基于自相似性和低秩先验的地震数据随机噪声压制

随机噪声的存在会降低地震资料信噪比(signal-to-noise ratio,SNR),影响后续资料的处理与分析。基于低秩先验的地震数据随机噪声压制方法将去噪问题通过建模转化为求解秩最小化问题,通过矩阵降秩实现随机噪声的去除。考虑到地震数据具有较强的相似特性,提出了基于自相似性先验(self-similarity prior,SP)和截断核范数正则化(truncated nuclear norm regularization,TNNR)的地震数据去噪方法,即SP-TNNR方法,以自相似块组为单元,用截断核范数代替传统的核范数在地震数据“组域”进行低秩约束去噪。首先搜索地震数据的自相似块,构成自相似块组;然后在自相似块组添加TNNR最小化约束;最后采用加速近端梯度法(accelerated proximal gradient line,APGL)对优化问题进行求解。仿真数据和实际地震数据实验结果均表明,SP-TNNR方法能够在保持边缘信息和有效信息的前提下压制随机噪声,去噪后的地震数据具有更高的信噪比。

The low-rank-based denoising approach has become one of the most popular methods to suppress random noise via a rank-reduction technique.In light of the high similarity of seismic data,a seismic denoising method (SP-TNNR) based on self-similarity prior (SP) and truncated nuclear norm regularization (TNNR) was proposed.In this study,each similar group was considered as a unit,and the truncated nuclear norm was utilized instead of the traditional nuclear norm.First,the self-similar blocks of the seismic data were searched to form a self-similar block group.Then,the TNNR minimization constraint was applied to the block group.Finally,the optimization problem was solved using the accelerated proximal gradient line (APGL) algorithm.Tests on both numerical and field data demonstrated that the SP-TNNR can suppress the random noise while preserving the effective signals.

国家重点研发计划项目(2018YFC1503705)、湖北省教育厅科学技术研究项目(B2017597)、“地球内部多尺度成像”湖北省重点实验室开放基金项目(SMIL-2018-06)和华中师范大学基本科研业务费(CCNU19TS020)共同资助。