Seismic data denoising is a crucial and challenging task for high-quality seismic exploration. Recent advancements in deep learning methods have demonstrated promising results in seismic denoising. However, the acquisition of ground truth data required for training remains unavailable, especially in field tests. We propose an unsupervised deep denoiser called the iterative diffusion denoising model (IDDM) based on a diffusion model to remove random noise. We present the diffusion process of IDDM according to the seismic noise model and the two-stage reverse process to iteratively train a deep restorer with the data pair created solely from the observed data. Hence, the IDDM is learned to approximate the reverse diffusion process of the seismic data, which leads to the effective seismic signal recovery and robustness to the variant noise level and complex distribution of the field seismic data. Moreover, the invariant features between adjacent states are introduced to the generative denoising model by the signal preserving module, enabling IDDM to gradually recover the effective seismic signals in high fidelity while thoroughly suppressing noise using only noisy data. The proposed approach shows excellent denoised results in synthetic and field data tests at low signal-to-noise ratios (SNRs), demonstrating its potential for practical applications in seismic data processing.

Seismic interpretation is crucial in seismic exploration to identify geological structures in the field. However, interpretation is often challenging due to inherent low-resolution (LR) limitations, and acquiring high-quality data is expensive with no guaranteed fidelity. To address these challenges, we propose a novel supervised deep learning-based method to enhance seismic data resolution by simultaneously focusing on dominant wavelet frequency and the spatial domain. First, we employ a deep learning module to estimate the location of low-frequency wavelets as semantic information, providing a prior that allows the model to process these signals and precisely enhance the dominant frequency. Subsequently, we use a feature wrapper to integrate the LR data with the semantic priors. We use them as conditions for a diffusion model to generate high-frequency features, considered priors with higher-frequency wavelets. Finally, we input the priors and the LR data into a feature fusion module (FFM) to generate the final output, doubling the sampling points and traces to achieve high-resolution (HR) data with high-frequency wavelets. The models are trained separately using cross-entropy, Kullback-Leibler divergence, and Charbonnier loss. The priors we use and the design of the generative diffusion model ensure high fidelity, preventing false seismic events and over-smoothing. Experiments on field data demonstrate the superiority of our method compared to three other approaches, highlighting its potential as a powerful seismic super-resolution tool in practical applications.

After mitigating noise pollution, the primary challenge in processing downhole distributed acoustic sensing (DAS) data is the effective separation of its wavefield. Wavefield separation networks specifically for DAS data are scarce. Existing vertical seismic profiling (VSP) wavefield separation methods include traditional techniques, establishing propagation models applied to neural networks, and using the results of traditional methods as labels. Traditional methods can lead to issues of spatial aliasing and artifacts. Using such “not-so-clean” data for network training results in suboptimal performance. In addition, constructing models under simplified conditions results in training data that are overly simplistic, leading to a loss of detailed information in modern, higher sampling frequency, and more densely sampled complex DAS data. Inspired by the Radon transform and neural networks, we propose a DAS wavefield separation framework that combines the Radon transform with parallel U-Net (RTPU-Net) to address the issue of spatial aliasing in the Radon transform. We identified two key features in wavefield separation based on Radon transform: phase-reversed spatial aliasing and high amplitude preservation. In addition to constraining the network with loss functions, we also used reconstruction loss (MSE) to associate these two features. Using the Radon transform as a preprocessing method, our approach can also synthesize a large amount of training data automatically from raw data. Applications to both synthetic and field DAS data demonstrate that RTPU-Net can be widely used for high-precision DAS wavefield separation. When comparing the MSE metric of the overlapped wavefield from separated field data, our method also consistently achieves the lowest value among all the tested methods.

Seismic wavelet interference limits the vertical resolution of seismic data, making it challenging to accurately characterize subsurface geological structures. Seismic reflectivity estimation is a key process for improving the vertical resolution of seismic data. Deep learning-based seismic reflectivity estimation methods typically rely on labels generated from well data, which can be costly to obtain. Moreover, seismic reflectivity estimation is an ill-posed problem, meaning that while the estimated seismic reflectivity may fit the observed data, it can still differ significantly from the true reflectivity, particularly concerning thin layers. To address these challenges, we propose an unsupervised deep learning deconvolution framework guided by a physical convolution model and super-resolution mathematical theory. The network is trained using a combination of reconstruction loss, position prior loss, and sparse loss. Specifically, reconstruction loss establishes a closed-loop connection between the low-resolution seismic data and the estimated seismic reflectivity using the Robinson convolution model, eliminating the need for labels in training. Position prior loss estimates the seismic reflectivity position based on the super-resolution mathematical theory, which is particularly effective for thin layers, improving the interpretability and accuracy of the seismic reflectivity estimation. Sparse loss, based on the$L1$norm, enforces sparsity in the seismic reflectivity estimation, enhancing its stability. Both synthetic and field data examples demonstrate that the proposed method outperforms conventional sparse-spike deconvolution method, providing better thin-layer seismic reflectivity estimates and improved lateral continuity.

Distributed acoustic sensing (DAS) has been progressively used in acquiring vertical seismic profiles. However, DAS signals are susceptible to be contaminated by diverse noise, causing many difficulties in the interpretation of DAS VSP. Most of the existing methods for DAS noise suppression rely on either global or local information for the extraction of signal features. They neglected that both local detail and long-distance relevant features are required for denoising. To address this issue, we propose a U-shaped network with a combination of convolutional neural networks (CNNs) and refining transformers, named Urefiner. We employ CNN as a preprocessing step for the transformer model. The transformer model relies on the attention map to extract global features, while the CNN module will aggregate similar features within the attention map to facilitate local information processing. To facilitate the fusion of local information and global information, the distributing-local-attention (DLA) module is induced to calculate the weighted aggregation in the attention map between CNN and transformer, which can improve the effective receptive field of the network in local areas. Additionally, to improve the network’s attention to seismic signals for signal protection, we introduce a learnable linear matrix to expand attention map. It can aggregate the information acquired from different attention heads into a learnable weight matrix for the attention calculation. This linear weighting scheme can promote the interconnections among diverse attention heads, thereby facilitating the fusion of extracted information. Based on the above designs, the proposed Urefiner can augment the effective receptive field to amplify the significance of signal features in the attention map. Experimental results show that the network can effectively suppress various noises in DAS VSP and accurately protecting weak seismic signals.

For subsequent seismic data processing and interpretation, it is important to obtain high-quality distributed acoustic sensing (DAS) signals from down-hole DAS data containing various complex noises. Model-based denoising methods mainly treat this signal estimation issue as a maximum a posteriori (MAP) optimization problem, for its relatively transparent mathematical model and wide range of applications. However, the manually designed prior assumption in MAP cannot accurately describe the actual distribution of DAS data, so the optimization parameters for obtaining high-quality solutions are difficult to determine, making it unavailable in DAS signal estimation. To solve these problems, we propose to emulate the optimization process of MAP with neural networks and accomplish the signal estimation task in feature space via some customized optimization modules. Specifically, we first construct an optimization unit (OPTU) to simulate the optimization process. And then, in order to further obtain the signal distribution of DAS data, we design in each OPTU, a multiscale dense feature aggregation (MDFA) module with the idea of back-projection fusion. With the help of OPTU, the optimization estimation process would be implemented more finely and automatically, expanding the application of MAP for accurate DAS signal estimation. Experiments on both synthetic and field DAS data demonstrate that our method can successfully estimate the high-quality signals from DAS data corrupted by complex noises, with less energy loss.

Nowadays, one of the predominant deep learning approaches to improve the quality of DAS VSP seismic data is executed through supervised learning, which requires paired training set including data simulation with relevant parameters and solutions of elastic wave equations. However, differences between simulated data and field data in terms of signal regulations and noise distributions often leads to poor results. An alternative approach is self-supervised learning, such as the representative framework--Blind Spot Network (BSN), but unfortunately, the effective information in blind spots cannot be fully utilized. To solve this problem, this paper considers BSN as a basis and establishes a novel self-supervised network--blind spot visualization (BSV) to suppress random noise and improve the quality of DAS VSP data. In BSV, one branch is dedicated to first produce more denoised data with blind spots and then recover the valid information covered by the blind spots, assuming that the signal is partially data-dependent and the DAS noise is conditionally data-independent. The other branch is designed to generate a target for training without blind spots, so that the dual-branch network can accomplish a self-supervised task in the way of supervised learning. More than that, unlike BSN, we utilize a tailor-made blind spot mapper (BSM) to recover effective information in the blind spots. Results of field data testing prove BSV’s advantages in suppressing random noise and improving the quality of DAS VSP data, although test on synthetic data is nearly identical to supervised learning.

As conventional reserves of oil and gas resources continue to decrease, the target of seismic exploration is progressively shifting to the unconventional field. Fine-amplitude structure can form rich oil and gas resources under favorable conditions, which is an important unconventional reservoir. Surface seismic exploration is capable of revealing a large range of stratum structure, but its resolution is limited, and it is unable to detect fine-amplitude structures of small closure. Distributed acoustic sensing (DAS) vertical seismic profile (VSP) technology is a new, high-precision method for oil and gas resource detection, but it can only collect stratum information from a small area in the vicinity of the well. To explore the stratum structure with finer profile information, expand the identification range, and take full advantages of these two exploration methods, this letter proposes the stratum correlation technology to calculate correlation coefficients between DAS VSP data and surface seismic data at the same interface. By analyzing the shape and variation of the correlation coefficient curves, it is possible to locate and extend the information on fine-amplitude structure with a closure of less than 12 m. Stratum correlation processing can improve the accuracy of surface seismic data, clarify the existence and location of fine-amplitude structures, and extend the lateral extent of borehole DAS fine profiles.

Suppressing various noises while achieving precise signal reconstruction in Distributed Acoustic Sensing Vertical Seismic Profiling (DAS VSP) remains a challenge. Existing denoising methods are insufficient due to factors such as the unknown noise-disturbing mechanism, low SNR, and limited training data. Therefore, this study proposes the Mean-Stochastic Differential Equation (SDE) diffusion model as an advanced solution. Built upon the standard diffusion model, which incorporates forward and backward diffusion processes, our model introduced three modifications to enhance performance. 1. Improving the forward diffusion process: Transforming the final state into a combination of the noisy DAS VSP and Gaussian noise. This adjustment allows precise representations of multi-type noise generation and facilitates backward sampling. 2. Enhancing noise prediction between successive steps in the backward process: A Nonlinear Activation Free Network (NAFnet) with a time Multi-Layer Perceptron (MLP) was employed to provide accurate noise predictions at different states. 3. Addressing training instability inherent in standard diffusion: The objective function is modified to seek the optimal trajectory of the best quality of signal reconstruction rather than directly evaluating the noise prediction. The forward diffusion is a dynamic evolution of adding noise to the pure signal, while the backward processing aims to remove the noise step by step. Comprehensive experiments demonstrate the superiority of our method in diverse noise suppression, signal resolution enhancement, and amplitude preservation. Moreover, grounded in physics-based equations, our method exhibits less dependency on training data compared to conventional deep learning methods.

