利用稀疏约束非平稳多项式回归去除地震噪声及拾取初至

doi:10.13810/j.cnki.issn.1000-7210.2020.03.008

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摘要非平稳多项式拟合是L₂范数下的优化问题，尽管考虑了信号的时变特征，但是仍然假设残差呈随机分布，当地震数据中存在较强非随机噪声时，常规的基于L₂范数的非平稳多项式拟合不再适用。为此，研究了稀疏约束非平稳多项式回归理论与方法。首先回顾了非平稳多项式回归的基本原理；针对复杂稀疏分布残差问题，在反问题正则化理论框架下，结合非平稳多项式回归和L₁范数约束，采用整形正则化和L₁范数联合约束策略，利用共轭梯度和投影算法联合求解多约束反问题，同时估计具有时变光滑特征的多项式回归系数和具有稀疏分布特征的回归残差，可克服稀疏分布强噪声对反演的影响，并给出了算法基本流程和参数分析。模拟和实际数据应用结果表明，稀疏约束非平稳多项式回归方法在地震噪声压制和初至拾取等方面具有较好的应用效果。

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	刘国昌
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关键词 ：非平稳多项式回归, L₂范数, L₁范数, 稀疏约束, 初至拾取, 噪声压制

Abstract：Nonstationary polynomial fitting relates to optimization with L₂ norm.Although the time-dependent characteristics of signals are considered,the residual is still assumed to be randomly distributed.In the case that there are strong non-random noises in seismic data,conventional nonstationary polynomial fitting based on L₂ norm is no longer applicable.This study investigated the theory and method of sparse-constrained nonstationary polynomial regression.First,we reviewed the basic principle of non-stationary polynomial regression.Second,to solve the problem related to the complex sparse residual,under the framework of inverse problem regularization theory,we combined non-stationary polynomial regression with L₁ norm constraint,followed the combined constraint strategy of shaping regularization with L₁ norm,and solved the multi-constraint inverse problem with conjugate gradient and projection algorithm.In addition,we estimated the coefficient of polynomial regression with time-varying smoothing characteristics and the residual sparsely distributed,which can reduce the influence of sparse strong noises on inversion.Finally,we proposed the basic process and parameter analysis of the algorithm.Synthetic and field data have proved that sparse constrained non-stationary polynomial regression is effective for noise suppression and pick up first arrival.

Key words： nonstationary polynomial regression L₂ norm L₁ norm sparse constraint pick up first arrival noise suppression

收稿日期: 2019-10-14

PACS:

P631

基金资助:本项研究受国家重点研发计划课题“智能化海上高精度地震数据处理关键技术”（2019YFC0312003）资助。

通讯作者: 刘国昌,北京市昌平区府学路18号中国石油大学(北京)地球物理学院,102249。Email:guochang.liu@cup.edu.cn E-mail: guochang.liu@cup.edu.cn

作者简介: 刘国昌,副教授,博士生导师,1982生;2006、2012年分别获中国石油大学(北京)信息与计算科学专业学士学位、地质资源与地质工程专业博士学位;2012年起在中国石油大学(北京)地球物理学院主要从事地震数据处理、地球物理参数反演和信息识别与分析等相关领域的教研。

引用本文:

刘国昌, 蔡加铭, 闫海洋, 李洁丽, 陈小宏. 利用稀疏约束非平稳多项式回归去除地震噪声及拾取初至[J]. 石油地球物理勘探, 2020, 55(3): 548-556. LIU Guochang, CAI Jiaming, YAN Haiyang, LI Jieli, CHEN Xiaohong. Using sparse-constrained nonstationary polynomial regression to remove seismic noises and picking up first arrival. Oil Geophysical Prospecting, 2020, 55(3): 548-556.

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