Coherent and incoherent noise in seismic data inevitably reduces the quality of subsequent processing, e.g., migration and inversion. Different from random noise, erratic noise follows the non-Gaussian distribution and has high amplitude, which is a challenge to the conventional denoising frameworks based on deep learning (DL). In this study, we propose an unsupervised learning framework with a multi-branch attention mechanism (MANet) to attenuate the erratic and random noise in 2-D and 3-D seismic data. MANet can adaptively attenuate noise in multi-dimensional seismic data without the need to manually generate labels to train the network. MANet integrates global features of waveforms extracted from multiple branches in a weighted way to enhance attention to significant features, thus obtaining a global and comprehensive representation of weights. To enhance the migration ability of shallow-level to deep-level features, we add some skip connections in the corresponding encoder and decoder. We use a robust mean-Huber loss function that is less sensitive to outliers to improve the denoising performance of erratic noise. We apply the proposed network for both 2-D and 3-D synthetic and field data. The denoising results demonstrate that the proposed method has better signal preservation and noise attenuation abilities compared with the conventional denoising methods and the state-of-the-art unsupervised learning framework. We improve the interpretability of the network by visualizing the weight matrices and different encoders. Besides, the visualization schemes proposed in this paper can be applied to more research, such as geological event interpretation, geological resource detection, and surface morphology analysis.

Linear noise attenuation is a troublesome problem in a variety of seismic exploration areas. Traditional methods often use differences in frequency or apparent velocity to separate the signals and linear noise. However, these applications are limited when the characteristics of the aforementioned differences between signals and linear noise are too small to be distinguished. For this reason, we proposed a rotate-time-shift FK (RTS-FK-CS) method based on compressed sensing (CS). Based on the deblending concept, the proposed method flattens the linear events using the rotating coordinate system and performs a lateral time shift for each time point. Because of the random time shift, events with different apparent velocities from the linear noise are disrupted as “a deblended data in common receiver domain,” and events with similar apparent velocities have a difference in frequency. To suppress linear noise, we apply the CS reconstruction algorithm in the frequency-wavenumber (FK) domain. The random time shift uniformly distributes the energy near the dominant frequency to each frequency in the FK domain, enhancing the sparsity in the transform domain. The proposed method can effectively suppress linear noise and reduce the loss of events whose apparent velocities and frequency are similar to linear noise. Synthetic and field data tests visually and quantitatively confirmed the superiority and robustness of the proposed method.

Ground roll is a type of coherent noise with low velocity, low frequency, and high energy, which negatively affects the quality of the seismic data. The contamination of the ground roll is a persistent problem in the seismic processing field. For this reason, we considered the predictability of useful signals in thefxdomain, introduced the time-varying filtering based on the empirical mode decomposition (TVFEMD) into thefxdomain, and therefore proposed a novel algorithm (Ada-fx-TVFEMD). Similar to the variational mode decomposition (VMD), the TVFEMD algorithm consists in adaptive decomposition of multicomponent signals. The TVFEMD algorithm is more suitable for nonstationary signals because of its time-varying characteristic. The proposed Ada-fx-TVFEMD algorithm performs decomposition of each frequency slice and reconstruction of partial intrinsic mode functions (IMFs). Moreover, it allows to accurately select the IMFs that contain ground roll based on automatic ground roll identification. A presented synthetic example illustrates the superiority of the Ada-fx-TVFEMD algorithm in ground roll attenuation. Applying the proposed method on field data further demonstrates its potential in industrial applications, compared with frequency–wavenumber (fk) filtering andfx-VMD.

In seismic exploration, there are abandoned mines and bad traces, leading to missing data. In addition, unsuitable processing methods will introduce randomized amplitude anomalies. The traditional smoothing term with the$l_{2}$-norm assumes that the random noise is a Gaussian distribution. For the Gaussian distribution, the representation of the$l_{2}$-norm has a short tail compared with the$l_{1}$-norm, abnormal values in the data cannot be suppressed, and the stability of the solution is poor. For the Laplacian distribution, the representation of the$l_{1}$-norm has a longer tail compared with the$l_{2}$-norm, and it has a good tolerance for abnormal values. We propose a new method, based on the theory of compressed sensing, which uses the$l_{1}$-norm as the data fitting term and a sparse reconstruction equation for missing data with abnormal amplitude noise. To solve the equation for the complete data with no abnormal values, we apply the approximate projected subgradient method. Model and field data tests confirm the increased robustness of the proposed method.

In this article, we proposed a weighted stacking algorithm for obtaining high-resolution data and constructed an optimization objective function using the similarity of the stacked amplitude spectrum and constant (amplitude spectrum of impulse function). The optimization problem is solved to obtain the stacking weights involved in the common midpoint (CMP) gathers by using the alternating iterative method of gradient descent and subgradient descent. Then, the weighted stacking is performed to obtain resolution-enhanced data. A traditional poststack deconvolution algorithm decomposes the data and performs frequency-weighted recombination, which alters the original frequency composition. Furthermore, most existing methods require wavelet estimation, which may be inaccurate. The amplitude-spectrum shape of CMP gather controls the resolution-enhanced data using the proposed method, which is a stacking scheme that does not require wavelet estimation. On the other hand, our proposed stacking algorithm can handle data containing white noise, and we introduce a penalty term to avoid the mutual offset between the effective signals caused by negative weight, which improves the stacked signal-to-noise ratio. Applications to synthetic and field seismic datasets demonstrate that data stacked using the proposed method have higher resolution and can be more easily interpretated compared to the traditional equal-weight stacking.