Full waveform inversion (FWI) is a powerful means for accurately reconstructing subsurface velocity models at high resolution. Yet it is nevertheless a nonlinear and ill-posed problem. Physics-driven FWI methods employ gradient-based optimization algorithms to minimize the error between the observed seismic data and the synthetically generated seismic data. The solution may converge to a local rather than global minimum. The cycle-skipping problem occurs when the synthetic data exceed a half-wavelength shift relative to the observed data. FWI relies on an accurate initial velocity model to mitigate the cycle-skipping problem. Moreover, due to the increasing size and desired resolution of seismic data, FWI costs a great deal of computational time. To obviate these problems, we present a data-driven FWI scheme based on a deep learning architecture called U-Net. The network consists of the ringed residual unit, which integrates residual propagation and residual feedback. It beneficially achieves correspondence between the seismic data domain and the velocity model domain. The features of the shallow layers are connected with the deep layers by a skip connection to facilitate seismic data spatial information propagation and utilization. They improve inversion accuracy and make the network more generalizable and robust. We utilize the Society of Exploration Geophysicists (SEGs)/European Association of Geoscientists and Engineers (EAGE) overthrust and salt models to verify our proposed method’s impressive performance. The experimental results clearly demonstrate that the proposed method can produce high-quality velocity models. Compared with the conventional physics-informed FWI, it has advantages in both computational time and initial model dependence.

In recent years, distributed acoustic sensing (DAS) technology has attracted much attention and has been applied to vertical seismic profiles (VSP). It has promoted the development of land exploration towards deep exploration and fine tectonic analysis. However, the acquired DAS VSP data are often disturbed by various types of noise generated by the environment and instruments. They exhibit quite different characteristics from traditional exploration noise, hindering the further development and application of DAS technology in the field of VSP. Frequency information plays an important role in the judgment and reduction of seismic noise. Since the noise and signals in DAS VSP data often have complex time-frequency relationships, it is difficult for traditional frequency-based methods to effectively separate them. Current deep learning DAS data processing methods did not consider the important frequency-domain features and affect the integrity of data feature extraction. This paper presents a new deep learning algorithm for DAS VSP data processing, Cosine Spectral Association Network (CSANet). The novel algorithm considers both the original time-offset and frequency information to achieve better DAS weak signal recognition and recovery. Moreover, a feature fusion module is designed to make sure the entire network to better utilize the composite information. The experimental results show that our CSANet can obtain high-precision DAS VSP weak signal recognition and recovery results with strong practical application value.

Seismic exploration is a crucial method for studying underground geological structures and oil/gas resources. However, the presence of various noise sources during seismic wave propagation hinders accurate interpretation and imaging. To address this challenge, effective denoising methods are essential. In recent years, deep learning, particularly Convolutional Neural Networks (CNNs), has shown promise in seismic data processing. Nevertheless, CNNs have limitations in capturing long-range dependencies and global coherence. As an alternative, we propose a Transformer-based model called Seismic Data Denoising Transformer (SDT) for seismic signal processing. By leveraging self-attention mechanisms, the SDT model overcomes the limitations of CNNs and effectively captures long-range features for seismic signal reconstruction. We also introduce a novel self-supervised pretraining strategy using a large-scale dataset to further enhance performance. Experimental results demonstrate the advantages of SDT in complex seismic noise attenuation and preserving weak signal amplitudes. The proposed method exhibits promising potential for real-world seismic data applications.

The comprehensive requirements of effectively suppressing various noises, preserving signal amplitudes, recovering weak signals, balancing the effects between local and global, and reducing computational costs have always been the crucial task of data processing of downhole DAS. Traditional methods, single-mechanism convolutional neural network models, and training methods with a single patch size, due to their simplistic structures, limited data processing capabilities, and a large number of network layers, often struggle to meet the aforementioned comprehensive requirements. In this paper, employing a progressive training method, we propose a novel non-local selective attention multi-scale residual network (NSKMRNet). At its core lies an iterative multi-scale residual block (MRB): multiple resolution convolution streams allow for the transfer of contextual information from the low-resolution stream to consolidate high-resolution features; parallel non-local contextual processing utilizes a distillation mechanism for extracting useful information, and weighted attention handling between adjacent scale streams for merging information. The feature maps selected from a randomly chosen training iteration clearly reflect the noise suppression process and the importance of iterative process. In experiments conducted on both synthetic and field DAS data, our method achieved an SNR (Signal-to-Noise Ratio) improvement of around 30 dB, surpassing other methods. It maximally preserves signal amplitudes, resulting in minimal signal residuals in the amplified field records. Moreover, in terms of FLOPs (Floating Point Operations) and training time, our method is within an acceptable range but significantly lower than more complex networks. The proposed network holds promise as a potentially valuable tool in meeting the comprehensive requirements for processing of downhole DAS data.

Distributed acoustic sensing (DAS) is a novel and revolutionary technology that is widely used in the field of seismic exploration. However, the problem of low signal-to-noise ratio (SNR) has always been a serious challenge affecting its processing and interpretation. At present, deep learning-based algorithms show remarkable potential in DAS vertical seismic profile (VSP) data denoising, but the recovery of deep-layer weak signals still needs to be further improved. To solve the above problems, we propose a dual attention denoising network (DADN) combining spatial attention (SA) and channel attention (CA) double attention block (DAB) to improve the recovery effect of deep-layer weak signals. The DADN consists of multiple DABs and utilizes encoder–decoder structure to extract signal features at multiple scales. At each scale, DADN uses a DAB to reassign the weights of feature maps on each channel and region to focus on useful information, which is beneficial for accurately extracting signal features and recovering deep-layer weak signals. The information flow undergoes downsampling and upsampling operations to finally achieve an accurate estimation of the DAS VSP signals. In addition, gradient-weighted class activation mapping (Grad-CAM) is introduced to visually interpret the signal features learned by the network. The visualization results show that the network does accurately distinguish between signals and noise. After training on the constructed semisynthetic DAS VSP dataset, DADN demonstrated competitive performance in both noise suppression and weak signals retention.

Distributed acoustic sensing (DAS), an emerging technology for signal acquisition, has been progressively applied to collect vertical seismic profile (VSP) data. Unfortunately, the obtained DAS VSP data are usually contaminated by various complex noise, which poses a major obstacle to subsequent processing; therefore, suppressing the noise in the DAS VSP data is a critical step. With the development of neural networks, deep learning is widely used for seismic data denoising. Supervised learning-based denoising methods, however, require massive amounts of training datasets with labels. The lack of labeled datasets limit the performance of supervised learning methods. The recently proposed unsupervised learning-based denoising methods reduce the reliance on labeled data, but they are not suitable for processing seismic data containing multiple types of complex noise. In this study, we propose a semi-supervised denoising network (SSDN) that contains both supervised and unsupervised paths. The supervised path is trained using a synthetic dataset to extract rich signal features. Unsupervised path exploits the distribution difference between signal and noise, using field dataset to extract realistic and accurate signal features. The backbone network consists of a three-layer pyramid structure and incorporates a multiscale fusion strategy to improve network performance. The idea of semi-supervised learning reduces the reliance on labeled data, takes full advantage of the distribution characteristic of the field data, and benefits the generalization ability of the denoising model. Experimental results on one synthetic data and four field DAS VSP data demonstrate that the proposed method obtains competitive performance in intense noise suppression and effective signal recovery.

Optical noise detected by borehole distributed acoustic sensing (DAS) system exhibits various multiplicative characteristics, including nonuniform distribution and simultaneous occurrence with seismic signals. These characteristics are likely associated with instrument defects and warrant further investigation. However, research on this topic remains limited. This study aims to substantiate the multiplicative nature of optical noise using an enhanced cepstrum method. Cepstral line amplification is integrated into the conventional cepstrum method as a necessary step to suppress redundant information caused by additive seismic noise, while a pseudo-time constraint is imposed based on the propagation rules of signal waves. These operations ensure precision in the analysis results, thereby contributing to noise suppression and instrumentation improvement. A typical common-shot-point record, affected by significant optical noise, is employed for verification. The separated cepstral lines in the cepstrum results indicate that optical noise acts as a multiplicative interference in the acquired DAS records. Both continuous seismic traces and entire noisy area are utilized to establish the mathematical relationship between seismic signals and optical noise. Consistent conclusions emerge from the 3-D cepstrum, average cepstral amplitude, and specific trace distributions. A quantitative measurement has been developed to validate these findings. We desire that this study will serve as a reference for practical applications, such as improving acquisition instruments and designing denoising algorithms.

Distributed acoustic sensing (DAS) technology has been applied in vertical seismic profiling to provide high-precision seismic records for oil and gas exploration in recent years. However, these records are often contaminated by various noises due to the limitations of acquisition instrument and borehole environment, resulting in an unclear reflection of the geologic structure. The object of this paper is to remove the severe noise contamination through signal decomposition, time-frequency description and feature classification. Firstly, we design an improved decomposition method to avoid signal distortion and reduce frequency aliasing during the decomposition process. A flexible sifting iterative stop condition is applied to sift through unevenly distributed noises in the DAS records. Secondly, we construct a high-dimensional attribute space using time and frequency factors to represent the confused decomposed components. This ascending-dimensional feature mapping facilitates the description of differences between seismic signal and noise. Finally, we establish a two-level ensemble framework based on tree-structure learners to complete the classification tasks in the high-dimensional feature space. Experiments have proved that this method effectively recovers seismic signal waves while accurately suppressing the complex noises. The improved decomposition method overcomes signal distortion and reduces frequency aliasing, providing clearer information for feature extraction. The tree-structure ensemble model exhibits high accuracy and strong generalization, ensuring the low-attenuation recovery of effective signals. Furthermore, this research reveals the mechanism by which noise interferes with signals and identifies the dominant frequency of random noise.

Deep learning (DL) exhibits excellent performance in seismic noise suppression, and DL successes are attributed to its ability to learn rich representations from a large amount of data. However, obtaining numerous high-quality labeled data is challenging owing to confidentiality, regional sensitivity, and manual labeling, which limits the capability of DL. To reduce data dependency and improve network generalization, this study proposes a novel denoising architecture based on small-sample transfer learning (TL). The proposed architecture uses a fully pretrained model on the source data as a feature extractor, and then copies and transfers the rich features from the extractor to the denoiser for fine-tuning on the target data. Moreover, to reduce the discrepancy between two different data and better reuse the transferred features, a noise attention block (NAB) is proposed to regularize the representations. The results of multiregion experiment indicate that the proposed network leads to a significant improvement in denoising performance, essentially outperforming existing denoising methods; additionally, it exhibits strong generalization for different types and regions of seismic noise. Moreover, the proposed method can effectively address the data dependency issue, thus, providing great potential for real-time processing or small device applications.

Distributed acoustic sensing (DAS) has been gradually applied to vertical seismic profiling (VSP), where the generated DAS VSP seismic data contains types of complex noise. Therefore, data denoising plays an important role in collecting high-quality geological information. Generative adversarial network(GAN) has been widely used in seismic exploration data denoising these years, but problems such as insufficient optimization objectives, poor signal retention continuity, and insufficient accuracy still remains when processing DAS VSP data. To address these problems, this paper proposes DuGAN, a deep learning network for multi-scale feature extraction and global information discrimination, to better meet the requirements of high-precision in DAS VSP data denoising. Our method takes GAN as the basic architecture and chooses the multi-scale codec network U-net to explore the potential correlation of DAS data at different scales and a more robust feature representation of DAS signals. In addition, DuGAN is more inclined to emphasize the global role of discriminator so that the entire network ensures the integrity of effective signal structure from a global perspective. Also, for more accurate recovery of the DAS reflected signal, we adjust the loss function in adversarial training and tilt the target optimized space towards the discriminator. Experiments on synthetic and field DAS seismic data show that DuGAN has better denoising performance-not only the noise-covered signal can be recovered, but also the overall effective events are better preserved.

