Seismic data is commonly contaminated by different types of noise with varying amplitudes, increasing the challenges of retrieving effective signals from strong background noise. Such issues become even worse when attenuation effects are considered because the amplitude of seismic waves will dissipate after propagation, making seismic signals easier to be inundated by noise, especially at deeper positions. To implement data enhancement and attenuation compensation without noise amplification, we propose a robust framework in a blind manner to reconstruct attenuation-compensated seismic data with a higher signal-to-noise ratio (SNR), namely, structural-oriented blind Q-compensated denoising (SBQD) method. Unlike classic Q-compensated denoising methods, the proposed SBQD does not require wavelet as a prior and can iteratively estimate wavelet and reflectivity series simultaneously, and the final stationary seismic data can be obtained by convolving the estimated wavelet with the reflectivity series. Moreover, guided by local adaptive structural regularization, the proposed SBQD can provide superior results with higher accuracy and fidelity and remove those noise-related artifacts during denoising and compensation. Compared with conventional two-step methods (e.g., denoising and attenuation compensation), the proposed SBQD can implement denoising and compensation simultaneously, which avoids introducing compensation-related errors (e.g., noise amplification) and effectively preserves useful signals. Synthetic and field examples are used to validate the robustness of the proposed SBQD method on noise removal and attenuation compensation for seismic data.

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.

Salt body segmentation is a critical part of structural interpretation and oil and gas exploration for subsalt reservoirs. Existing automatic salt body segmentation techniques mostly use supervised learning strategies. It is challenging to generate a large number of labels by manual labeling, especially for 3-D salt bodies. Here, we propose a self-supervised learning (SSL) framework called Salt3DNet, for 3-D salt body segmentation. This framework is divided into two stages: pretraining and fine-tuning of downstream tasks. In the pretraining stage, we use the Barlow twins (BTs) method to pretrain the encoder and reduce redundancy in a contrastive learning manner to learn high-level data representations. In the fine-tuning stage, we construct two encoders to reconstruct 3-D seismic data and segment salt bodies in a multitask collaborative learning way. The encoder and decoder are composed of the 3-D fully convolutional DenseNet and soft attention mechanism, where the latter represents the selective kernel block (SKB) with multiple kernels of different sizes. Salt3DNet calculates the correlation matrix of features from different perspectives in the pretraining stage and makes it close to the identity matrix to obtain a more prosperous feature representation. Then, Salt3DNet uses a limited number of labeled samples for training. According to the evaluation metrics, the proposed network has demonstrated promising salt segmentation performance in 3-D SEG advanced modeling (SEAM) synthetic data and$F3$block real seismic data. In addition, the proposed network is demonstrated to have higher prediction accuracy than state-of-the-art salt segmentation frameworks through ablation experiments.

3-D salt segmentation is important for many research topics spanning from exploration geophysics to structural geology. In seismic exploration, 3-D salt segmentation is directly related to the velocity modeling building that affects many processing steps, such as seismic migration and full waveform inversion. Manually picking the salt boundary becomes prohibitively time-consuming when the data size is too large. Here, we develop a highly generalized fully convolutional DenseNet for automatic salt segmentation. A squeeze-and-excitation network is used as a self-attention mechanism for guiding the proposed network to extract the most significant information related to the salt signals and discard the others. The proposed framework is a supervised technique and shows robust performance when applied to a new dataset using transfer learning and a small amount of training data. We test the robustness of the proposed framework on the Kaggle TGS salt segmentation dataset. To demonstrate the generalization ability of the framework, we further apply the trained model to an independent dataset synthesized from the 3-D SEAM model. We apply transfer learning to finely tune the trained model from the TGS dataset using only a small percentage of data from the 3-D SEAM dataset and obtain satisfactory results.

Accurate estimation of reservoir parameters (e.g., permeability and porosity) helps to understand the movement of underground fluids. However, reservoir parameters are usually expensive and time-consuming to obtain through petrophysical experiments of core samples, which makes a fast and reliable prediction method highly demanded. In this article, we propose a deep learning model that combines the 1-D convo- lutional layer and the bidirectional long short-term memory network to predict reservoir permeability and porosity. The mapping relationship between logging data and reservoir parameters is established by training a network with a combination of nonlinear and linear modules. Optimization algorithms, such as layer normalization, recurrent dropout, and early stopping, can help obtain a more accurate training model. Besides, the self-attention mechanism enables the network to better allocate weights to improve the prediction accuracy. The testing results of the well-trained network in blind wells of three different regions show that our proposed method is accurate and robust in the reservoir parameters prediction task.

Amplitude variation with offset (AVO) refers to the amplitude variation with offset. This relationship can be used to analyze lithology and identify the oil and gas reservoirs in seismic exploration. Traditional AVO inversion is a typical ill-posed problem. When deep learning is directly used for seismic inversion, there are three main issues. First, the label data are insufficient. Second, a network trained for one working area is not applicable to other working areas. Third, there are spatial discontinuities and instability problems in the inversion results. In this letter, we propose the AVO inversion method that combines transfer learning and low-frequency component constraints. Transfer learning strategy is introduced to solve two main problems: The label data are insufficient to train the network, and the trained network is not applicable to other regions. Taking the low-frequency component as the constraint term makes the solution easier to converge to the true value. The experimental results of a typical example show that our method not only effectively improves the prediction accuracy and spatial continuity of the inversion results, but also reduces dependence on logging data.

