Seismic data deconvolution is vital for enhancing resolution and accurate subsurface interpretation. Traditional methods heavily rely on predefined assumptions that limit their robustness to noisy data. As state-of-the-art generative models, diffusion models excel in capturing accurate prior distributions, which are beneficial to inversion. Moreover, diffusion models inherently resist noise due to their training in reverse noisy processes. Building on this foundation, we introduce an unsupervised diffusion model for seismic deconvolution, leveraging diffusion posterior sampling (DPS) to incorporate observed seismic data into the sampling process to guide high-accuracy reflectivity generation. Unlike traditional single-trace approaches, our method performs deconvolution across entire 2-D profiles, effectively capturing spatial continuity. Though solely trained on synthetic data, our method exhibits satisfactory performance when applied to synthetic and field datasets, demonstrating strong noise resistance and remarkable generalization capabilities.

Seismic acoustic impedance (AI) inversion is essential for reservoir prediction and characterization. In recent years, deep learning has shown immense potential as a data-driven approach in seismic data processing, inversion, and interpretation. As a data-driven method, deep learning-based seismic inversion results better when sufficient labeled data are provided. Overfitting and poor generalization often occur when labels are insufficient. Due to the lack of labeled data in seismic inversion problems, the difficulty of inversion increases, leading to unstable and poor generalization of prediction results. To partially address this issue, we propose a constrained seismic inversion strategy. Since seismic records are time series, we exploit the convolutional neural network (CNN) and bidirectional LSTM (Bi-LSTM) network structures that are more applicable to time series. We combine the physical model and the initial model as constraints to improve the network stability and generalization ability, and impose sparse constraints on the reflection coefficient to further improve the prediction accuracy. The network structure transformation improves the efficiency and stability of the training process. Through numerical experiments and real data tests, it is proved that the proposed method improves the vertical resolution and geological reliability, providing a more stable and efficient method for seismic inversion under conditions of limited labeled data. The overall performance improved by 2% through comparative analysis.

Distributed Acoustic Sensing (DAS) systems offer a promising framework for advanced subsurface imaging and monitoring. Despite the great potential, the complex noise characteristics inherent in seismic data, such as environmental, mechanical, and instrumental disturbances, pose significant challenges to data fidelity and stability. Conventional noise suppression methods cannot be adequately adapted to dynamic seismic environments due to the need to design filters for different a priori conditions. To overcome these limitations, we introduce the conditional diffusion probabilistic model (C-DDPM), which is shown to have strong a priori extraction capabilities and can better cope with seismic signal extraction under different noise combinations. In addition, we incorporate a adaptive FK conditioning approach into the diffusion process, allowing C-DDPM to better learn the data distribution. We also use asymmetric dilated convolution (ADConv) to effectively suppress noise. Our approach is rigorously tested on both synthetic and real-world seismic datasets, demonstrating satisfactory improvements in noise reduction and signal clarity. Comparative analyses with existing classical methods reveal that our framework not only achieves higher PSNR but also reveals previously obscured waveform details, outperforming existing methods in challenging geophysical scenarios.

How to represent a seismic wavefield? Traditionally, while seismic wavefields are conceptualized continuously, acquisition geometries capture seismic data discretely using 2-D spatial coordinates. Motivated by recent advances in neural radiance fields for 3-D reconstruction through implicit neural representation, we introduce implicit seismic representation (ISR) for 5-D seismic data interpolation. This approach processes seismic data coordinates as inputs and outputs amplitude values at those coordinates with multilayer perceptrons (MLPs). Due to the continuous nature of the coordinates, ISR can achieve representations at any desired resolution and is easily scalable to a 5-D representation. To achieve a continuous representation of seismic data, we employ a self-supervised learning strategy to train the ISR on observed data. The trained network is then capable of interpolating missing seismic traces by querying every coordinate of the missing data. Our approach’s effectiveness is validated through synthetic and field data experiments, showcasing superior reconstruction abilities. Our findings highlight the potential of the implicit neural representation framework to achieve precise parametrization of continuous seismic wavefields, marking a significant advancement in seismic data processing and analysis.