In recent years, distributed acoustic sensing (DAS) has been widely used for vertical seismic profile (VSP) data acquisition. Compared with conventional geophones, the data collected by DAS usually contains more noise. Therefore, denoising is an essential step in DAS VSP data processing. Benefiting from the development of neural networks, learning-based methods are widely used for seismic data denoising. However, supervised learning-based denoising methods are often limited in practical applications due to the scarcity of labeled datasets. Although recently proposed self-supervised learning-based methods, such as blind spot network (BSN), alleviate the reliance on ground-truth data, the harsh conditions that noise should satisfy zero-mean and statistical independence are also difficult to meet. In this study, we propose an improved BSN for spatially correlated noise suppression in DAS VSP data. Specifically, we observe that the spatial correlation of DAS noise decreases as the distance between noise pixels increases, and that the rate of decrease is direction-dependent. Based on this observation, we improve the pixel-shuffle down-sampling (PD) strategy to sample and recombine the DAS VSP data to increase the distance between adjacent pixels, thereby weakening the spatial correlation of noise to meet the application conditions of BSN. In addition, we also propose a signal detail enhancement strategy to compensate for the effect of PD strategy on signal detail recovery. Qualitative and quantitative analysis on the denoising results of one synthetic and three field DAS VSP data show that the proposed method can effectively remove noise with certain spatial correlation, showing competitive performance.

Distributed fiber-optical acoustic sensing (DAS) is a new and booming technology in seismic exploration. DAS technology has been gradually applied to the exploration of vertical seismic profile (VSP) due to its strong resistance to high temperature and pressure, high sensitivity, high precision (trace interval can be accurate to about 1 m), and so on. However, real DAS-VSP data are always contaminated by both random and coherent noises, which greatly affects the quality of DAS-VSP data. In order to suppress the background noise and increase the signal-to-noise ratio (SNR), a convolutional neural network (CNN) based on leaky rectifier linear unit (ReLU) and forward modeling is proposed and named L-FM-CNN. In terms of network architecture, Leaky ReLU is adopted as the activation function of CNN, which can enhance the recovery ability of trained CNN denoising model to the weak effective signals. As for the training data set, we construct a high-authenticity theoretical pure seismic data set for DAS-VSP data through the complexity of forward models and the diversification of physical parameters. In addition, we propose a new mean square error (MSE) loss function combined with an energy ratio matrix (ERM). The ERM can adjust the SNR between the signal patch and noise patch during the network training and thus increase the robustness of trained CNN denoising model for the DAS-VSP data with different SNRs, especially the DAS-VSP data with extremely low SNR. Both synthetic and real experiments prove the effectiveness of the proposed L-FM-CNN.

In recent years, methods based on rank reduction, such as nuclear norm minimization (NNM), have achieved remarkable results in seismic signal processing. These methods are used to threshold the singular values of the degraded signals, so as to estimate the singular values of the clean signals directly. Although the effect is obvious, it is easy to produce the result that the estimated singular values deviate greatly from the actual singular values, which will lead to the loss of the effective signals. Therefore, we adopt a novel framework composed of rank residual constraint model and enhanced block matching to suppress low-frequency noise in seismic signals. In each iteration, we first use the singular value of the degraded signals to estimate a reference singular value, and then obtain the denoised signals by minimizing the residual (difference) between the singular value we want to recover and the reference singular value. In this manner, both the reference and the recovered singular values are updated gradually and jointly in each iteration. In order to make the underlying clean matrix satisfy the low-rank criterion, we use a bandpass filter to enhance the accuracy of block matching before denoising. The experimental results on both simulated and actual seismic records indicate that our method has a better effect on low-frequency noise suppression of seismic data.

Noise reduction is an essential step in seismic exploration. Formally, the random broadband noise in the desert seismic is characterized as nonlinear, nonstationary, and non-Gaussian, and the energy is concentrated mainly in the low-frequency range. Moreover, the reflected signals generally cover the same spectral region as a strong random broadband noise. In this letter, a method combining unsupervised feature learning and the time–frequency transform (TFT) technique is proposed to reduce random broadband noise in desert seismic data. First, as a TFT technique, the variational mode decomposition (VMD) is carried out to decompose the multicomponent desert seismic signal into an ensemble of band-limited modes. Then, we apply an unsupervised feature learning method on each decomposed mode for detecting desert seismic events. Finally, the inverse VMD transform is conducted to obtain the final denoised result. This method is tested on both synthetic and field desert seismic data, demonstrating its preferable performance in reducing random broadband noise and preserving reflected signals.

For imaging and interpretation, high-quality seismic data are necessary. However, noise, which is strong in field desert seismic data, inevitably diminishes the quality of the data and reduces the signal-to-noise ratio. Moreover, the effective signals and noise in field desert seismic data are mostly distributed in the low-frequency band, which leads to severe spectral aliasing. Recently, some deep learning methods have improved the quality of desert seismic data in certain aspects. However, due to limitations of their networks and the serious spectral aliasing of desert seismic data, the denoising results usually show some false seismic reflections. To solve the above problems, we introduce Unsupervised Generative Attentional Networks with Adaptive Layer-Instance Normalization for Image-to-Image Translation (U-GAT-IT) to the denoising of desert seismic data in a semisupervised manner. U-GAT-IT is an unsupervised attentional generative adversarial network (GAN) combined with an attention module guided by the class activation map (CAM). The attention module guided by the CAM can guide the model to better distinguish between noise and effective signals. The experiment shows that the U-GAT-IT can effectively suppress desert seismic noise. Also, the denoising result has fewer false seismic reflections.

Since seismic data will be interfered with by a host of complicated noise during the acquisition process, the quality of the acquired seismic data is usually poor. The overlap of signals and noise makes it difficult to extract effective signals from desert seismic records. Therefore, the suppression of seismic noise and the retention of seismic signals are key issues in seismic signal processing. In order to improve the quality of the data obtained, we propose an unsupervised relative attributes-based generative adversarial network (RAGAN), which includes a generator, a discriminator, and an attribute match-aware discriminator. By encoding the data of different attributes in seismic records, the denoising task can be regarded as the conversion process of the data corresponding to the attributes. The relative attributes obtained by the difference between the target attribute and the original attribute are used to control the attributes of the data generated by the generator, so as to achieve the purpose of noise suppression. Experimental results of both synthetic and field seismic records show that the proposed method performs better than part of conventional methods.

With their powerful feature extraction ability, convolutional neural network (CNN) models achieve excellent signal reconstruction and recovery performances compared with those of traditional methods. The CNN-based approaches mainly use supervised learning approaches; thus, they require large numbers of ground-truth labeled samples. However, in the seismic denoising field, collecting large numbers of labeled samples is impossible; thus, the main challenge to using deep learning methods is a lack of labeled data. Moreover, the data that are available contain noise. To resolve these shortcomings, this letter proposes a novel self-supervised learning framework to reconstruct and perform blind denoising of seismic data images; this approach requires no labeled training data. We utilize a masking procedure to modify an observation input to a CNN to create a$\mathcal {J}$-invariant function and incorporate a specific CNN architecture known as U2Net, which implements a two-level nested autoencoder that extracts complex feature information from different scales. We modify the network to make it more suitable for seismic signal reconstruction. Finally, we use the self-supervised loss between the original observation and the net output to update the weights of U2Net through backpropagation. Tests on both synthetic and field data demonstrate the superior performance of our algorithm on low signal-to-noise ratio data.

In recent years, supervised deep learning-based denoising methods have been popularized and developed rapidly in the field of seismic data processing. Supervised training, however, is limited by the quality and quantity of the paired training data (noisy clean or noisy noise). Data labeling is a time-consuming and expensive work. Compared with raw seismic data, only a small amount of seismic data have been correctly labeled, which, to some extent, limits the long-term development of supervised deep learning-based methods in the field of seismic data denoising. In this letter, we propose an improved denoising framework based on an unsupervised deep learning-based denoising method Noise2Noise, which only needs unprocessed raw seismic data to train the denoising model. Moreover, unlike Noise2Noise, the proposed method does not need to repeatedly collect seismic data to obtain a training pair with similar signal, which is more convenient and effective. Specifically, we propose a block random sampler that can generate training pairs using raw seismic data, which satisfies the training assumption of Noise2Noise that the training pair has a similar signal. In addition, our method has no requirements for the network structure and noise distribution prior and is flexible. Both synthetic seismic data and field seismic data denoising results show that our method can effectively suppress the random noise, and the denoising performance is equivalent to that of supervised deep learning-based denoising methods. In addition, our method may provide a certain reference for geophysical-related research.

Distributed acoustic sensing (DAS) is a new downhole vertical seismic profile (VSP) acquisition technology, which has many advantages of low cost, sensitive signal capture capability and high spatial-temporal resolution. It can provide dense wavefield information for subsequent processing. Although DAS has obvious advantages over geophones, some weakness may limit its application. The main challenge is that DAS data are polluted by various types of noise, including optical abnormal noise, random background noise, fading noise, and so on. The noise brings great difficulties to the interpretation of seismic data. In order to suppress the noise and recover the buried weak effective signals, we design a new sparse parallel-subnet network (SPSNet) in this paper. It includes a parallel-subnet feature extraction module with sparse mechanism, simultaneously extracting global and local dual features. In this way, we can extract as much detailed information as possible from DAS seismic data. Then the following enhancement module fuses these features for signals complement. Another outstanding advantage is its high efficiency owing to the parallel structure. Compared with the complex networks with the same noise suppression effect, SPSNet has higher work efficiency. We generate a large number of geologic structure models with different parameters to optimize SPSNet. The denoising results show that the proposed method can effectively suppress a variety of noise in DAS seismic data. And the deep layer signals with weak energy are also well recovered.

In recent years, the denoising of low-frequency desert noise has been the significant and difficult point in processing seismic data. Traditional random noise suppression methods could not get a good result in processing seismic data in desert areas. Moreover, convolutional neural network (CNN) has made notable achievements in many fields recently. In order to denoise seismic data in desert areas and improve the signal-to-noise ratio (SNR), CNN is introduced to process seismic data. According to the characteristics of desert seismic data, we designed a new network suitable for desert seismic data training and denoising, which is named DnResNeXt. Then, to form a mapping from the noisy data to the pure desert noise, we build a mass of training sets to train the denoising network. Thus, the network can predict the noise, then by subtracting the predicted noise from the noisy data, the denoised data are obtained. Consequently, compared with the traditional methods in suppressing random noise, DnResNeXt network has obvious advantages in both simulation and actual experiments.

