【摘要】 本文从稀疏信号恢复理论出发,采用形态分量分析(MCA)方法重建地震数据。MCA方法的核心是选取合适的字典。首先从地震数据的特点和计算复杂性出发,选取非抽样小波变换(UWT)字典和曲波变换(Curve-let)字典,UWT字典用来稀疏表示地震数据的局部奇异部分,Curvelet字典用来稀疏表示地震数据平滑和线状变化部分;其次将数据分解为形态特征不同的两个分量,采用BCR(Block Coordinate Relaxation)算法求解目标函数;最后对两个分量进行插值重建、合并得到最终的重建结果。模型测试和实际资料处理结果表明:利用MCA方法不仅可以对非均匀和大间距数据进行插值重建,而且可消除空间假频;同时该方法本身还具有去噪功能,不受数据带宽的限制。更多还原

【Abstract】 According to the theory of sparse signal recovery,morphological component analysis(MCA) method is used to reconstruct the seismic data in this paper.The key of MCA method is to select the appropriate dictionaries.In view of the characteristics of seismic data and computational complexity,two kinds of dictionaries are selected,that is the undecimated wavelet transform(UWT) dictionary and curvelet transform dictionary.One sparsely represents for local singular part of seismic data,the other sparsely represents for smooth and linear part of seismic data.BCR(Block Coordinate Relaxation) algorithm is used to solve the objective function,and seismic data is decomposed into two morphologically different components.Then the reconstruction results are obtained by summing the components after interpolated and inpainted.Model testing and real data processing show that MCA method can be used not only for reconstruction large spacing uneven data,but also for space aliasing elimination.At the same time,the method itself has the denoising effect without bandwidth restriction.更多还原