The basic assumption of low‐rank methods is that noise‐free seismic data can be represented as a low‐rank matrix. Effective noise reduction can be achieved through the low‐rank approximation of Hankel matrices composed of the data. However, selecting the appropriate rank parameter and avoiding expensive singular value decomposition are two challenges that have limited the practical application of this method. In this paper, we first propose symplectic geometric decomposition that avoids singular value decomposition. The symplectic similarity transformation preserves the essence of the original time sequence as well as the signal's basic characteristics and maintains the approximation of the Hankel matrix. To select an appropriate rank, we construct the symplectic geometric entropy according to the distribution of eigenvalues and search for high‐contributing eigenvalues to determine the needed rank parameter. Therefore, we provide an adaptive approach to selecting the rank parameter by the symplectic geometric entropy method. The synthetic examples and field data results show that our method significantly improves the computational efficiency while adaptively retaining more effective signals in complex structures. Therefore, this method has practical application value.

中文翻译：

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基于低秩自适应辛几何分解的地震噪声衰减方法

低秩方法的基本假设是无噪声地震数据可以表示为低秩矩阵。通过由数据组成的汉克尔矩阵的低秩近似可以实现有效的降噪。然而，选择适当的秩参数和避免昂贵的奇异值分解是限制该方法实际应用的两个挑战。在本文中，我们首先提出避免奇异值分解的辛几何分解。辛相似变换保留了原始时间序列的本质以及信号的基本特征，并保持了汉克尔矩阵的近似。为了选择合适的等级，我们根据特征值的分布构造辛几何熵，并搜索高贡献的特征值以确定所需的等级参数。因此，我们提供了一种通过辛几何熵方法来选择秩参数的自适应方法。综合例子和现场数据结果表明，我们的方法显着提高了计算效率，同时自适应地保留复杂结构中更有效的信号。因此，该方法具有实际应用价值。