Distributed acoustic sensing (DAS) is widely recognized as a new technology to replace conventional geophones for the acquisition of seismic data. However, the collected data often contain a lot of coupled noise due to cable slapping and ringing along the borehole casing, which brings great difficulties to the interpretation of seismic data. The existing conventional coupled noise reduction methods often need to estimate the parameters of each coupled noise (such as amplitude, noise period, attenuation coefficient, etc.), which takes a lot of time and cannot meet the requirements for large-data-volume DAS seismic data processing. In addition, some deep learning-based denoising methods lack detailed analysis on coupled noise and have problems in the construction of training sets, resulting in insufficient generalization ability of the denoising model. To solve these problems, we propose a coupled noise reduction method based on the convolutional neural network (CNN). The proposed method does not need to estimate the parameters of coupled noise, and the denoising process is more convenient and efficient. In addition, through the analysis of DAS seismic data, we also construct a training set for coupled noise reduction using real data and synthetic data. The denoising results of both synthetic data and field data show that the proposed method can effectively reduce the coupled noise in DAS seismic data, and the effective signal has almost no energy loss. After processing, the signal affected by coupled noise becomes clear and continuous, providing high-quality data support for subsequent interpretation.

Recently, distributed optical fiber acoustic sensing (DAS) is regarded as a transformative technology in seismic exploration. However, both various complex background noise and weak desired signals significantly limit its practical application. To explore an effective denoising method for the vertical seismic profile (VSP) record received by DAS, we propose an improved residual encoder–decoder deep neural network (RED-Net) enhanced by deep iterative memory block (DMB) and channel aggregation block (CAB), called residual channel aggregation encoder–decoder network (RCEN). Here, DMB uses the weight accumulation theory to improve the feature extraction ability and achieve accurate noise elimination. Meanwhile, CAB, using the multi-channel analysis architecture, enhances the weak signal retention performance. In addition, we leverage both the synthetic data obtained by forward modeling and real DAS noise data to construct a sufficient training dataset with high authenticity, thereby meeting the requirement of network training. Both the synthetic and field DAS-VSP data processing results demonstrate the advantage of RCEN compared with competing algorithms, including singular value decomposition (SVD), conventional RED-Net, and feed-forward denoising convolutional neural network (DnCNN).

Seismic background noise often damages the desired signals, thereby resulting in some artifacts in the seismic imaging that follows. Since about 2016, some supervised-deep-learning methods have shown impressive performance in seismic data denoising, but they usually only consider single-scale features and neglect the multi-scale strategy. To further reinforce their denoising performance, a novel multi-scale convolutional neural network (CNN) combined with spatial attention mechanism, called multi-scale spatial attention denoising network (MSSA-Net), is proposed to tell weak reflected signals apart from strong seismic background noise. Unlike conventional single-scale CNNs, this proposed MSSA-Net can achieve the extraction of multi-scale features which is beneficial for the suppression of strong noise and the recovery of weak reflected signals. Specifically, MSSA-Net contains a principal denoising network and two auxiliary networks. The former utilizes the widen convolution composed of multiple parallel convolution layers with different kernel sizes to capture the informative multi-scale features; the latter two leverage up and down sampling to extract local fine and global coarse features, respectively. Furthermore, a spatial attention block is adopted to fuse these multi-scale features, thereby distinguishing weak reflected signals from strong seismic background noise. Multiple experiments of synthetic and real seismic records demonstrate the effectiveness of MSSA-Net. In addition, compared with two classical single-scale CNNs, MSSA-Net performs better in signal recovery, indicating the positive effect of multi-scale strategy.

Distributed acoustic sensing (DAS) is a new tool with low cost, sensitive signal capture, and complete coverage for vertical seismic profile (VSP) acquisition. Although DAS has obvious advantages over geophones, some weaknesses may limit its application. The main challenge is that DAS is polluted by various types of noise, including optical abnormal noise, random background noise, fading noise, and so on. To suppress these novel noises, we developed a new denoising neural network based on singular spectrum analysis—multichannel singular value decomposition denoising convolutional neural network (SVDDCNN). The network can simultaneously extract data features from singular spectrum instead of the time domain, which can represent geophysical features more accurately and help separate signals from noises. Second, a multichannel input layer is designed, and the input is decomposed into three subspaces by singular spectrum analysis, which provides records of different signal-to-noise ratios (SNRs) for training and improves generalization ability of the network. Third, to enhance the quality of the data set, we added the noise subspace records removed by SVD into the training set to provide various forms of noise with different singular spectra. Both synthetic and field examples show that our network has achieved impressive denoising of DAS VSP and demonstrated competitive performance compared with other methods. Furthermore, the structure similarity (SSIM) map is introduced to evaluate the signal leakage by calculating the similarity between the denoised record and the removed noise record. The lowest SSIM index of the proposed network indicated superior signal preservation ability.

Distributed acoustic sensing (DAS) is a new exploration technology widely used to acquire vertical seismic profiles (VSPs). DAS can achieve low-cost and high-density observations, but the signal-to-noise ratio (SNR) of the VSP data collected by DAS is low compared with traditional electrical geophones. Moreover, DAS VSP data cover many types of noise, including random noise, fading noise, checkerboard noise, and long-period noise. These noises bring many difficulties to the imaging and interpretation of DAS VSP data. To solve this problem, we proposed a multi-stage denoising network (MSDN) to denoise DAS VSP data. MSDN is a progressive denoising network consisting of four stages. MSDN can recover the signal details better than a single-stage denoising network, which is beneficial when processing deep reflection signals. In addition, MSDN combines residual structure and an attention mechanism. The residual structure can prevent the degradation of the deep neural network, while the attention mechanism can make the network focus on effective signals, making network learning more accurate and efficient. Both synthetic data and field data denoising results showed that MSDN could effectively remove various complex noises and restore signals covered by noise. Compared with other denoising methods, our method has improved signal amplitude preservation ability and noise suppression ability.

Desert seismic data are often characterized by low signal-to-noise ratio (SNR) due to the fickle surface conditions and desert random noise with nonstationarity, nonlinearity, spatial directivity, and low-frequency characteristics. This low SNR is likely to affect the following inversion and interpretation. Therefore, robust noise attenuation is crucial to improve the SNR of desert seismic data. We propose a novel method alternating direction method of multipliers-based denoising convolutional neural network (ADMM-CNN) by combining low-rank decomposition with feed-forward denoising convolutional neural network (DnCNN). DnCNN is a deep-learning-based method for noise removal, which can make good noise attenuation performance through training. However, there is no feature extraction procedure before model learning in its structure, so DnCNN cannot make full use of the prior information of signals. Combining low-rank decomposition just addresses this issue. Compared with DnCNN, our method has two main novelties. First, we use the synthetic seismic data that resemble the characteristics of field desert seismic data and desert noise to train the ADMM-CNN. Second, we use ADMM to decompose the data into three layers (low-rank, sparse, and perturbation) which are used as the inputs of three channels neural network. Through this decomposition, the neural network can capture more features and prior information of desert seismic data. Both synthetic field data tests demonstrate the robuster performance of ADMM-CNN compared to traditional methods and DnCNN, also that the ADMM-CNN method suppresses the desert noise more thoroughly and greatly improves SNR of desert seismic data at the same time.

With the goal of obtaining high-quality downhole distributed acoustic sensing (DAS) data from multiple types of complex noise, denoising plays an important role. However, conventional denoising methods cannot achieve a satisfactory effect toward multiple types of complex noise. Recently, convolutional neural networks (CNNs) exhibit dramatic improvements over conventional methods. The existing CNN-based methods typically operate through incorporation with conventional methods for adaptive threshold, additional multiscale idea, or attentional mechanism for more features extraction. In these cases, serious signal loss or artificial events are usually generated. Maybe, the recovered events are not continuous with some breakpoints and derangement. To resolve these problems in current networks, we propose a novel iterative parallel-attention guided multibranch residual network (PA-MRNet) with the collective goals of suppressing multiple types of complex noise and recovering buried weak signals. The core of our method is an attentional multibranch residual block (AMRB) containing: parallel multiresolution convolution streams for multiresolution features extraction, proposed parallel attention block (PAB) design for interested features capture, and novel parallel-attention guided fusion block for features fusion. In a word, our method can learn an enriched set of features to suppress multiple types of complex noise and simultaneously recover weak signals continuously with less energy loss. Experiments on synthetic and field DAS data demonstrate the better performance of the proposed iterative PA-MRNet.

Distributed acoustic sensing (DAS) technology is a rapidly evolving fiber-optic sensing technology that has been gradually applied to vertical seismic profile (VSP) data. The DAS VSP data are often contaminated by multiple interference waves, such as random noise, coupled noise, horizontal noise, and the existing methods can only map it from noisy data to effective reflections. However, interference waves are also a relative concept, and many interference waves still have certain application values. Therefore, this article proposes an innovative algorithm called attribute-guided target data separation network (Att-TDSN), which can not only complete the conventional signal-noise separation task but also achieve noise-noise separation task. Specifically, we first propose a flexible and efficient training set, namely, multidimensional weak label training set (Mul-WLTS), which introduces attribute features as the weak labels and specifies the dimension of weak labels according to the number of target data types (effective reflections and several common interference waves). Then, we use the weak labels to guide our network to map training data to specified data types, assisting the network to focus its attention on each kind of target data. Finally, the network parameters are trained by a training mode called “one-way matching and two-way constraint.” “One-way matching” makes data separation result unique, and “two-way constraint” can improve the algorithm’s amplitude preserving ability. Experiments on synthetic and field DAS VSP data show that our network can accurately separate target data. Moreover, for the traditional denoising task, Att-TDSN also has a better denoising performance than existing methods.

Distributed acoustic sensing (DAS), increasingly mature technology for signal acquisition, has been gradually applied in the field of environmental monitoring and seismic exploration. However, the usually strong noise in DAS data and the huge amplitude contrasts among direct waves, reflected waves, and converted waves significantly complicate subsequent data processing and interpretation, which would further limit the wide application and rapid development of DAS in the seismic exploration field. Taking the high-accuracy processing requirements of DAS data into consideration, we propose a multiscale progressive fusion attention network (MPFAN) with pyramidal structure trained by small samples, which explores the collaborative representation of complementary information between DAS noise and its multiscale versions in a multiscale direction to realize the fine modeling of DAS noise and then achieve the suppression of DAS noise. At each scale, MPFAN uses a recurrent calculation to explore the potential correlation of complex DAS noise and learn the global texture, and reassigns the weights of feature maps on each channel through an attention mechanism to focus on detailed information. At each hierarchy, the information flow converges from the bottom to the top layer of the network to finally achieve an accurate estimation of DAS noise. Experiments show that, after training on a forward DAS dataset, which is composed of synthetic noise-free DAS signals and some DAS noises from both synthetic and field data, MPFAN performs better in high degree than some classical methods—not only more noises are obviously suppressed but also more reflected signals are better preserved.

The low-frequency seismic noise has partially overlapping frequency band and similar waveform with seismic signals, making identification of seismic signals difficult in the seismic data at low signal-to-noise ratio (SNR). For improving the quality of seismic data, a deep complex reaction–diffusion (DCRD) model is proposed by combining the convolutional neural network (CNN) with the complex shock diffusion (CSD) which consists of a diffusion term and a shock term. By introducing a reaction term with an adjustable weight into the CSD, the CNN model can be embedded to learn the reaction term, leading to more effective signal preservation. The DCRD feeds smoothed signal components to the evolution process, by fusing the intermediate result based on low-level seismic features of data to be processed and the result of CNN model that learns deep seismic features. Moreover, the learnable reaction term facilitates the DCRD to apply effective diffusion for filtering out low-frequency seismic noise with spatiotemporally variable levels. Finally, the diffusion and shock terms in the DCRD can adjust the deviation of CNN model when the noise statistics of noisy seismic data having spatiotemporally variable levels deviate from training data, which also expand the practical application of CNN model. The DCRD is tested on synthetic and field seismic data and the results demonstrate that the DCRD achieves a great performance in suppressing low-frequency seismic noise with spatiotemporally variable levels and preserving seismic signals.

