One of the most important goals of seismic stratigraphy studies is to interpret the elements of the seismic facies with respect to the geologic environment. Prestack seismic data carry rich information that can help us get higher resolution and more accurate facies maps. Therefore, it is promising to use prestack seismic data for the seismic facies recognition task. However, because each identified object changes from the poststack trace vectors to a prestack trace matrix, effective feature extraction becomes more challenging. We have developed a novel data-driven offset-temporal feature extraction approach using the deep convolutional autoencoder (DCAE). As an unsupervised deep learning method, DCAE learns nonlinear, discriminant, and invariant features from unlabeled data. Then, seismic facies analysis can be accomplished through the use of conventional classification or clustering techniques (e.g., K-means or self-organizing maps). Using a physical model and field prestack seismic surveys, we comprehensively determine the effectiveness of our scheme. Our results indicate that DCAE provides a much higher resolution than the conventional methods and offers the potential to significantly highlight stratigraphic and depositional information.

Erratic seismic noise, following a (known or unknown) non-Gaussian distribution, poses a formidable challenge to conventional methods of random noise attenuation. Many erratic noise cancellation methods, for instance, robust reduced-rank and sparsity-promoting filtering, have been proven to achieve promising results in overcoming this challenge. Among them, deep learning (DL) methods require no assumptions about the underlying clear seismic image and are also more robust against erratic and random noise. However, the success of existing DL-based denoising methods strongly depends on supervised learning from a large number of ground-truth seismic images affected by erratic noise and their clean counterparts, which are typically unavailable in a real-world setting. As an alternative, this article presents an unsupervised DL method for erratic-plus-Gaussian noise removal based on a robust deep convolutional autoencoder (RDCAE). In the RDCAE, the mean squared error (mse) loss in a classic DCAE is replaced by the smooth Welsch function to exploit the concept of robust image denoising. In this way, the erratic noise is downweighted by means of a curbed weight defined in terms of the Welsch function. In contrast, the random noise is diluted by combining the mean square in the Welsch function and the total variation (TV). Subsequently, the training procedures required for solving the RDCAE are derived on the basis of the backpropagation (BP) algorithm for a neural network. Experiments conducted on both synthetic and real field datasets are reported to illustrate the efficacy of the proposed method.

The core challenge of seismic data interpolation is how to capture latent spatial-temporal relationships between unknown and known traces in 3-D space. The prevailing tensor-based interpolation schemes seek a globally low-rank approximation to mine the high-dimensional relationships hidden in 3-D seismic data. However, when the low-rank assumption is violated for data involving complex geological structures, the existing interpolation schemes fail to precisely capture the trace relationships, which may influence the interpolation results. As an alternative, this article presents a basic deep tensor autoencoder (DTAE) and two variants to implicitly learn a data-driven, nonlinear, and high-dimensional mapping to explore the complicated relationship among traces without the need for any underlying assumption. Then, tensor backpropagation (TBP), which can be essentially viewed as a tensor version of traditional backpropagation (BP), is introduced to solve for the new model parameters. For ease of implementation, a mathematical relationship between tensor and matrix autoencoders is constructed by taking advantage of the properties of a tensor–tensor product. Based on the derived relationship, the DTAE weight parameters are inferred by applying a matrix autoencoder to each frontal slice in the discrete cosine transform (DCT) domain, and this process is further summarized into a general theoretical and practical framework. Finally, the performance benefits of the proposed DTAE-based method are demonstrated in experiments with both synthetic and real field seismic data.

The inherent challenge of 3-D seismic noise attenuation is determining how to uncover high-dimensional concise structures that only exist in true signals to eliminate random noise. The prevailing deep learning (DL) denoising methods have achieved promising performance in revealing the compact structures underlying contaminated seismic data. However, as clean ground-truth seismic data are generally unavailable in real-world settings, most existing matrix-based DL denoising schemes fail to automatically describe this type of high-dimensional structure in an unsupervised manner, potentially rendering them unable to effectively perform 3-D seismic data denoising tasks. To tackle this challenge, this article presents a tensor convolutional neural network (TCNN)-based data denoising scheme using Stein’s unbiased risk estimate (SURE) (called SURE-TCNN) to learn intrinsic high-dimensional structures without ground-truth seismic data. Considering that SURE provides an almost unbiased estimate of the mean squared error (MSE), SURE-TCNN has the potential to provide similar results to those of the supervised MSE-based TCNN with ground-truth data. For ease of implementation, the properties of a transform-based tensor-tensor product (t-product) are followed to establish a solid theoretical connection between the SURE-TCNN tensor and matrix. Derived from this connection, the SURE-TCNN weight parameters are determined by implementing matrix-based SURE-convolutional neural networks (CNNs) on each frontal slice in the time-frequency domain (e.g., the wavelet domain). Synthetic and field data examples demonstrate the superior performances of the proposed model against three state-of-the-art (SOTA) methods.

Seismic acquisition footprints appear as stably faint and dim structures and emerge fully spatially coherent, causing inevitable damage to useful signals during the suppression process. Various footprint removal methods, including filtering and sparse representation (SR), have been reported to attain promising results for surmounting this challenge. However, these methods, e.g., SR, rely solely on the handcrafted image priors of useful signals, which is sometimes an unreasonable demand if complex geological structures are contained in the given seismic data. As an alternative, this article proposes a footprint removal network (dubbed FR-Net) for the unsupervised suppression of acquired footprints without any assumptions regarding valuable signals. The key to the FR-Net is to design a unidirectional total variation (UTV) model for footprint acquisition according to the intrinsically directional property of noise. By strongly regularizing a deep convolutional autoencoder (DCAE) using the UTV model, our FR-Net transforms the DCAE from an entirely data-driven model to a prior-augmented approach, inheriting the superiority of the DCAE and our footprint model. Subsequently, the complete separation of the footprint noise and useful signals is projected in an unsupervised manner, specifically by optimizing the FR-Net via the backpropagation (BP) algorithm. We provide qualitative and quantitative evaluations conducted on three synthetic and field datasets, demonstrating that our FR-Net surpasses the previous state-of-the-art (SOTA) methods.

The 3-D seismic data reconstruction can be understood as an underdetermined inverse problem, and thus, some additional constraints need to be provided to achieve reasonable results. A prevalent scheme in 3-D seismic data reconstruction is to compute the best low-rank approximation of a formulated Hankel matrix by rank-reduction methods with a rank constraint. However, the predefined Hankel structure is easily damaged by the low-rank approximation, which leads to harming its recovery performance. In this article, we present a structured tensor completion (STC) framework to simultaneously exploit both the Hankel structure and the low-tubal-rank constraint to further enhance the performance. Unfortunately, under the assumption of elementwise sampling used by existing methods, STC is intractable to be solved since Hankel constraints cannot be expressed as linear tensor equations. Instead, tubal sampling is proposed to describe the missing trace behavior more accurately and further build a bridge between tensor and matrix completion (MC) to overcome the solving issue in two aspects: through the bridge from tensor to MC, STC can be solved efficiently using MC from random samplings of each frontal slice in the Fourier domain. Through the bridge from matrix to tensor completion, various tensor models within the framework can be developed from noise-specific MC to meet the need for data reconstruction in changeable noise environments. Moreover, alternating-minimization and alternating-direction methods of multipliers are developed to solve the proposed STC. The superior performance of STC is demonstrated in both synthetic and field seismic data.