基于迭代最小化稀疏学习的三维地震数据重建

受采集技术、现场环境及经济成本等因素的影响,地震勘探中采集的原始数据往往存在缺炮或缺道等现象,这种数据的不完整性对后续数据处理和成像会造成不良影响,故必须重建此类缺失数据。为此,提出基于迭代最小化稀疏学习（Sparse Learning via Iterative Minimization,SLIM）的方法,主要利用三维地震数据频率切片的二维谐波结构特性,对三维随机缺失地震数据进行重建。即先对三维地震数据沿时间轴方向做傅里叶变换,再利用循环最小化算法（Cyclic Minimization,CM）对频率切片的二维谐波谱进行迭代求解,最后对谱估计做傅里叶逆变换而重构缺失数据。此外,采用共轭梯度最小二乘法实现数据重建过程中的求逆运算,以缩短数据重建时间。试验结果表明：所采用的基于频率切片的SLIM方法对合成和实际三维地震数据均取得了较好的重建效果;该方法的重建性能优于基于频率切片的Hankel矩阵降秩的多道奇异谱分析方法（Multi-channel Singular Spectrum Analysis,MSSA）。

3D seismic data reconstruction based on sparse lear-ning via iterative minimization

In seismic exploration,affected by the factors such as acquisition environment,technology and cost,some shots or traces can be missing in field data.The incompleteness of seismic data will have adverse effect on later seismic data processing and imaging,thus the reconstruction of these missing data is essential.In this paper,a sparse learning via iterative minimization (SLIM) method was proposed to reconstruct random missing 3D seismic data.It reconstructs 3D missing seismic data based on the 2D harmonic structure of frequency slice.Firstly,apply Fourier transform to 3D seismic data along time direction.Secondly,use cyclic minimization (CM) algorithm to solve the 2D harmonic spectrum of frequency slice iteratively.Finally,apply inverse Fourier transform to the estimated spectrum,and thus reconstruct the missing data.Besides,conjugate gradient least squares(CGLS) is applied to calculate the inverse in data reconstruction,in order to speed up the reconstruction.Test results indicate that the proposed SLIM method achieved good performance on both synthetic and real 3D seismic data,and it performed better than multi-channel singular spectrum analysis(MSSA) method using singular Hankel matrix based on frequency slice.