Distributed acoustic sensing (DAS) is a novel technology, which has the advantages of full well coverage, high sampling density, and strong tolerance to harsh environments. However, compared with conventional geophones, the signal-to-noise ratio (SNR) of vertical seismic profile (VSP) data obtained using DAS is low, and there are many types of noise (such as random noise, coupled noise, fading noise, background abnormal interference, horizontal noise, and checkerboard noise). These noises bring great difficulties to the interpretation of seismic data. Existing DAS VSP data denoising methods generally can only suppress one type of noise. Faced with DAS VSP data with many types of noise, the denoising process is extremely complicated. To solve the above problems, we propose a DAS VSP data denoiser based on the convolutional neural network (CNN), which can suppress a variety of common noise at one time, and the denoising process is more convenient and efficient. In addition, since there is currently no publicly available training set for DAS VSP data, we also use field data and synthetic data to construct a training set for the denoiser. The denoising results show that the proposed method can effectively suppress a variety of common noise in DAS VSP data and the effective signal has almost no energy attenuation. Both the shallow layer signal affected by strong noise and the deep layer signal with weak energy are well recovered.

At present, almost no denoising method can effectively suppress the seismic random noise in different areas. This phenomenon is partially because of two reasons: 1) the variable dominant frequency (DF) distribution of random noise in different areas and 2) the different signal-to-noise ratios (SNRs) of the seismic data acquired from different areas. We have developed a deep-learning denoising method to suppress the random noise in different areas based on convolutional neural network (CNN). For a certain area, we leverage the wave equation and power spectrum analysis to construct a noise set whose DF distribution is close to that of the real random noise in this area, and then a CNN denoising model for this area can be obtained via the training of this noise set. In addition, an energy ratio factor is used to adjust the energy ratio of effective signal patch and noise patch in the training process, so as to improve the generalization ability of CNN denoising model to different SNRs. Experiments demonstrate that our method can effectively suppress the random noise in different areas and completely recover the effective events.st no denoising method can effectively suppress the seismic random noise in different areas. This phenomenon is partially because of two reasons: 1) the variable dominant frequency (DF) distribution of random noise in different areas and 2) the different signal-to-noise ratios (SNRs) of the seismic data acquired from different areas. We have developed a deep-learning denoising method to suppress the random noise in different areas based on convolutional neural network (CNN). For a certain area, we leverage the wave equation and power spectrum analysis to construct a noise set whose DF distribution is close to that of the real random noise in this area, and then a CNN denoising model for this area can be obtained via the training of this noise set. In addition, an energy ratio factor is used to adjust the energy ratio of effective signal patch and noise patch in the training process, so as to improve the generalization ability of CNN denoising model to different SNRs. Experiments demonstrate that our method can effectively suppress the random noise in different areas and completely recover the effective events.

The seismic data with high quality are the essential foundation of imaging and interpretation. However, the real seismic data are inevitably contaminated by noise, which affects the subsequent processing and interpretation of seismic data. In desert seismic data, the energy of noise is stronger. Also, the frequency-band overlap between noise and effective signals is more serious. Recently, some methods based on supervised learning can suppress the desert seismic noise to some extent. Generally, supervised learning-based methods use synthetic noisy data and paired pure data as training sets to train model. However, the difference between synthetic noisy data of training and real seismic data of testing leads to the degradation of the model, and the denoising results often have many false seismic events when dealing with field seismic data. To solve the above problem, we introduce Cycle-generative adversarial networks (GANs) into the denoising of desert seismic records. Cycle-GAN is an unsupervised learning-based method. It can learn the domain mapping from noisy data domain to effective signal data domain through unpaired data training. So we use unpaired real desert common-shot-point data and synthetic pure data to train Cycle-GAN, so as to effectively improve the denoising ability of the method for real seismic data. Finally, the denoising of desert seismic data is realized. The experiment shows that the Cycle-GAN with unpaired data training can effectively suppress desert seismic noise and retain the effective signal amplitude. Also, the denoising result has less false seismic reflection.

Seismic random noise reduction is an indispensable step in seismic data processing. Due to complex geological condition and acquisition environment, random noise in the desert seismic data has spatiotemporally variant noise levels and weak similarity to the signals, which severely obscures the seismic signals and increases the difficulty to extract the reflected seismic signals. This letter focuses on suppressing the desert random noise based on a convolutional neural network (CNN) and proposes a branch construction-based denoising network (BCDNet). The BCDNet contains a denoising main network and a branched network added to the downsampled layer of the main network. With the branched network, the global context feature of the seismic data is obtained early in the network to guide the denoising task of the subsequent main network, which allows a flexible denoising for the desert random noise. Moreover, the downsampled layer is able to enlarge the receptive field of the network without increasing the network depth, thus leading to the better retention of the structural features in the seismic records. The extensive experiments and the field desert data application confirm that our BCDNet not only has a significant denoising capacity to desert seismic data but also is competitive in training time and memory cost.

Desert seismic data have the characteristics of low signal-to-noise ratio (SNR) and low-frequency, which pose a major challenge to noise attenuation. In this letter, we propose a denoising method for desert seismic data that combines the Gaussian conditional random field (GCRF) and the sparsity measurement. The sparsity measurement method is designed to replace the noise sampling method in the posterior frame. To calculate the block sparsity, first the seismic data blocks are divided into three groups: high sparsity blocks, medium sparsity blocks, and low sparsity blocks. Then different denoising parameters are determined according to the sparsity of seismic signal and the nonsparsity of desert low-frequency noise. Consequently, this targeted parameter setting achieves a more thorough suppression of noise and less attenuation of seismic signals. Both the synthetic and real data experiments prove the effectiveness of the method in this letter.

Distributed optical fiber acoustic sensing (DAS) is a new and rapid-developing detection technology in seismic exploration. Unfortunately, due to the weak energy of scattered optical signals and the inferior coupling between DAS cable and receiving interface, the seismic data received by DAS are often characterized by low signal-to-noise ratio (SNR); this low SNR is likely to affect some subsequent analysis, such as inversion, imaging, and interpretation. In addition, the noise caused by the inferior coupling is a new kind of noise not presented on conventional seismic data. To enhance the SNR of DAS seismic data and suppress the DAS noise effectively, we propose a convolutional adversarial denoising network (CADN) based on the basic strategy of generative adversarial network (GAN) and the usage of a denoiser to replace the original generator in GAN. In CADN, the performance of denoiser is significantly strengthened via its own mean square error (MSE) loss and the adversarial loss between it and the discriminator. To balance the two losses and thus ensure the optimization of denoiser, we construct a novel loss function, where the optimal ratio of MSE and adversarial losses is determined by quantifying the denoising performance. Both real and synthetic examples are included to testify the denoising performance of CADN. Experimental results have demonstrated that CADN can suppress most of the DAS noise and enhance the SNR of DAS seismic data; also, it can recover the effective signals completely, even the extremely weak effective signals reflected by deep layers.

Seismic exploration is a kind of exploration method for oil and gas resources. However, the disturbance of numerous random noise will decrease the quality and signal-to-noise ratio (SNR) of real seismic records, which brings difficulties to the following works of processing and interpretation. The seismic records of desert region pose a particular problem because of the strong energy noise and the spectrum overlapping between effective signals and random noise. Recent research works demonstrate that a convolutional neural network (CNN) can increase the SNR of seismic records. The optimization of denoising methods based on CNN is principally driven by the loss functions that largely focus on minimizing the mean-squared reconstruction error between denoising records and theoretical pure records. The denoising results estimated by the CNN model are often lacking the perfection of the signal structure. Therefore, when processing seismic records with low SNR, the denoising results often have a lack of effective signal in some traces, which leads to the poor continuity of events. In order to solve this problem, we adopt the strategy of generative adversarial network (GAN) to construct a GAN for denoising. It is divided into two parts: the generator (the denoising network based on CNN) is used to remove noise, while the discriminator is used to guide the generator to restore the structure information of effective signals. The generator and discriminator enhance the performance of each other through adversarial training, and the generator after adversarial training can greatly recover events and suppress random noise in synthetic and real desert seismic data.

At present, most of the seismic data denoising methods based on deep learning attempt to establish a synthetic seismic data set as the network training set to train network parameters. However, the synthetic data set cannot completely reflect the structural characteristics of the field seismic data, resulting in some false seismic reflections in field denoised results. For this reason, this article proposes an attribute-based denoising algorithm for seismic data called attribute-based double constraint denoising network (Att-DCDN). This method applies encoder-decoder and attribute classifier to constitute the generative adversarial network (GAN) and attenuates seismic noise by controlling with/without target attributes (noise attribute and signal attribute). Compared with the noise-free field seismic data, attribute vectors of the field data are easier to obtain. Therefore, our training set includes not only the synthetic seismic data but also the field seismic data, so as to reduce accuracy requirement of the synthetic noise-free data. In addition, we propose a double-constraint training way to reduce the losses of effective reflections during the denoising process. Specifically, we consider both noise attenuation and signal retention, i.e., reconstruction loss and residual loss are introduced to constrain recovery of effective reflections, and attribute classification loss and adversarial loss are applied to constrain the attenuation of seismic noise. Both the experimental results of synthetic and field seismic records show that our algorithm can effectively suppress the seismic noise and recover the effective reflections almost completely, even the weak signal areas that are seriously polluted by the seismic noise.

Attenuating the random noise and improving the signal-to-noise ratio (SNR) for the seismic data are of great significance in industrial exploration. In recent years, fractal conservation law (FCL) has been proposed and applied to seismic random noise suppression successfully. However, in conventional FCL, the filtering parameter selection strategy is relatively simple and a fixed parameter set is always used for the whole seismic record. In addition, it is very difficult to make an excellent tradeoff in random noise attenuation and signal preservation only by fixed parameters especially under the low-SNR conditions. Thus, accurately recognizing the effective signals and adaptively choosing appropriate filtering parameters is a feasible approach to improve the performance of the conventional FCL. In this article, an adaptive FCL methodology is proposed by combining the seismic noise analyzing theory and stationarity testing techniques. It is known that the random noise and reflection signals have different properties in stationarity and thus, the signal and noise segments can be divided by stationarity testing. As a consequence, different filtering parameters can be adopted for signal and noise segments to achieve the noise suppression and signal preservation simultaneously. Synthetic and field data experiments demonstrate that the proposed method can remove the random noise from seismic record and effectively preserve the reflection events.

