Five-dimensional (5D) seismic data reconstruction becomes more appealing in recent years because it takes advantage of five physical dimensions of the seismic data and can reconstruct data with large gap. The low-rank approximation approach is one of the most effective methods for reconstructing 5D dataset. However, the main disadvantage of the low-rank approximation method is its low computational efficiency because of many singular value decompositions (SVD) of the block Hankel/Toeplitz matrix in the frequency domain. In this paper, we develop an SVD-free low-rank approximation method for efficient and effective reconstruction and denoising of the seismic data that contain four spatial dimensions. Our SVD-free rank constraint model is based on an alternating minimization strategy, which updates one variable each time while fixing the other two. For each update, we only need to solve a linear least-squares problem with much less expensive QR factorization. The SVD-based and SVD-free low-rank approximation methods in the singular spectrum analysis (SSA) framework are compared in detail, regarding the reconstruction performance and computational cost. The comparison shows that the SVD-free low-rank approximation method can obtain similar reconstruction performance as the SVD-based method but with a large computational speedup.@en

Prestack seismic inversion has emerged as a powerful technique for reconstructing parameters attribute to the subsurface properties and building the geophysical parameter models. However, the inversion algorithms always suffer from spatial blur and low resolution. Total variation (TV) regularization preserves the spatial variation boundary of data by highlighting the sparsity of the first-order difference, which is regarded as an important technical means for image restoration. However, when the data do not change along the spatial grid direction, TV regularization is prone to a staircase effect. In this article, a directional TV (DTV) method is proposed to conduct the prestack amplitude variation with offset/angle (AVO/AVA) inversion. The method consists of three essential steps: estimating the seismic slope attribute from the seismic data, introducing seismic slope attribute to the TV regularization to establish the objective function, and optimizing the objective function by the split-Bregman algorithm. Finally, the conventional and proposed methods are applied to the synthetic and the real seismic data. The comparison of different methods demonstrates that the proposed method is applicable to reveal the detailed subsurface models, alleviate the staircase effect or artifact substantially, and further upgrade the quality of prestack inversion results.@en

The local signal-to-noise orthogonalization algorithm has been widely used in the community of seismic processing and imaging. It helps orthogonalize the signal-and-noise components in an elegant way so that the noise does not contain the signal leakage in seismic denoising. The traditional local signal-to-noise orthogonalization is based on solving a highly underdetermined, ill-posed inverse problem with local smoothness constraint. Due to the inversion nature, the local orthogonalization method requires a large number of iterations and thus is computationally demanding in large-scale applications. Here, we proposed a much accelerated signal-and-noise orthogonalization method, where we design an efficient way for calculating the orthogonalization weight. When new samples are involved in the calculation, we calculate the orthogonalization weight of the new samples by connecting them with the calculated weights of the previous samples. The orthogonalization weight needs to be smoothed and scaled after all samples have been processed to make the resulted orthogonalization weight smooth across the seismic data and match the amplitude level of the initially suppressed noise. In this way, we avoid iterations when calculating the orthogonalization weight. We apply the proposed method to several synthetic and field data examples, have a benchmark comparison with state-of-the-art algorithms, and demonstrate its much accelerated efficiency compared with the traditional local signal-and-noise orthogonalization.@en

The local signal-to-noise orthogonalization algorithm has been widely used in the community of seismic processing and imaging. It helps orthogonalize the signal-and-noise components in an elegant way so that the noise does not contain the signal leakage in seismic denoising. The traditional local signal-to-noise orthogonalization is based on solving a highly underdetermined, ill-posed inverse problem with local smoothness constraint. Due to the inversion nature, the local orthogonalization method requires a large number of iterations and thus is computationally demanding in large-scale applications. Here, we proposed a much accelerated signal-and-noise orthogonalization method, where we design an efficient way for calculating the orthogonalization weight. When new samples are involved in the calculation, we calculate the orthogonalization weight of the new samples by connecting them with the calculated weights of the previous samples. The orthogonalization weight needs to be smoothed and scaled after all samples have been processed to make the resulted orthogonalization weight smooth across the seismic data and match the amplitude level of the initially suppressed noise. In this way, we avoid iterations when calculating the orthogonalization weight. We apply the proposed method to several synthetic and field data examples, have a benchmark comparison with state-of-the-art algorithms, and demonstrate its much accelerated efficiency compared with the traditional local signal-and-noise orthogonalization.@en