(6): 1668-1677.
[3] 余楚, 张翼龙, 孟瑞芳, 曹文庚. 河套平原浅层地下水动态监测网优化设计[J]. 吉林大学学报(地球科学版), 2015, 45(4): 1173-1179.
[4] 王兆国，程顺有，刘财. 地球物理勘探中几种二维插值方法的误差分析[J]. 吉林大学学报(地球科学版), 2013, 43(6): 1997-2004.
[5] 徐明华，李瑞，路交通，蒙杉，龚幸林. 基于压缩感知理论的缺失地震数据重构方法[J]. 吉林大学学报(地球科学版), 2013, 43(1): 282-290.
[6] 叶佩,李庆春. 旅行时线性插值射线追踪提高计算精度和效率的改进方法[J]. 吉林大学学报(地球科学版), 2013, 43(1): 291-298.
[7] 佴磊, 彭文, 袁明哲, 周能娟. 基于经验模态分解和加权最小二乘支持向量机的采空区地面塌陷预测[J]. J4, 2011, 41(3): 799-804.
[8] 李湘凌, 张颖慧, 杨善谋, 袁峰, 周涛发. 合肥义城地区土壤重金属污染评价中典型插值方法的对比[J]. J4, 2011, 41(1): 222-227.
[9] 张继锋, 汤井田, 喻言, 刘长生. 基于二次插值的线源可控源有限元数值模拟[J]. J4, 2009, 39(5): 929-935.
[10] 张东良, 孙建国. F-K反偏移中的插值映射[J]. J4, 2009, 39(4): 749-754.
[11] 孙 建 国. 均匀介质中的F-K反偏移：基本概念、基本公式及其在非均匀介质中的应用[J]. J4, 2008, 38(1): 135-0143.
[12] 翁爱华,王雪秋. 高精度地面核磁共振数据正演计算[J]. J4, 2007, 37(3): 620-0623.
[13] 熊 彬. 大回线瞬变电磁法全区视电阻率的逆样条插值计算[J]. J4, 2005, 35(04): 515-0519.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 《吉林大学学报(地球科学版)》编辑部
地址：长春市西民主大街938号(130026)　电话：+86-431-88502374；13756165364　E-mail: xuebao1956@jlu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发