非凸L_p范数三维地震数据重建

3D seismic data reconstruction based on non-convex L_p norm

多道奇异谱分析(MSSA)是三维地震数据重建的经典方法之一。通过随机奇异值分解,MSSA方法对地震数据频率切片构造的块Hankel矩阵直接降秩以达到重建的目的,但得到的解往往不是最优解。Lp范数是介于L0范数和L1范数之间的非凸函数,比凸核范数更接近秩函数。本文提出基于非凸Lp范数Hankel重建方法对三维地震数据进行降秩重建。由于该问题是非凸优化问题,在求解时通过设置权重约束奇异值,进行迭代求解,保证了重建数据的低秩性。数值实验结果表明,本文方法优于MSSA方法和正交矩阵匹配追踪Hankel重建方法,恢复的数据信噪比更高。

The multichannel singular spectrum analysis(MSSA)is a classical method to deal with 3 Dseismic data reconstruction.With the random singular value decomposition,the rank of block Hankel matrix constructed by frequency slices of seismic data is reduced by MSSA to reconstruct seismic data,but the solutions are not always optimal ones.Lp norm is a non-convex function between the L0 norm and the L1 norm,and it is closer to the rank function than the convex nuclear norm.So a nonconvex Lp norm Hankel reconstruction method is proposed for 3 Dseismic data rank-reduction reconstruction.Since this is a non-convex optimization problem,singular values are constrained by setting weights for an iterative process,which ensures a low-rank of reconstructed data.Numerical experiment results demonstrate that the proposed me-thod obtains the higher signal-to-noise ratio reconstructed data compared with MSSA and the orthogonal matrix pursuit Hankel reconstruction.