基于双重Bregman迭代的地震数据重构与去噪

Seismic data reconstruction and denoising based on dual Bregman iteration

受采集环境、成本及设备等因素的影响,野外采集的地震数据往往存在缺失道和噪声干扰,快速有效的迭代插值方法对地震数据重构与去噪技术具有重要的实际意义。针对含有随机噪声的缺道地震数据,根据压缩感知理论,提出了一种基于双重Bregman迭代的地震数据重构与去噪方法。首先对含有随机噪声的缺道地震数据通过傅里叶变换进行稀疏表示,选取掩膜算子作为观测矩阵,然后将Bregman迭代重构算法作为外部迭代,分裂Bregman迭代去噪算法作为内部迭代,两者结合形成双重Bregman迭代,在迭代控制准则条件下,对含噪声的缺道地震数据进行重构和去噪。数值模拟实验和实际数据测试结果表明,双重Bregman迭代算法同时考虑了地震数据的重构与去噪,将独立的两种算法融合在一起,在对地震数据进行插值重建的同时去除了部分随机噪声。该算法迭代次数少,重构得到的地震数据精度高于线性Bregman迭代算法的重构精度,可以更有效地恢复含随机噪声的缺失地震信息,为地震数据恢复提供了一种可供选择的缺失地震数据处理方法。

Seismic data collected in the field often have missing traces and interference noise due to the influence of the acquisition environment cost,and exploration equipment.This causes spatial false frequency or false diffraction on migration sections.Conventional methods of interpolation reconstruction make it difficult to balance reconstruction accuracy and iteration efficiency,and interference by random noise is a common problem that results in insufficient reconstruction of missing data.Consequently,a method of seismic simultaneous reconstruction and denoising using dual Bregman iteration was proposed,based on the theory of compressed sensing.First,seismic data with missing traces and random noise were sparsely represented using a Fourier transform.The mask operator was then selected as the observation matrix with elements set as zero for the positions of the data to be reconstructed and one for the other positions.Next,the linear Bregman iterative reconstruction algorithm was taken as the external iteration for seismic data reconstruction,and the split Bregman iterative denoising algorithm was taken as the internal iteration for seismic data denoising.The two iteration algorithms were combined to form the dual Bregman iteration.Under the condition of iterative control criterion,seismic data with missing traces and noises were reconstructed and denoised simultaneously.Tests on model and field data verified the effectiveness of the proposed method.The dual Bregman iterative algorithm can obtain reconstructed seismic data with higher accuracy and fewer iterations than the linear Bregman iterative algorithm under the same conditions.This provides an alternative method for seismic data recovery.