Abstract: Singular Value Decomposition（SVD） has a better development in noise reduction for seismic data. SVD can achieve a better result for the horizontal events that show linear models. However, it can not achieve a good result for the curve events that show nonlinear models. This limits in practice. This paper proposes a random noise reduction method for seismic data based on Locally Linear Embedding（LLE）. The idea is that it only considers the reconstruction properties of LLE, not considers its properties of dimension reduction. The method uses the reconstruction of Locally Linear Embedding to reconstruct each sample of seismic data by its neighborhoods. Then, the results after reducing random noise are obtained. The conducted results on forward model and real seismic data show that the proposed method not only can effectively reduce random noise, but also can keep the effective signals that show nonlinear models. And it is better than the SVD filtering result.

Key words: Locally Linear Embedding（LLE）, seismic data, random noise, noise reduction, Singular Value Decomposition（SVD）, reconstruction

摘要： 奇异值分解（SVD）方法在地震数据去噪中得到了较好的发展。在时间域或频率域进行随机噪声压制时，SVD技术往往对呈现线性模式的水平同相轴有较好的去噪效果。然而，对呈现非线性模式的弯曲同相轴效果不佳，从而限制了其在实际中的应用。为此，提出一种基于局部线性嵌入（LLE）的地震数据随机噪声压制方法，其思想是不考虑LLE方法的降维特性，而仅考虑其重构特性，利用局部线性嵌入的重构思想，对地震数据采样点用其近邻进行重构，得到去除随机噪声后的结果。正演模型及实际资料处理结果对比表明，该方法在有效压制随机噪声的同时，能够较好地保留非线性模式的有效信号，优于常规SVD滤波结果。

关键词: 局部线性嵌入, 地震数据, 随机噪声, 去噪, 奇异值分解, 重构