When compared to traditional seismic data acquisition, irregular blended acquisition significantly promotes the acquisition efficiency. Yet, the blending noise of subsampled blended data introduces new obstacles for the subsequent processing of seismic data. Due to the predictability of linear events in the frequency–space domain, the constructed Hankel matrices exhibit low‐rank characteristics. However, the blending noise of subsampled blended data increases the rank, so deblending and interpolation can be implemented via rank‐reduction algorithms such as the singular spectrum analysis. The significant computing cost of the singular value decomposition, however, makes the traditional singular spectrum analysis inefficient. An alternative algorithm, known as the randomized singular spectrum analysis, employs the randomized singular value decomposition instead of the traditional singular value decomposition for rank‐reduction. The randomized singular spectrum analysis significantly enhances the efficiency of the decomposition process, particularly when dealing with large Hankel matrices. There still remains some random noise when using the singular spectrum analysis or randomized singular spectrum analysis for subsampled blended data, because the noise subspace and signal subspace are coupled together. Thus, we incorporate a damping operator into the randomized singular value decomposition and propose a novel damped randomized singular spectrum analysis method. The damped randomized singular spectrum analysis combines the advantages of the randomized singular value decomposition and the damping operator to enhance the computational efficiency and suppress the remaining noise. Moreover, an iterative projected gradient descent strategy is introduced to achieve deblended and interpolated seismic data for subsequent processing. Examples from synthetic data and field data are used to demonstrate the effectiveness and superiority of the proposed damped randomized singular spectrum analysis method, which enhances the accuracy and efficiency during simultaneous deblending and interpolation.

中文翻译：

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基于阻尼随机奇异谱分析的子采样混合地震数据去混合和插值

与传统地震数据采集相比，不规则混合采集显着提升了采集效率。然而，下采样混合数据的混合噪声给地震数据的后续处理带来了新的障碍。由于频率空间域中线性事件的可预测性，构造的汉克尔矩阵表现出低秩特征。然而，下采样混合数据的混合噪声会增加秩，因此可以通过奇异谱分析等降阶算法来实现去混合和插值。然而，奇异值分解的巨大计算成本使得传统的奇异谱分析效率低下。另一种算法称为随机奇异谱分析，它采用随机奇异值分解而不是传统的奇异值分解来进行降级。随机奇异谱分析显着提高了分解过程的效率，特别是在处理大型 Hankel 矩阵时。当对子采样混合数据使用奇异谱分析或随机奇异谱分析时，仍然存在一些随机噪声，因为噪声子空间和信号子空间耦合在一起。因此，我们将阻尼算子纳入随机奇异值分解中，并提出了一种新颖的阻尼随机奇异谱分析方法。阻尼随机奇异谱分析结合了随机奇异值分解和阻尼算子的优点，提高了计算效率并抑制了剩余噪声。此外，引入迭代投影梯度下降策略来获得去混合和插值的地震数据以供后续处理。使用合成数据和现场数据的例子来证明所提出的阻尼随机奇异谱分析方法的有效性和优越性，该方法提高了同时去混合和插值期间的准确性和效率。