Diffractions in the seismic data are associated with the small-scale subsurface structures, thus their separation and imaging are helpful in characterizing the underground discontinuities with a high resolution that cannot be reached by traditional reflection imaging methods. Traditional seismic slope-based diffraction separation methods are strongly affected by the accuracy and stability of the slope estimation methods, e.g., the plane-wave destruction (PWD) method. When the local seismic slope is not properly estimated, the separated seismic diffraction waves suffer from the mixture between the reflection and diffraction energy due to their coupling in the slope map. We propose an automatic local rank-reduction (LRR) method to separate 3D diffraction waves from zero-offset seismic data, based on which we conduct 3D migration to output the diffraction images. Due to the difficulty in choosing the rank in each local 3D window, we apply an adaptive strategy to obtain the optimal rank. The proposed LRR method with adaptively selected ranks (LRRA) is applied to several 3D synthetic and field data examples and demonstrated to perform better than the traditional PWD, the LRR, and the global rank-reduction (GRR) methods.

Recently, studies on multidimensional seismic data interpolation through rank-constrained matrix or tensor completion have led to many effective methods, with satisfactory results. Despite the success of the rank-constrained matrix completion methods, e.g., damped rank reduction (DRR), and the rank-constrained tensor completion methods, e.g., high-order orthogonal iteration (HOOI), strong noise and highly decimated traces could still make the reconstruction results not acceptable. In this article, we find that implementing only one rank constraint to solve the multidimensional seismic data recovery problem is not sufficient. Therefore, we consider a hybrid method to reconstruct the noisy and incomplete traces based on a new mixed rank-constrained (MRC) algorithm. The proposed MRC algorithm aims to take advantage of the merits of both the rank-constrained matrix and tensor completion models to restore the missing data. We first apply the unfolding and folding operator to the 4-D spatial hypercube data. Then, for each iteration, we connect the DRR and the HOOI approaches in the same framework to solve the proposed MRC model. The proposed MRC model aims to provide an enhanced level of rank constraint to improve the signal-to-noise ratio (SNR) of the recovered data. Synthetic and field 5-D seismic data are used to compare the performance of the new method with the HOOI and DRR methods. The comparison via visual inspection and numerical analysis reveals the better performance of the proposed MRC algorithm.

We develop a deep learning framework based on deep image prior (DIP) and attention networks for 3-D seismic data enhancement. First, the 3-D noisy data are divided into several overlapped patches. Second, the DIP network has a U-NET architecture, where the input patches are encoded to extract the significant latent features, while the decoder tries to reconstruct the input patches using these extracted features. Besides, the attention network is used to scale the extracted features from the encoder and the decoder. Third, the attention network output of the encoder is concatenated with that of the decoder to obtain high-order features and guide the network to extract the most significant information related to the seismic signals and discard the others. Finally, the 3-D seismic data are reconstructed using the output patches obtained by the DIP network. The proposed algorithm is an iterative and unsupervised approach, which does not require labeled data. We evaluate the proposed algorithm using several synthetic and field data examples. As a result, the proposed algorithm shows the ability to enhance the 3-D seismic data by attenuating the random noise and preserving the 3-D seismic signal with minimal signal leakage. Moreover, the proposed algorithm shows good denoising performance when tested using various types of events, e.g., linear, hyperbolic, low and high dominant frequencies, and weak amplitude. In addition, the proposed method outperforms the predictive filtering (PF) and damped rank-reduction (DRR) methods. To further understand the principle of the proposed method inside the DIP network, we analyze the weighting matrices in the encoder and decoder parts in detail. We attribute the denoising ability of the DIP network to the improvement of the extracted basis features from the encoder to the decoder layers through a deep network.

5D data is the original recorded form in the 3D seismic acquisition, which includes sufficient information from all five dimensions. However, environmental and economic logistic difficulties often severely impact the data acquisition geometry, leading to raw data with missing traces and strong contaminating random noise. This deficiency often causes troubles in subsequent processing. Thus, an efficient interpolation and denoising method is required to recover useful signals. Unfortunately, practical applications of many existing reconstruction algorithms are limited by their intensive computational cost when applied to the 5D data. Additionally, the stability of these algorithms is also challenged by complex geological structures, which often degrades the reconstruction performance. To seek solutions to the aforementioned problems, we design a simple and effective framework for fast reconstruction and denoising of under-sampled 5D seismic data via a two-step process. First, we prepare the initial model from the original recordings by constructing a 3D gather at each common offset point. This step effectively interpolates the missing traces in 3D common offset gathers by exploiting the data coherency in the adjacent areas (i.e., nearby mid-points). In the second step, the processed 5D data is reorganized into 3D common mid-point gathers, with each of them further sorted into a 2D section according to absolute offset values. Then a conventional 2D processing algorithm (e.g., F-X prediction, wavelet thresholding, or multichannel singular spectrum analysis) is invoked to filter the obtained 2D section. The proposed workflow has a low overall computational cost and preserves signal fidelity. We use this framework to simultaneously denoise and interpolate the low-quality and extremely sparse seismic data. The synthetic and field examples both demonstrate the superb performance of the proposed framework in comparison with conventional methods.

Effective random noise attenuation is critical for subsequent processing of seismic data, such as velocity analysis, migration, and inversion. Thus, the removal of seismic random noise with an uncertainty level is meaningful. Attenuating 3-D random noise in a supervised way based on deep learning (DL) is challenging because clean labels are difficult to obtain. Therefore, it is necessary to develop an adaptive unsupervised-based method for random noise attenuation. In this article, we propose a deep-denoising unsupervised learning (DDUL) network to attenuate random noise in 2-D/3-D seismic data. A patching technique is used to split 2-D/3-D seismic data into several patches to be fed into the network, which helps to expand the number of samples for training. We use the fully symmetrical structure of the autoencoder to construct the network. In each corresponding encoder and decoder layer, skip connections are added to enhance the learning of seismic data features. We construct three blocks to extract waveform features in seismic data, i.e., encoder, decoder, and skip blocks. Among them, the skip is connected between the encoder and decoder blocks of each hidden layer. The use of multiple blocks not only improves the network’s ability to extract seismic data features but also solves the problem of excessive training parameters caused by hidden layer stacking. Five 2-D/3-D synthetic and field seismic datasets are used to test the denoising performance of our proposed method. The denoising results demonstrate that our proposed method has good signal-preserving and noise attenuation capabilities in real-world applications.