In seismic exploration, random noise is an obstacle to the extraction of the effective signals, so the investigation aimed at random noise is the basis of signal processing. It is of great significance to analyze the noise properties and establish accurate noise models. Since the complex changes of the actual medium seriously affect propagation characteristics, it is necessary to establish a noise model in a more realistic medium. In this letter, we suppose a weakly heterogeneous medium whose properties vary with the position. And the link between the Lam constants of the medium and noise properties is established. Therefore, a wave equation is deduced in that medium to describe the propagation law of desert seismic exploration random noise. Based on the Greens function, the random noise field is obtained by superimposing all wave fields excited by each pointlike source. Afterward, quantitative comparisons between the actual random noise and the proposed random noise model are given. The results manifest that there are significant similarities in mathematical characteristics between them. Moreover, compared with the noise model in the homogeneous medium, the proposed noise model is more reliable. In order to prove the application value of the random noise model, it is first applied to construct a complete training set for denoising convolutional neural networks, which is valuable for attenuating the desert seismic exploration random noise. This is an effective way to extend noise data. Consequently, this feasible application will strongly promote the application of neural networks in seismic exploration.

Noise suppression is a crucial step before seismic data analysis. The noise in desert areas has the characteristics of nonstationary, non-Gaussian, and low-frequency, which makes some traditional methods cannot suppress the noise well. The weighted nuclear norm minimization (WNNM), one of the most effective methods to suppress noise in all low-rank matrix approximation methods, assigns different weights to different singular values. The good denoising performance of the WNNM is based on the accuracy of block matching, and the theoretical basis of block matching is the nonlocal self-similarity of clean signals. However, the noise will destroy the nonlocal self-similarity and greatly affect the accuracy of block matching. In this article, to reduce the influence of noise on block matching, we use a bandpass filter to process each noisy block before block-matching and use the similarity between the filtered blocks to represent the similarity between the original noisy blocks, then stack the most similar noisy blocks to construct a matrix for further denoising. Experimental results demonstrate the efficiency of the proposed method for low-frequency noise suppression.

High-quality seismic exploration data are the basis of geological exploration. However, due to the increasingly complex environment in the exploration area, the signal-to-noise ratio (SNR) of seismic data is getting lower and lower. Eliminating noise is the most direct mean to improve the SNR and quality of seismic data. The Tarim Basin with a desert surface in China is rich in energy, but due to the variability of surface conditions, the desert noise has nonstationary, nonlinear, spatial directivity, low frequency, and other characteristics, which make noise attenuation very difficult. Aiming at this problem, we develop an extension of complex diffusion filter, namely approximate-message-passing-based complex diffusion, which is used to eliminate noise in desert seismic exploration data and enhance effective signals. Compared with the traditional complex diffusion, this letter adds a noise estimate in its diffusion processing, which improves the algorithm's ability to eliminate desert noise. The experimental results of synthetic and field seismic data show that the proposed method is more effective than other methods. Not only it can remove the noise and surface wave in the desert seismic record but also can preserve the effective signal. Therefore, we believe that the proposed method can provide a new idea for desert seismic signal processing.

In desert seismic records, random noise with complex characteristics such as nonstationary, non-Gaussian, nonlinear, and low-frequency will contaminate effective signals, which will greatly reduce the continuity and resolution of the seismic events. In order to achieve the requirements of high signal-to-noise ratio (SNR), high resolution, and high fidelity of seismic records after denoising, and to obtain high quality seismic exploration data, we present a method for suppressing low-frequency noise of desert seismic data, which combines variational mode decomposition (VMD) with low-rank matrix approximation algorithm. This method can further avoid the effect of spectrum aliasing on the denoising results because of using VMD. At first, the proposed method decomposes seismic signals into different modes by VMD and then arranges all modes into a signal matrix. An algorithm named OptShrink is used to extract the low-rank noise components, and great denoising effect is achieved by making a difference between the low-rank noise components and the original seismic record. The method is applied to synthetic desert seismic data and real desert seismic data. The experimental results show that the denoising effect of this method is better than that of previous methods in desert low-frequency noise. The effective signal remains intact, the resolution and continuity of the seismic events are improved obviously. The suppression of surface wave is also very thorough.

The convolutional neural network (CNN) has achieved excellent performance in many fields, which has attracted much attention. CNN is a kind of feedforward neural network with convolution computation and depth structure. In this letter, aiming at the intense interference of seismic exploration noise in the desert of China, a desert seismic noise reduction system based on deep residual encoder-decoder network is proposed. In order to extract the characteristics and variation law of desert seismic noise, a noise set containing a large number of desert seismic noise is utilized for training the network so that the network forms the end-to-end mapping between the noisy records and the noise. Consequently, the effective signals are obtained by subtracting noise from the noisy records so as to achieve a satisfactory denoising performance. Compared with the traditional random noise suppression methods, the advantages of the proposed method are fully demonstrated in the processing of the synthetic records and the field records. Especially when the signal-to-noise ratio (SNR) is very low, this proposed method can still have a very good denoising effect.

The fractal conservation law (FCL) is a partial-differential-equation-based filtering approach. Analysis of the frequency response of the FCL indicates that it can eliminate high frequencies and preserve or amplify low/medium frequencies. Generally, the shape of the frequency response is fixed. Thus, the FCL cannot track the signal beyond the threshold, which corresponds to the cutoff frequency. Besides, the FCL recovers seismic events only along the time direction, thereby ignoring the coherence between neighboring traces. To resolve these shortcomings, this letter presents a novel spatiotemporal adaptive FCL method. We use a group of frequency responses of the FCL determined by different parameters to construct a convex hull of the filtering results. Then, we introduce an objective function based on the penalized least squares criterion with respect to FCL estimation on this convex hull and take the directional derivative as the penalty term. Thus, the correlations between the adjacent channels are taken into account in the algorithm. Therefore, the 2-D adaptive FCL is equivalent to a convex optimization problem with box constraints, which can be solved using the projected gradient descent algorithm. The application of gradient descent consists of taking the derivative of an objective function, which can be implemented quickly by means of the discrete cosine transform (DCT). The experimental results illustrate that our proposed algorithm has a higher output signal-to-noise ratio (SNR) than the 1-D adaptive FCL on some synthetic records and field seismic data.

Lots of low-frequency noise including random noise and surface waves seriously reduces the quality of desert seismic data. However, the suppression for desert low-frequency noise faces three main problems: nonstationary and non-Gaussian of random noise; strong energy of low-frequency noise; a more serious frequency-band overlap between effective signals and low-frequency noise. Robust principal component analysis (RPCA) is a classical low-rank matrix (LM) recovery method which is very suitable for processing nonlinear noise. It can decompose noisy data to the optimal LM and sparse matrix (SM), which include most effective signals and noise, respectively. Therefore, the RPCA is introduced to suppress desert low-frequency noise. However, due to the low signal-to-noise ratio (SNR) and serious frequency-band overlap, much low-frequency noise still remains in the LM of desert seismic data after the decomposition of RPCA. Meanwhile, some nonnegligible effective signals are decomposed into the SM of desert seismic data. To solve this problem, the convolutional neural network (CNN) is introduced to extract effective signals from SM and LM. By constructing suitable training sets to guide the CNN's training, the CNN denoising models after training are used to predict the effective signals from these two matrices, respectively. In this article, to approach real desert seismic data, we use a variety of seismic wavelets to simulate different types of seismic events, and then use these synthetic seismic events and real desert low-frequency noise to construct training set. In experiments, our method can raise the SNR of synthetic noisy data from -8.69 to 9.63 dB.

In seismic exploration, effective seismic noise attenuation along with seismic signal preservation is a key problem for seismic signal processing. The seismic data acquired from complex environments usually have a low signal-to-noise ratio (SNR) and nonstationary random noise that makes it difficult to accurately restore seismic signals. For enhancing seismic signals and filtering nonstationary random noise, we propose a structure-adaptive nonlinear complex diffusion method (ANCD) based on the regularized complex shock diffusion (CSD) by exploiting the structure-adaptive diffusion coefficients. The proposed complex diffusion method makes use of the imaginary value which is generated by a complex diffusion process as a directional structure indicator to guide the diffusion coefficients, by cooperating with spatially variant structure factors associated with the eigenvalues and eigenvectors of the structure tensor. In this way, the structural-adaptive diffusion term of ANCD allows the diffusion process along seismic structures, and the resulting imaginary part in turn enables the shock term to enhance the seismic signals with steep dips and rapidly varying slopes. The proposed method is tested on the synthetic seismic data and field seismic data acquired from the forest belt and desert area. The results show that the ANCD achieves a superior tradeoff between suppressing complicated random noise and preserving the seismic structures compared with the state-of-the-art seismic denoising methods.

Existing denoising algorithms often need to meet some premise assumptions and applicable conditions, such as the signal-to-noise ratio (SNR) cannot be too low, and the noise needs to obey a specific distribution (such as Gaussian distribution) and to satisfy some properties (such as stationarity). For the desert noise that shares the same frequency band with the effective signal and has complex characteristics (nonlinear, nonstationary, and non-Gaussian), it is difficult to find a universally applicable method. In response to this problem, a multiscale geometric analysis (MGA) convolutional neural network (CNN) is proposed in this article. One of the most important features of the CNN is that it can extract data-rich intrinsic information from the training set without relying on a priori assumption. By introducing the CNN into the MGA, a new kind of denoising method can be created, which can achieve good results even under a low SNR. This article takes the non-subsampled contourlet transform as an example to create a denoising network named NC-CNN for high-efficiency and intelligent denoising of desert seismic data. The processing results of synthetic seismic records and field seismic records prove that NC-CNN can effectively suppress the low-frequency noise (random noise and surface wave), and the effective signal almost has no energy loss. In addition, the reconstruction ability of the missing signals is also an advantage of this method.

High-quality seismic data are the basis for stratigraphic imaging and interpretation, but the existence of random noise can greatly affect the quality of seismic data. At present, most understanding and processing of random noise still stay at the level of Gaussian white noise. With the reduction of resource, the acquired seismic data have lower signal-to-noise ratio and more complex noise natures. In particular, the random noise in the desert area has the characteristics of low frequency, non-Gaussian, nonstationary, high energy, and serious aliasing between effective signal and random noise in the frequency domain, which has brought great difficulties to the recovery of seismic events by conventional denoising methods. To solve this problem, an improved feed-forward denoising convolution neural network (DnCNN) is proposed to suppress random noise in desert seismic data. DnCNN has the characteristics of automatic feature extraction and blind denoising. According to the characteristics of desert noise, we modify the original DnCNN from the aspects of patch size, convolution kernel size, network depth, and training set to make it suitable for low-frequency and non-Gaussian desert noise suppression. Both simulation and practical experiments prove that the improved DnCNN has obvious advantages in terms of desert noise and surface wave suppression as well as effective signal amplitude preservation. In addition, the improved DnCNN, in contrast to existing methods, has considerable potential to benefit from large data sets. Therefore, we believe that it can open a new direction in the area of seismic data processing.

The expected patch log likelihood (EPLL) is a patch-prior based denoising method which ensures denoising performance in ensemble approximation by local patch denoising. Basing on that, we propose a classification based EPLL method to attenuate seismic random noise, of which the level varies spatiotemporally. In EPLL method, the Gaussian mixture model (GMM) learned from samples is taken as a prior to statistically model patches, then the seismic signal is reconstructed by weighted averaging the noisy image and summation of denoised patches. Since the accuracy of the local statistic modeling and global signal reconstruction is related to the variance of the noise of the patches that have various noise variance in seismic image, we classify the patches into several groups in order to minimize the within-class variance. Therefore, appropriate regularization parameter and most likely prior are assigned to each patch according to the noise variance of the patch in EPLL. Experimental results of synthetic and field seismic data show that the classification based EPLL achieves a desired performance in seismic events preservation and nonstationary random noise attenuation.