Ground-penetrating radar (GPR) is a pivotal noninvasive tool that yields subsurface images critical to archeology, near-surface characterization, geotechnical studies, and disaster response. The antenna central frequency of the GPR system has a significant impact on penetration depth and resolution. Lower antenna frequencies penetrate deeper but at lower resolutions, while higher frequencies offer detailed images at reduced depths. Therefore, improving the resolution of low-frequency radar with increased detection depth is an essential research focus. Inspired by image super-resolution advancements, supervised deep learning methods that rely on strictly paired training data have achieved remarkable success. However, acquiring such paired samples in practical scenarios is often a formidable challenge. To tackle this, we propose a novel resolution enhancement technique through weakly supervised learning, effectively addressing the scarcity of strictly paired samples in real-world situations. We utilize two sets of antennas with different central frequencies to construct our training data, with a low-frequency antenna as input and a high-frequency antenna as the learning target. A cycle-consistent generative adversarial network (Cycle-GAN) is trained to discern the mapping between low-resolution inputs and unpaired high-resolution data. The refined network is then employed to improve low-frequency GPR data resolution. Our work is validated on synthetic and real-world datasets. The proposed method effectively strengthens critical high-frequency details for finer imaging and broadens the frequency bandwidth. Significantly, it enhances resolution without compromising the detection depth of low-resolution GPR data, marking a substantial advancement in subsurface imaging technology.

During seismic acquisition, the received seismic data typically comprise many components, such as effective reflections and various interferences. Some components, such as industrial electrical interference and traffic vibrations, manifest as the equidistant narrowband discrete spectra (ENBD-spectra) in the frequency domain. Morphological component analysis (MCA) is widely used for separating different component from complicated seismic data. Therefore, it has been successfully used to extract the narrowband components from seismic data. However, the conventional MCA method overlooks equidistant feature of ENBD-spectra component in seismic data separation. In this study, we propose an improved MCA method that uses the interval between neighboring spectrum peaks as a constraint to separating the data with ENBD-spectra component. Two types of seismic datasets are used to show the proposed MCA’s effectiveness. The first type of dataset contains industrial electrical interference, while another type of dataset contains high-speed train (HST)-induced seismic signals. Both synthetic data examples and real data examples show that the proposed method has better performance in separating the seismic data with ENBD-spectra component and keeping the fidelity of separation compared with the conventional MCA method.

Time–frequency (TF) analysis represents a potent tool for processing and interpreting seismic data. Synchrosqueezing transforms (SSTs) remarkably enhance frequency resolution by accumulating coefficients along the frequency axis. However, their TF resolution is related to their mother’s TF transforms. The high-order Fourier-based SST (FSST) with a long window exhibits improved frequency resolution, albeit at the cost of mixing detailed frequency variations. Conversely, a high-order FSST with a short window provides enhanced time resolution but suffers from low-frequency resolution and component interference between multiple components of a complex signal. To ameliorate this, our study proposes a cascaded high-order FSST. Our proposed approach commences with a long-window high-order FSST to decompose a complicated signal into multiple components. Subsequently, a short-window high-order FSST is applied to each component. By summing the squeezed TF representations of all components, we generate a TF representation that boasts the improved TF resolution with the cost of involving multiple high-order FSSTs. The visual evaluation and sparsity measure are used to show our method’s efficacy and TF resolution over common high-order FSST through a synthetic multicomponent signal (MCS) with two components. The wavelets interference would make the seismic signal’s frequency component change. Therefore, further substantiation comes from two wavelet-interference-related examples: the field data example about cycle interbeds and an HST-induced seismic data example, wherein our proposed transform demonstrates its superior ability in precisely tracking subtle frequency variations with time and its advantages over common high-order FSST in extracting cycle thin-interbeds’ thickness variation along depth and characterizing the HST speed.

The moving high-speed train (HST) generates strong and repeatable vibrations in the railway roadbed, resulting in the propagation of complicated seismic waves into the subsurface medium. Therefore, the moving HST could be considered as a novel seismic source to detect the subsurface structure near high-speed railways (HSRs). An HST consists of several carriages. Therefore, the moving HST is one typical combined moving source that stimulates complex interference wavefields. Seismic interferometry (SI) is one commonly used method to generate virtual shot gather. However, the HST-induced seismic signal has one typical equidistant narrowband discrete (ENBD) spectrum feature, which means many frequency components are missing. Thus, the virtual shot gather based on an HST-induced seismic signal does not have sufficient bandwidth. In this study, we propose a processing scheme to construct broadband virtual shot gathers by distinguishing the moving direction of the HST and the propagation direction of seismic waves and stacking the HST events with different speeds. The feasibility of our proposed method is validated using both synthetic and real HST data, providing a broadband virtual shot gathers from HST-induced seismic signals.

