基于收缩多道奇异谱分析的含噪地震信号重建

Noisy Seismic Signal Regularization Based on Shrinked Multichannel Singular Spectrum

基于矩阵秩减理论的联合去噪与重建方法已被广泛应用于勘探地震和天然地震的波形数据重建。经典的多道奇异谱分析(MSSA)方法在对频域切片分量数据投影的块Hankel矩阵降秩过程中采用了常规截断奇异值分解,其固有理论缺陷及不适当的秩选参数均容易在迭代插值过程中引入含有残余噪声的次优解,本文在此基础上提出了一种收缩多道奇异谱分析(SMSSA)方法,通过引入在大维渐近矩阵框架下最小化核范数损失函数的优化奇异值收缩方法对原始数据奇异值进行收缩约束,以低秩逼近有效波信号,并将其嵌入凸集投影(POCS)加权迭代框架中以对含噪缺道地震数据进行联合去噪与规则化重建。合成模型和实际资料处理结果表明,本文所提SMSSA方法优于传统的MSSA方法、正交秩-1矩阵追踪(OR1MP)方法和格拉斯曼流形重建(Grouse)方法,能够在重建数据同时有效压制干扰噪声,重建结果信噪比更高,具有较好的适用性和稳定性。

Simultaneous seismic data denoising and regularization techniques based on rank-reduction method have been widely applied in the field of exploration seismology and natural earthquake seismology.Considering the problem that the traditional multichannel singular spectrum analysis(MSSA)method usually get sub-optimal solutions with residual noise in the iterative interpolation process,due to the uncertain rank-selection parameters when using the truncated singular value decomposition to block Hankel matrix.In this paper,there is a shrinked multichannelsingular spectrum analysis(SMSSA)method proposed for seismic data rank-reduction reconstruction which combining an optimal shrinkage operator of singular values,which derived by minimizing the nuclear norm loss under the asymptotic matrix framework with a projection onto convex sets(POCS)iterative algorithm.The new method is tested with synthetic models and field datasets,and the results illustrate that the proposed SMSSA method obtains the higher signal-to-ratio regularized data is superior to the MSSA method,the OR1MP method and the Grousemethod,which has better applicability and stability.