Time picking is of great concern in the processing of microseismic data. However, the traditional method based on time/frequency domain cannot pick the first arrival time accurately in low signal-to-noise ratio. Besides, the traditional time picking methods which based on clustering are sensitive to selecting the initial clustering centers and easy to converge to local optimal value. To solve the above problems, we propose a time picking method for microseismic data based on locally linear embedding (LLE) and improved particle swarm optimization (PSO) clustering algorithm. First, the LLE algorithm can obtain the inherent characteristics and the rules hidden in high-dimensional data by calculating Euclidean distances and reconstruction weights between microseismic data points. The input is represented in a low-dimensional form. Then, the improved PSO clustering algorithm is used to select the optimal clustering centers from low-dimensional data through global search method. After that, the low-dimensional data can be classified into noise cluster and signal cluster by the K-means algorithm. Finally, the initial time of the signal cluster can be considered as the first arrival time of microseismic data. The experimental results show that accuracy of the proposed method is higher than that of the improved PSO clustering algorithm, Akaike information criterion method, and short- and long-time window ratio method (short-time window averaging/long-time window averaging).

P-wave time picking is of great significance in microseismic data processing. However, traditional time picking methods do not consider the difference of low-dimensional manifold features between signal and noise which can be extracted more effectively in low signal to noise ratio scenarios. In this letter, we develop a new method named spectral multimanifold clustering for picking P-wave arrivals. It can extract the low-dimensional manifold features from a suitable affinity matrix. In this approach, the manifold features of data are concentrated by residual statics estimation and a suitable affinity matrix is constructed using structural similarity and local similarity. Then, by using unnormalized spectral clustering, the low-dimensional manifold features extracted from the affinity matrix can be classified into noise cluster and signal cluster. Finally, the initial time of the signal cluster is considered to be the first arrival time in microseismic data. We design a series of experiments using both synthetic and field microseismic data. Our proposed method demonstrates higher accuracy, better stability, and noise immunity than either the short and long time average method or the akaike information criterion method.

In seismic exploration, random noise suppression is one of the key problems in seismic data processing. For random noise attenuation, the most important thing is the understanding of seismic random noise generation and propagation. Seismic random noise is considered as temporal and spatial random processes, and it can be analyzed only qualitatively for now, due to its high variability. In this paper, we classify seismic random noise sources by their generation factors and simulate the random noise of the desert in West China. According to Green's function, it can be assumed that seismic random noise sources are point-like sources that are distributed around geophones. A seismic random noise record is taken as the superimposed wave field exited by all the independent sources in a homogeneous isotropy half-infinite surface. Based on the wind vibration theory and preliminary study about ambient vibrations, the noise source functions are determined. We obtain the waveforms of different kinds of noise by solving the inhomogeneous wave equations and analyze the characteristics qualitatively and quantitatively. The seismic synthetic record with a 1.6-s time and 250-m distances is obtained, and the characteristics are compared between the simulated and the real noise record in time domain and space domain, respectively. The comparative results show the same characteristics of the simulated noise and the real noise, which demonstrates the feasibility of the proposed method. According to the noise modeling, it is known that the near-field cultural noise is the main component of the random noise in the desert, on the basis of which complex diffusion filtering is selected. The filtered results by complex diffusion filtering is compared with the results of time-frequency peak filtering, which is a popular filtering method of seismic random noise suppression in recent years. The comparative results show that complex diffusion filtering is more suitable for the noise of the desert in the Tarim Basin. This result proves that seismic random noise modeling can provide the guidance for noise attenuation. It lays a foundation for researching the propagation characteristics and better attenuation of seismic random noise in the future.

Noise contamination is a significant issue in microseismic data processing due to the low magnitude of high-frequency downhole microseismic signals induced during fluid injection. In this letter, a noncoherent noise attenuation technique based on cycle spinning shearlet transform (CSST) is presented. The CSST algorithm is implemented in three steps. In the first step, we forcibly shift signals so that their features change positions and orientations and then transform the noisy data into shearlet domain to obtain coefficients of different scales and directions. In the second stage, we apply hard thresholding to the resulting coefficients of individual component. Finally, we transform them back into the original domain and averagely superimpose the filtering results to preserve the amplitudes of the signals. The resulting methodology is tested on the synthetic and field datasets that were recorded with a vertical array of receivers. The experimental results show that the proposed CSST algorithm has better performance than the conventional threshold-based shearlet transform denoising method in terms of both high-frequency signal preservation and noise attenuation.

Time picking is an essential step in microseismic data processing, as the hypocenter location requires the arrival times of P- and/or S-waves. However, it is difficult to obtain arrival times accurately using traditional methods when the signal-to-noise ratio (SNR) of data is low. In this letter, we propose a new time picking method based on the fuzzy C-means clustering (FCM) algorithm, which can divide microseismic data into two clusters according to the different levels of similarity between the signals and noise. Using the FCM, we can obtain a membership degree matrix that represents the similarity of data. Data points whose values of the membership degree matrix are high show a high level of similarity and we assign these into the signal cluster. We regard the initial time of the signal cluster as the arrival time of data. To verify the reliability of the method, we conduct a large number of tests and give receiver operating characteristic curves with different SNR of signals. Our method is tested on both synthetic and real microseismic signals. Furthermore, we compare the FCM method with the short and long time average algorithm and the Akaike information criterion. The results indicate that our method can pick arrival times precisely even when the SNR of data is as low as -8 dB and the accuracy rate is superior to the other two methods.

Recently, the time-frequency peak filtering (TFPF) has been frequently applied to seismic random noise attenuation. Conventionally, TFPF recovers seismic events in association with a fixed window length along the time direction. Thus, the spatial information of the events is ignored. Moreover, TFPF is approximately equivalent to a time-invariant low-pass filter, which cannot adapt quickly enough to track the rapidly changing signal. To solve these problems, we propose a spatiotemporal adaptive TFPF (ST-ATFPF) algorithm. In this approach, we recover the events by the ATFPF, which is based on convex sets and Viterbi algorithm in intercept time-slowness domain. The high-resolution Radon transform concentrates the energy of the events effectively, and the correlations between wavelets, which form the events in a seismic record, are exploited by ST-ATFPF, consequently. Additionally, ST-ATFPF can track the rapidly changing signal. Numerical results have demonstrated the validity of our algorithm with higher output SNR and less signal information loss than the traditional TFPF, Radon TFPF, and ATFPF.

Seismic signals are nonlinear, and the seismic state-space model can be described as a nonlinear system. The particle filter (PF) method, as an effective method for estimating the state of a nonlinear system, can be applied to deal with seismic random noise attenuation. However, PF suffers from sample impoverishment caused by resampling, which results in serious loss of valid seismic information and leads to inaccurate representation of the reflected signal. To address the impoverishment issue and to further improve the particle quality, we propose a novel method to suppress seismic random noise-the adaptive fission particle filter (AFPF). In AFPF, all the particles undergo a fission process and produce “offspring” particles to maintain particle diversity. To implement the adaptation and to monitor the degree of fission, we apply a fission factor, which takes into account weights that indicate the quality of the particles. This leads to significant improvements in the particle quality, i.e., the proportion of highly weighted particles is increased. The effective seismic information provided by the resulting particles reproduces the true signal more reliably, reducing the bias of PF. In addition, we establish a dynamic state-space model suitable for seismic signals. Experimental results on synthetic records and field data illustrate the superior performance of AFPF in noise attenuation and reflected signal preservation compared with the PF.

Time-frequency peak filtering (TFPF) is an effective seismic random noise attenuation method at low signal-to-noise ratio (SNR). However, the conventional TFPF is biased for seismic signals with high frequency. We propose a spatial-trace TFPF (ST-TFPF) algorithm for reducing random noise in seismic data and simultaneously the bias of TFPF. The proposed method takes into consideration the lateral coherence between the neighboring traces as constraint of TFPF. To reduce bias, this algorithm takes TFPF along seismic events. The first stage of the proposed method preliminarily identifies the position of seismic reflection events using matching pursuit. The second stage consists of analyzing time delay of neighboring traces to construct spatial traces along seismic events. The last stage of algorithm consists of encoding seismic data along the constructed spatial traces and detecting the pseudo-Wigner-Ville distribution peaks of the encoded signals to reduce random noise. We assess our method on the synthetic and field data. The results illustrate that the ST-TFPF extends the signal preserving ability of TFPF in a wider range of window length at low SNR. Furthermore, comparison with conventional TFPF and wavelet denoising method shows that our method outperforms the two methods in random noise attenuation and seismic signal enhancement.

In this letter, we have applied a new filtering method for the simultaneous noise reduction and enhancement of seismic signals using a fractal conservation law, which is simply a partial differential equation (PDE) modified by a nonlocal fractional antidiffusive term of lower order. By using an integral formula, which is based on Taylor-Poisson's formula and Fubini's theorem for an antidiffusive term, and then taking the fast Fourier transform of the PDE, the filter in the frequency domain can be derived. The study showed that this filter eliminates the high frequencies, amplifies the medium frequencies, and preserves the low frequencies. Thus, some features of the signal, such as relative maxima or minima, can be preserved or even amplified. Usually, these features are flattened by other denoising methods. The properties of this novel method are tested on both synthetic seismic data and real common shot point seismic records. Additionally, we compared this method with time-frequency peak filtering (TFPF), which has a good performance under low signal-to-noise ratio. The experimental results illustrate the superior performance of our method versus TFPF in the recovery of seismic events by removing random noise and enhancing valid signal.

The time-frequency peak filtering (TFPF) uses the instantaneous frequency estimation technique based on the Wigner-Ville distribution (WVD) to recover signal corrupted by random noise. TFPF is equivalent to a time-invariant low-pass filter whose impulse response is determined by the window function used in windowed WVD. Thus, TFPF cannot track the quick changes of signal, which means that the frequency components of signals higher than some cutoff frequency are attenuated. To solve this problem, we present a novel adaptive algorithm for TFPF. In this algorithm, we first construct the convex set of TFPF estimations at each sample index. Subsequently, we search the optimal estimations from the sequential convex sets to minimize a quadratic functional globally. This leads to a box-constrained convex optimization problem, which can be solved by the Viterbi algorithm. Applications to random seismic noise attenuation have demonstrated the validity of our algorithm with higher output signal-to-noise ratio and less signal information loss than in the traditional TFPF.

Time-frequency peak filtering (TFPF) is a method commonly used for seismic random noise attenuation due to its excellent practical application. However, a conventional TFPF often produces significant deviations at the peak or valley of the signal where the linearity is poor. Here, we propose a novel hyperbolic-trace TFPF (HT-TFPF) approach to reduce these deviations and recover the effective signal more completely. In this method, a hyperbolic trace with a certain curvature is ascertained by fitting the reflection event to scan the seismic record. Data sequences are extracted from the seismic record along these hyperbolic traces, and their linearity is greatly improved. Then, they are taken as a new input for TFPF. HT-TFPF can preserve the signal amplitude while achieving an excellent performance of noise suppression with a long unbias window length. Tests on both synthetic records and common shot point data indicate that the HT-TFPF method can attenuate more random noise and recover events more clearly and continuously than the conventional TFPF.

