摘要
地震数据重建在地震数据处理中是非常关键的问题,针对传统地震数据重建方法受奈奎斯特采样定理的限制较大,重建数据易出现假频,以及变换基函数对于复杂地震波前信息的稀疏表示不够准确的问题,结合波原子对于简单纹理模型具有最优的稀疏表示能力,可以较好稀疏表示地震数据同相轴信息的特点,提出基于波原子域的地震数据压缩感知重建算法.首先,在波原子域建立地震数据压缩感知重建正则化模型,通过Landweber迭代算法,稀疏反演求解L1范数最小优化问题.其次,为克服波原子变换缺乏平移不变性,易在地震数据缺失道邻域产生伪吉布斯现象的缺点,数据重建过程中在检波器轴采用循环平移技术,对重建结果线性平均以抑制失真.最后,利用指数阈值收缩模型在迭代初期加速促进编码系数的稀疏程度,去除噪声,迭代接近结束时减缓阈值收缩,加强保留地震数据的细节信息与数据的主要特征.利用合成地震模型及实际数据,通过与现有算法对比实验,表明本文算法能有效提高重建地震数据SNR,并且可以更好的保持地震数据同向轴复杂区域的局部特征.理论及实验证明了以波原子域稀疏表示为基础,建立、求解地震数据压缩感知重建模型的合理性,以及结合循环平移技术、指数阈值收缩模型抑制重建数据中噪声的有效性.
Seismic data reconstruction is the critical problem in seismic data processing. Aiming at the problems that the traditional seismic data reconstruction methods are seriously limited by the Nyquist sampling theorem,which usually leads to aliasing,and the basis functions of common sparse transform can not accurately represent the complex wavefront in seismic data,a algorithm of seismic data compressed sensing reconstruction based on wave atoms domain is proposed,with the characteristics that the wave atom shows the ability of optimal sparse representation to the simple texture model,which can be used to accurately represent the events information in seismic data. Firstly, the regular reconstruction model of seismic data based on the compressed sensing framework is established in wave atoms domain,and then the L1 norm minimum optimization problem is solved by Landweber iterative sparseconstrained inversion algorithm. Secondly,cycle spinning is applied to compensate for the lack of translation invariance property of the wave atoms transform,and suppress pseudo-Gibbs phenomena of missing traces neighborhood in seismic data,by linear average of the reconstructed results. Finally,In order to accelerate the sparse degree promotion of coding coefficients and noise removal at the beginning of iteration,and reserve the details and main features of seismic data,by slowing down the threshold shrinkage at the end of iteration,the exponential threshold shrinkage model is adopted.Through the contrast with the existing algorithms in synthetic seismic models and real data,the proposed algorithm yields higher SNR,and preserves the local features in the regions of the complex events better. The theory and experiment proved that it is reasonable to establish and solve the compressed sensing reconstruction model,based on the sparse representation of wave atoms domain,as well as it is effective to suppress the noise in the reconstructed data,combined with the cyclic translation technique,and the exponential threshold shrinkage model.
作者
张岩
任伟建
唐国维
ZHANG Yan;REN Wei-jian;TANG Guo-wei(School of Computer and Information Technology, North East Petroleum University,Heilongjiang Daqing 163318, China;School of Electrical Engineering and Information, North East Petroleum University,Heiloagjiang Daqing 163318, China)
出处
《地球物理学进展》
CSCD
北大核心
2017年第5期2152-2161,共10页
Progress in Geophysics
基金
国家自然科学基金项目"基于信道衰落的非线性随机系统分布式滤波及故障检测"(61374127)
大庆市指导性科技计划项目"基于压缩感知的地震数据重建技术研究"(zd-2016-009)联合资助
关键词
地震数据重建
压缩感知
波原子
稀疏表示
seismic data reconstruction
compressed sensing
wave atoms
sparse representation