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.

The omnidirectional plane-wave destruction (OPWD) algorithm can estimate the large dip by using circle-interpolating plane-wave destruction (PWD) filter but at the expense of causing potential instabilities due to the small values of the denominator in the regularized division problem. To mitigate the instability, one needs to use a relatively larger smoothing radius for a stronger regularization of the element-wise division, which however significantly decreases the resolution of dip estimation. We propose a new OPWD method without compromising the dip resolution for the large dip calculation by applying a nonstationary smoothness constraint to the model. We use a larger smoothing radius for areas that tend to cause instabilities and vice versa. The nonstationary smoothing is carried out in a simple and efficient recursion way. The synthetic and real seismic data examples demonstrate the performance of the proposed algorithm.

Due to its time-variant nature, the computationally expensive hyperbolic Radon transform (RT) is not easy to be accelerated, e.g., based on the convolution theorem in the frequency domain. However, the hyperbolic RT better matches the trajectories of reflection events in prestack gathers than other time-invariant RTs, e.g., linear or parabolic RTs. Hence, despite its large computational cost, the time-domain hyperbolic RT is still preferred in many seismic processing applications. We propose a fast high-resolution hyperbolic RT (HRHRT) with a fast butterfly algorithm. The forward and adjoint RTs can be greatly accelerated based on a fast butterfly algorithm by reformulating the time-space domain Radon operator as a frequency-domain Fourier integral operator (FIO). The fast butterfly algorithm solves the FIO problem by a blockwise low-rank approximation scheme. The single-step hyperbolic RT can be much faster (e.g., hundreds of times faster for a large problem) than the traditional implementation, resulting in a significant computational boost when the transform is taken in an iterative fashion to estimate the high-resolution Radon coefficients. We demonstrate the similar performance and the much different computational efficiencies between the proposed fast HRHRT and the traditional method over several different problems, i.e., random noise suppression, big-gap seismic reconstruction, and multiples attenuation.

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.

The unsplit complex frequency-shifted perfectly matched layer (CFS-PML) has been widely used in the first-order wave equation in velocity and stress while rarely formulated for the wave equation recast as a second-order system in displacement. Among different variants of PML, the unsplit CFS-PML for the second-order wave equation enjoys better absorbing performance and numerical stability, compared to the traditional PML, due to the presence of the general form of CFS stretching factors, as well as higher computational efficiency over the split PMLs since it avoids wave equation order reduction and splitting the state variables into multiple directional components. This study aims to develop an unsplit CFS-PML scheme for the second-order wave equation and devote specific attention to fractional viscoacoustic simulation where fractional time derivatives are involved and hard to be reformulated into a first-order form. In the complex space, PML is typically regarded as an analytical continuation of the real coordinates; thus, we define an explicit coordinate stretching operator acting on the Laplacian operator. This stretching operator consists of several convolution terms; each of them can be efficiently resolved by a recursive convolution updating strategy. Viscoacoustic simulations on homogeneous Pierre Shale, Marmousi model, and 3-D SEG/EAGE overthrust model verify the feasibility and absorbing the performance of our proposed scheme.

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.

Deblending plays an important role in preparing high-quality seismic data from modern blended simultaneous-source seismic data. The conventional methods become problematic when the random ambient noise becomes extremely strong and the inversion iteratively fits the random noise instead of the signal and blending interference. In this article, an improved method is proposed to separate blended seismic data. We treat the deblending problem as a regularization problem under the frame of compressed sensing (CS), and propose a new nonlinear Bregman iterative shaping (BIS) algorithm to solve the minimization problem. Based on the principle of CS, we transform the simultaneous-source data to the seislet-domain for inversion and separation, and verify the effectiveness and superiority of the proposed method by two theoretical model data and an actual marine streamer blended data. Compared with the traditional iterative shaping (TIS) algorithm, BIS adds data residuals to the observed data (the blended data) in each iteration, so that the error between the calculated data after each iteration and the main source signal in the known blended data is the smallest, and helps to recover the weaker information in the seismic data and obtain higher precision separation results. BIS uses a fixed soft threshold, which speeds up the convergence speed. In addition, BIS can effectively improve the separation accuracy when the given sparse domain threshold is not suitable.

Because a high signal-to-noise ratio (SNR) is beneficial to the subsequent processing procedures, the noise attenuation is important. We propose an adaptive random noise attenuation framework based on convolutional neural networks (CNNs). The framework transforms the target function from effective signal learning to noise learning through residual learning, so as to improve the training efficiency. After sufficient training, the network transfers the learned seismic data features using a large synthetic data set to the testing of complex field data with unknown noise levels and, thus, attenuates the noise in an unsupervised way. Unsupervised noise reduction requires certain representativeness of the training data and a sufficient amount of training data sets. In the network architecture, we introduce residual learning and batch normalization (BN) to reduce the training parameters of the network, thereby shortening the time for feature learning. The activation function with leakage correction function can effectively retain negative information, and its combination with the double convolutional residual block can enhance the generalization ability and feature extraction performance of the network. In the test of synthetic data and complex field data with unknown noise levels, by comparing the noise reduction results of some classic denoising algorithms, the adaptive CNN proposed in this article can more effectively attenuate the noise and reconstruct the seismic waveform.