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。
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there are strong non-random noises in seismic data,conventional nonstationary polynomial fitting based on L2 norm is no longer applicable.This study investigated the theory and method of sparse-constrained nonstationary polynomial regression.First,we reviewed the basic principle of non-stationary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 nonstationary 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 nonstationary polynomial regression is effective for noise suppression and pick up first arrival.
作者
刘国昌
蔡加铭
闫海洋
李洁丽
陈小宏
LIU Guochang;CAI Jiaming;YANHaiyang;LI Jieli;CHEN Xiaohong(College of Geophysics,China University of Petroleum(Beijing),Beijing 102249,China;Geophysical Research Institute,BGP,CNPC,Zhuozhou,Hebei 072751,China;Division of Marine Geophysical Exploration,BGP,CNPC,Tianjin 300450,China)
出处
《石油地球物理勘探》
EI
CSCD
北大核心
2020年第3期548-556,469,共10页
Oil Geophysical Prospecting
基金
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
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
nonstationary polynomial regression
L2norm
L1norm
sparse constraint
pick up first arrival
noise suppression
