中文摘要：

地震数据重建是地震数据处理流程中关键步骤之一,重建效果的好坏直接影响到后续的多次波消除以及偏移成像效 果.为了获得更好的重建效果,提出了以压缩感知为理论基础,采用jitter欠采样的Shearlet变换稀疏约束地震数据重建 方法.将 Shearlet变换与凸集投影（ POCS）算法结合起来在动校正预处理后对地震数据进行重建,增强了地震数据在 Shearlet域的稀疏性.理论分析和实际地震数据验证结果表明,该方法可以在部分地震数据缺失的情况下取得很好的重建 效果,有效地解决了假频问题.

英文摘要：

Seismic data reconstruction is a key step in seismic data processing. Reconstruction result will directly affect the multiple elimination and subsequent migration imaging. To get better reconstruction result,on the basis of the theory of com-pressed sensing,a new seismic data reconstruction method based on the Shearlet transform sparse constraint using j ittered undersampling is proposed. Shearlet transform is a kind of multi-scale transform to express multi-dimensional data well, which has the optimal sparseness,orientation and the characteristics of localization We combine the Shearlet transform with the projection onto convex sets （POCS） algorithm for seismic data reconstruction Then we conduct normal moveout correction （NMO） prior to reconstruction to streng then the sparseness of the seismic data in the Shearlet domain. The experiments on synthetic data as well as actual data show that even though some seismic data are missing, the reconstruction method based on the Shearlet transform performs excellent and effectively solves the al iasing problem.