Rank-reduction methods are effective for separating random noise from the useful seismic signal based on the truncated singular value decomposition (TSVD). However, the results that the TSVD operator provides are still a mixture of noise and signal subspaces. This problem can be solved using the damped rank-reduction method by damping the singular values of noise-contaminated signals. When the seismic data include highly linear or curved events, the rank should be large enough to preserve the details of the useful signal. However, the damped rank-reduction operator becomes less powerful when using a large rank parameter. Hence, the denoised data contain significant remaining noise. More recently, the optimally damped rank-reduction method has been proposed to solve the extra noise problem as the rank value increases. The optimally damped rank-reduction operator works well for a moderately large rank, but becomes ineffective for a very large rank. We introduce an adaptive damped rank-reduction algorithm to attenuate the residual noise for a very large rank parameter. To elaborate on the proposed algorithm, we first construct a gain matrix by only using the input rank parameter, which we introduce directly into the adaptive singular-value weighting formula to make it more stable as the rank parameter becomes too large. Then, we derive a damping operator based on the improved optimal weighting operator to attenuate the residual noise. The proposed method, which can be regarded as an improved version of the optimally damped rank-reduction method, is insensitive to the input parameter. Examples of synthetic and real three-dimensional seismic data show the denoising improvement using the proposed method.

基于截断奇异值分解 (TSVD)，降秩方法可有效地将随机噪声从有用的地震信号中分离出来。然而，TSVD 算子提供的结果仍然是噪声和信号子空间的混合。这个问题可以通过阻尼噪声污染信号的奇异值使用阻尼降阶方法来解决。当地震数据包括高度线性或弯曲的事件时，等级应该足够大以保留有用信号的细节。然而，当使用大秩参数时，阻尼降秩算子变得不那么强大了。因此，去噪数据包含大量剩余噪声。最近，已经提出了最优阻尼秩降低方法来解决随着秩值增加而产生的额外噪声问题。最佳阻尼降阶算子适用于中等大的秩，但对于非常大的秩无效。我们引入了一种自适应阻尼秩降低算法来衰减非常大的秩参数的残余噪声。为了详细说明所提出的算法，我们首先仅使用输入秩参数构建增益矩阵，我们将其直接引入自适应奇异值加权公式中，以使其在秩参数变得太大时更加稳定。然后，我们在改进的最优加权算子的基础上推导了一个阻尼算子来衰减残余噪声。所提出的方法可以看作是最优阻尼秩降低方法的改进版本，对输入参数不敏感。