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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.
The reconstruction of seismic data is very crucial in the seismic data processing. In view of the limitation of the Nyquist sampling theorem, the traditional seismic data reconstruction method is more limited, the aliasing is easy to occur in the reconstructed data, and the sparseness of the transform basis function for complex seismic wavefront information Which is not accurate enough, combined with the ability of wave atoms to represent the sparse representation of simple texture model, we can sparsely represent the characteristics of seismic data from the information of the seismic events, and propose a wavelet-based seismic data compression perceptual reconstruction algorithm.Firstly, Wave atomic domain to establish the regressive model of seismic data compression perception reconstruction and solve the L1 norm least optimization problem by Landweber iterative algorithm and sparse inversion.Secondly, to overcome the lack of translational invariance of wave atomic transformation, The false Gibbs phenomenon, the data reconstruction process uses a cyclic shift in the detector axis, and the reconstruction results are linearly averaged to suppress the distortion.Finally, the exponential threshold shrinkage model is used to accelerate the sparseness of the coding coefficient at the initial stage of iteration to remove the noise As the iteration approaches the end, the threshold shrinkage is mitigated and the seismic data is preserved And the main features of the data.Using the synthetic seismic model and the actual data, the experimental results show that this algorithm can effectively improve the SNR of the reconstructed seismic data, and can better maintain the seismic data in the same axis with the complex region Local features: Theoretical and experimental results demonstrate the rationality of establishing and solving compressed seismic data reconstruction models based on the sparse representation of wave atomic domains, and the effectiveness of suppressing the noise in reconstructed data by using cyclic shift and exponential threshold shrinkage models.