With the improvement of computing power and the rapid development of deep learning, deep-learning-based methods are widely used in the field of seismic data noise suppression. Supervised learning has proven to be effective but its performance largely relies on noise-free data labeling, which is often unavailable or an expensive process. Therefore, as a form of unsupervised learning, self-supervised learning emerged to overcome this difficulty, with its labels coming from the training dataset itself. In this letter, we propose a self-supervised learning method that requires only raw seismic data to train the model by using the Noise2Noise strategy, which takes advantage of the unpredictability of noises to regress from noisy data to clean data. Our method aims at improving the noise suppression effect for common-reflection-point (CRP) gathers. By comparing with conventional methods, both synthetic and field data show that the proposed framework is not only effective in suppressing random noise, but also remains effective for coherent noise.

The attenuation of coherent noise in land seismic data, specifically ground roll and near-surface scattered energy, remains a longstanding challenge. Although recent advances in deep learning have improved signal separation from coherent noise, supervised methods are limited by the necessity for realistic training samples. To circumvent this issue, we propose an unsupervised deep learning approach to attenuate ground roll and scattered energy, eliminating the requirement for training labels. Our method leverages the inherent low-frequency bias of a generator network, which is naturally prone to learn self-similar features during training. This empowers the network to extract the desired component exhibiting self-similarity in the time-space domain, while disregarding unwanted components. Notably, horizontal components in seismic data exhibit pronounced self-similarity. To enhance the self-similarity of ground roll, we apply a linear moveout (LMO) correction to horizontally align it and utilize the generator network for separation. Additionally, for scattered energy attenuation, we employ the generator network to extract flattened reflections after normal moveout (NMO) correction. Our strategy distinctively merges model-driven procedures, specifically NMO and LMO, anchored in the geological velocity model. The synergy between data-driven deep learning and model-driven processes underscores the success of our approach. We demonstrate the validity of our proposed method using both synthetic and field shot data. The field data examples highlight the superior attenuation capabilities of our method, surpassing conventional denoising techniques by effectively reducing both random and coherent noise.

The attenuation of coherent noise plays a crucial role in reflection seismology but still poses some technical challenges. The multiple reflection–refraction (MRR) is one of the main coherent noises in land seismic surveys. The Cadzow filter can effectively attenuate incoherent noise. But it struggles in attenuating coherent noise. After keeping reflection events relatively horizontal, some researchers randomly rearrange the trace orders of the input data to realign coherent noise in an incoherent position so that the Cadzow filter can treat the realigned coherent noise as incoherent noise. Accordingly, a random-derangement-based FX Cadzow filter is proposed to attenuate MRRs in 2-D common-shot gathers based on the linear feature of MRR events and randomization of limited trace orders of the input data. In practice, after linear-move-out (LMO) with an estimated dip, the input data are divided into several small windows to obtain a group of relatively horizontal MRR events. Then, these windows are randomized and filtered one by one. Due to the limited trace orders of each window, there are many possible rearrangements after randomization. Some rearrangements may lead to undesirable filtering performance. To obtain the rearrangements that lead to good filtering performance, each window’s trace orders are randomly deranged by resampling from the input orders with uniform distribution. A 2-D synthetic data experiment shows the influence of different rearrangements on the filtering performance. Both 2-D synthetic data and 2-D field data demonstrate that the proposed method outperforms the 2-D FK filter to attenuate both aliased and nonaliased MRRs.

Deep-learning-based methods have been successfully applied to seismic data random noise attenuation. Among them, the supervised deep-learning-based methods dominate the unsupervised ones. The supervised methods need accurate noise-free data as training labels. However, the field seismic data cannot meet this requirement. To circumvent it, some researchers utilized realistic-looking synthetic data or denoised results via conventional methods as labels. The former ones encounter the problem of weak generalization ability because it requires the same distribution of test and training data. The latter ones encounter the issue of insufficient denoising ability because its denoising ability is difficult to significantly exceed the conventional methods which were used to generate labels. To avoid preparing noise-free labels, we propose a novel deep learning framework for attenuating random noise of prestack seismic data in an unsupervised manner. The prestack seismic data, such as common-reflection-point (CRP) gathers and common-midpoint (CMP) gathers after normal moveout (NMO) correction, have high self-similarity. It is because their events are coherent in the time–space domain and approximately horizontal from shallow to deep layers. The generator convolutional neural network (GCN) first learns self-similar features before any learning. The useful signals are more self-similar than random noise, which is incoherent and randomly distributed. Therefore, the GCN extracts features of useful signals before random noise. We select the specific training iteration and adopt the early stopping strategy to suppress random noise. Both synthetic and field prestack seismic data examples demonstrate the validity of our methods.

