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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (3): 328-336.doi: 10.3969/j.issn.1005-3085.2015.03.002

• • 上一篇    下一篇

稳健稀疏反褶积方法研究

高  倩1,   刘建朝1,   常象宇2   

  1. 1- 长安大学地球科学与资源学院数字油田研究所，西安 710045
    2- 西安交通大学数学与统计学院信息与系统科学研究所，西安 710049
  • 收稿日期:2014-04-24 接受日期:2014-10-27 出版日期:2015-06-15 发布日期:2015-08-15
  • 基金资助:
    国家自然科学基金 (11401462).

Study on Robust Sparse Deconvolution

GAO Qian1,  LIU Jian-chao1,   CHANG Xiang-yu2   

  1. 1- Digital Oil Field Institute, School of Earth Science and Resource, Chang'an University, Xi'an 710045
    2- Institute of Information and System Science, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049
  • Received:2014-04-24 Accepted:2014-10-27 Online:2015-06-15 Published:2015-08-15
  • Supported by:
    The National Natural Science Foundation of China (11401462).

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摘要： 地震勘探数字信号处理领域中一个重要而基本的方法是地震信号的反褶积方法．在地震数据的采集过程中往往会遇到异常点的干扰，这种干扰严重影响了利用反褶积方法对真实反射系数与地震子波的重构效果．本文在Canadas等人提出的针对高斯噪声的贝叶斯反褶积数学框架的基础之上，提出一种能够克服异常点干扰的稳健稀疏反褶积方法．新方法针对具有重尾分布的异常点噪声与稀疏的反射系数建模，并使用交替迭代与线性规划的算法求解．最后，通过实验证明该方法在克服异常点噪声的基础上，能实现对地震子波与反射系数的同步估计，所得到的估计有效地消除了重尾分布异常点噪声的影响，提高了地震信号反褶积处理的精度．这也能证明所提算法是收敛的，并且模型是有效的．

关键词: 反褶积, 反射系数, 稳健估计, 稀疏性

Abstract:

A fundamental and important approach in the field of seismic signal processing is the deconvolution of seismic signals. However, seismic signal acquisition can be contaminated by outliers, and the outliers affect the performance of deconvolution results. In this paper, we follow the Bayesian deconvolution framework, which was proposed by Canadas, and propose a new robust sparse deconvolution method for overcoming the influence of outliers. The new approach properly models the heavy-tail outliers and sparse reflection coefficients simultaneously. For solving the approach, we derive a type of alternative algorithm. Finally, we demonstrate the performance of the algorithm by a series of simulations, which show that the new approach can eliminate the influence of heavy-tail outliers and recover the reflection coefficients. This further indicates the approach is valid and the algorithm is convergent.

Key words: deconvolution, reflection coefficient, robust estimation, sparsity

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