The seismic volumetric dip is a crucial seismic geometric attribute, which can provide useful information for assisting subsequent processing and interpretation. Waveform similarity scanning-based dip estimation (WSSB) delivers reliable dip estimation but encounters problems of expensive computation. To improve computing efficiency, we use multitask deep learning to simultaneously estimate the inline dip and crossline dip directly from a 3-D field seismic dataset. Our method considers dip estimation as a regression problem and trains a multilayer convolutional neural network with dual-channel output. It aims to output continuous values of seismic apparent dip from two directions simultaneously. To train the network, we propose an effective and efficient workflow to create a training sample dataset, which consists of field seismic cubes and the corresponding dip labels estimated by WSSB. After training, the network automatically learns how to extract rich and proper features that are important for dip estimation. By sliding the extraction window within the full 3-D seismic data, the network can output many overlapping dip cubes that are stacked to get two complete 3-D volumes of seismic dip. The final results of dip estimation by our method are similar to those by WSSB. We further demonstrate the accuracy of our approach by comparing the structural curvature. However, the computation time of our method is much less than that of WSSB. The proposed method can accurately estimate seismic volumetric dips with high computational efficiency.

Five-dimensional seismic reconstruction is receiving increasing attention and can be viewed as a tensor completion problem, which involves reconstructing a low-rank tensor from a partially observed tensor. Tensor train (TT) decomposition and tensor ring (TR) decomposition are two powerful tensor networks for solving this problem. However, updating core tensors leads to high computational costs in practical applications. We propose two efficient methods to exploit low TT-rank and low TR-rank structures by theoretically establishing the relationship between tensor ranks and matrix unfoldings, respectively. Specifically, the former uses a well-balanced matricization scheme, and the latter employs a tensor circular unfolding. Furthermore, we utilize the randomized parallel matrix factorization to accelerate the solution of these problems. Both synthetic and real data experiment demonstrates that the proposed algorithm can also achieve remarkable reconstruction performance; in the meantime, the computational cost is significantly reduced.

Deblending can extract good quality seismic data from blended seismic data. Generally, the deblending methods can be categorized as model- and data-driven methods. The model-driven deblending methods usually suffer from a massive computational burden, while the data-driven ones need to implement a forward blending process to construct training samples for network training. To solve these issues, we develop a plug and play (PnP) method that integrates a trained convolutional neural network (CNN) Gaussian denoiser as the prior for seismic intelligent deblending. Specifically, we propose to use acquired blended common shot gathers (CSGs) as training dataset for the CNN Gaussian denoiser training to avoid constructing or collecting any extra data. According to the theory and dedicated designed experiments, this training mode can greatly improve network performance. Then, the trained CNN Gaussian denoiser is plugged into the alternating direction method of multiplier (ADMM) algorithm to solve the deblending problem. Furthermore, based on the${l}_{{\mathrm{2}}} $norm data fidelity term and the special structure of the network architecture, the PnP-ADMM method converges to a fixed point. Experiments on synthetic and field data demonstrate that the presented PnP method with blended CSGs trained deep CNN Gaussian denoiser has superior deblending performances over the dictionary learning and discriminative deblending CNN methods.

Deep learning has been successfully applied to image denoising. In this study, we take one step forward by using deep learning to suppress random noise in poststack seismic data from the aspects of network architecture and training samples. On the one hand, poststack seismic data denoising mainly aims at 3-D seismic data. We designed an end-to-end 3-D denoising convolutional neural network (3-D-DnCNN) that takes raw 3-D cubes as input in order to better extract the features of the 3-D spatial structure of poststack seismic data. On the other hand, denoising images with deep learning require noisy-clean sample pairs for training. In the field of seismic data processing, researchers usually try their best to suppress noise by using complex processes that combine different methods, but clean labels of seismic data are not available. In addition, building training samples in field seismic data has become an interesting but challenging problem. Therefore, we propose a training sample selection method that contains a complex workflow to produce comparatively ideal training samples. Experiments in this study demonstrate that deep learning can directly learn the ability to denoise field seismic data from selected samples. Although the building of the training samples may occur through a complex process, the experimental results of synthetic seismic data and field seismic data show that the 3-D-DnCNN has learned the ability to suppress the Gaussian noise and super-Gaussian noise from different training samples. Moreover, the 3-D-DnCNN network has better denoising performance toward arc-like imaging noise. In addition, we adopt residual learning and batch normalization in order to accelerate the training speed. After network training is satisfactorily completed, its processing efficiency can be significantly higher than that of conventional denoising methods.