The time–frequency peak filtering (TFPF) algorithm is an effective method for seismic random noise attenuation. The conventional TFPF filters seismic data only along the channel direction, ignoring the spatial characteristics of the reflection events, which results in the loss of directional information. In order to improve the filtering performance of TFPF, we adopt a Radon transform to implement spatiotemporal 2-D TFPF, which is doing TFPF in the Radon domain. Since this method takes the spatial correlation of the reflection events into account, it could extract the reflection events better than the conventional TFPF. As the conventional Radon transform may produce a smearing phenomenon, we apply an improved least squares high-resolution Radon transform to assist TFPF in this letter. Thus, the events can be highly focused to energy points in different positions of the Radon domain. Then we identify the signal parts and process them by TFPF with short window length (WL). The other parts are considered as noise, and we process them by TFPF with long WL. By virtue of this new method, we can preserve the valid signal better and suppress the random noise more effectively. Through experiments on the synthetic seismic records and the field seismic data, the new method possesses a superior performance in random noise attenuation and seismic event preservation compared with the conventional TFPF and Radon TFPF methods.

Time-frequency peak filtering (TFPF) is effective in suppressing random noise in seismic records. However, the signal may be attenuated at the same time, especially for the high-frequency signal. In this letter, we propose a curvature-varying hyperbolic trace TFPF to reduce the error. We sample the seismic record along the time-distance curve of the event. For the event area, the sampled signal in each sampling trace is approximately linear (low frequency) due to the correlation of the signal along the time-distance curve, which reduces the bias of the seismic wave estimation brought by TFPF. However, the curvatures of seismic events are various, so adopting traces with a single curvature to sample the whole seismic record is not reasonable. As the events with different curvatures are located in different areas in Radon domain, the events with almost the same curvature can be separated out by an inverse Radon transform of only part of the Radon data. The optimal hyperbolic sampling traces are chosen for each separated subrecord, and we filter the data along the traces by TFPF. The denoised signal is reconstructed by summing all of the processed subrecords. Compared with TFPF, our method gets a good performance in both seismic reflection event preservation and noise attenuation.

Time-frequency peak filtering (TFPF) has been widely applied to suppress the random noise in seismic data in recent years. Conventional TFPF adopts a pseudo-Wigner-Ville distribution to ensure the approximate linearity of the signal. However, a short window length (WL) cannot effectively attenuate the random noise and a long WL can hardly recover the subtle structures of seismic events. In this letter, we discuss the different correlation integral values of signal and noise in the radial-trace domain for identifying the noise and signal segments. Then, a longer WL according to the noise intensity is used to remove the random noise and a shorter WL according to the frequency characteristics of the signal is used to preserve the details of the signal. The experiment results on both the synthetic model and the field seismic data show that this method can effectively remove noise from seismic record and maintain the amplitude of the valid signal.

Time-frequency peak filtering (TFPF) with fixed window length effectively attenuates random noise in seismic data, but performs well only for slow-varying seismic signals. To surmount the limitation, we propose the adaptive time-frequency peak filtering with the signal-dependent window length related to the belongings of seismic data to the signal, the signal nonlinearity and the local noise variance. The fuzzy c-means clustering algorithm is used to obtain the belongings in feature space, which incorporates spatial information including local similarity feature, local mean and local median in immediate neighborhood. As a result, the window length is set different for signal and noise and relatively small for the signal with high nonlinearity. We test the proposed method on both synthetic and field seismic data, and our experimental results illustrate that the adaptive method achieves better performance over the conventional TFPF both in random noise attenuation and the effective components preservation.

Time-frequency peak filtering (TFPF) is a classical filtering method in time-frequency domain. It applies Wigner-Ville distribution to estimate the instantaneous frequency of an analytical signal. There is a pair of contradiction in this method, i.e., selecting a short window length may lead to good preservation for signal amplitude but bad random noise reduction whereas selecting a long window length may lead to serious attenuation for signal amplitude but effective random noise reduction. In order to make a good tradeoff between valid signal amplitude preservation and random noise reduction, we adopt empirical mode decomposition (EMD) to improve the TFPF results. The new idea is to utilize the decomposition characteristic of EMD which decomposes a signal to several modes from high to low frequency and to take advantage of the time-frequency filtering characteristic of TFPF which can recognize the valid signal component in the time-frequency plane in order to achieve effective random noise reduction together with good amplitude preservation. Through some experiments on synthetic seismic models and field seismic records, we show the better performance of the new method compared with the conventional TFPF.

Time-frequency peak filtering (TFPF) has been applied to seismic random noise attenuation in recent years. In the conventional TFPF, a fixed window length (WL) is used for all frequencies signals. Different frequencies signals have different optimal WLs. A fixed WL cannot effectively attenuate random noise for all frequencies signals. In this letter, we present a nonlinear parabolic-trace TFPF (PT-TFPF) to resolve this problem. In the novel approach, a new data matrix is extracted by resampling seismic record along some parabolic traces. It contains both temporal and spatial information of the seismic record and is taken as the new input of TFPF. In each data sequence, the linearity of the effective signals is improved and the degree of improvement is associated with the similarity of the filtering trace to the event. In addition, the dominant frequencies of the effective signals are concentrated to be similar. Thus, a fixed WL can effectively attenuate the random noise with less distortion. The optimal filtering traces are selected based upon the Canny edge detection algorithm. Finally, the effectiveness of the proposed approach is tested on the synthetic record and field data. The experimental results show that the proposed PT-TFPF has better performance than the conventional TFPF.

In this letter, we research a spatiotemporal-domain-based time-frequency peak filtering (TFPF) method in order to remove the large error (bias) of the conventional TFPF in intermediate-frequency seismic record discrimination. An intermediate-frequency seismic signal is one whose dominant frequency is about 40 Hz or higher. To find a balance between noise attenuation and reflected signal preservation, the radial-trace TPFT (RT-TFPF) takes both the unbiased condition and the adjacent seismic traces' correlation into consideration, and uses the RT transform to obtain a reduced-frequency input to decrease the TFPF error. Therefore, this method can discriminate some reflection events weakened by the conventional TFPF algorithm. First, we decrease the intermediate frequencies along RTs nearly aligned with the reflection event. Then, we obtain a less biased TFPF estimation with suitable window length τ. Finally, we recover the original intermediate frequency with the inverse RT transform. With the RT-TFPF, we can enhance reflection events without sacrificing frequency components while attenuating as much random noise as possible. Experiments on both synthetic model and field data demonstrate that the RT-TFPF performs well both in random noise attenuation and intermediate-frequency preservation, in addition to presenting advantages over the conventional TFPF.

We address the directional derivative trace transform (DDTT) for seismic wavefield separation. The goal is to separate the different seismic waves, which is a practical requirement for seismic exploration and geophysics. The DDTT is based on the trace transform, which is a generalization of the Radon transform (RT). It calculates the integral of a directional derivative along the trace line. The directional derivative is the pointwise rate of change of a function in a certain direction. Therefore, the DDTT better reflects the property of linear wavefields and other wavefields than the F-K filtering and RT methods. The DDTT domain consists of two parts: One part mostly represents linear wavefields such as surface waves, and the other part mostly represents the reflection signals. Based on this property, a parametric method is proposed for separating the ground roll better. In order to return data to the time-offset domain, we derive the inverse DDTT using the properties of the Fourier transform and the Hilbert transform. We show the potential of our method for the removal of ground roll on synthetic and real data examples.

Seismic noise attenuation to improve signal-to-noise ratio plays an important role in seismic data processing. In recent years, time-frequency peak filtering (TFPF) has been introduced and applied to seismic random noise attenuation successfully. However, in the conventional TFPF, the window length (WL) is fixed and used for all frequency components. As a consequence, serious loss of the effective components is unavoidable due to the inappropriate WL. The recently proposed radial-trace TFPF adapts radial-trace transform to reduce the dominant frequencies of the effective signals. Nevertheless, the radial traces with a fixed inclination angle have some limitations for bent reflection events. To resolve these shortcomings, this paper presents a novel variable-eccentricity hyperbolic-trace TFPF. In this novel method, the noisy record is first resampled along a family of spatial-temporal hyperbolic filtering traces of different bending degrees. In this way, the spatial correlation between the adjacent channels is taken into account, the linearity of the input signals is enhanced, and the estimation bias of the instantaneous frequency is reduced. Moreover, there is little difference between the reduced dominant frequencies. A fixed WL is suitable for all reduced dominant frequencies without distortion of the effective components. Finally, we evaluate the performance of our method on some synthetic records and field data. The experimental results illustrate that our proposed method attenuates random noise effectively and recovers the effective reflection events smoothly and more continuously compared with the other methods.

Time-frequency peak filtering (TFPF) is a new and effective tool for random-noise attenuation in the time-frequency domain. The conventional TFPF processes each channel of the seismic record independently with a fixed window length (WL). However, different frequency signals have different optimal WLs. Obviously, a fixed WL cannot effectively attenuate random noise for all frequency components at the same time. Depending on the geometry of the reflection, we can assume that the moveout of the reflected event is locally linear. With this in mind and taking the spatial correlation of the reflection events between adjacent channels in different layers into account, we propose a novel approach which is to do the TFPF along the local direction of the reflection event instead of along the channel. This method is called the local parallel radial-trace TFPF. It not only has the advantage of TFPF in denoising but also reduces the sensitivity of WL, making the filtering more flexible and effective. Both the synthetic model and seismic data have proved its better performance in noise attenuation and effective component preservation.

The time-frequency peak filtering (TFPF) is an effective method for seismic random noise reduction. To achieve a higher level of noise suppression in seismic records, we propose a novel approach in which we apply the TFPF method in Radon domain. This method, called spatiotemporal TFPF, can be applied with different types of Radon transforms (linear, parabolic, etc.) depending on the geometry of the reflection. The new method is similar to the principle of ridgelet, which is doing 1-D wavelet in linear Radon domain so that there is a parameter representing direction brought in the filtering process. Although the ridgelet has the wonderful ability to process reflection events with linearly changing characteristics, for curving events, it shows lack of effectiveness. With this in mind, and taking the superiority of TFPF into consideration, the new method as mentioned previously is proposed. Thus, it breaks the limitation of doing filtering in linear Radon domain to make the filtering more flexible and plays the advantage of TFPF in denoising. Using both synthetic and real seismic data, we show the better performance of the new method in random noise reduction and higher continuity and clarity of reflection events compared to the conventional TFPF.

A novel method based on nonnegative matrix factorization (NMF) spectral unmixing is proposed for land seismic additive random noise attenuation. In the method, the noisy seismic signal is first decomposed into a collection of intrinsic mode functions (IMFs) instead of being directly processed. These IMFs can be considered as a new set of observations. In the short-time Fourier transform (STFT) spectrum of each IMF, the degree of mixing from the effective signal and the random noise is considerably reduced. Then, a sparse NMF is used to unmix the STFT spectrum of each IMF. We get the subsignals out of the separated subspectrums by the inverse STFT. Finally, the desired signal is reconstructed from the subsignals by$K$-means clustering algorithm. Experimental results of both synthetic and real seismic records show that the proposed method can significantly suppress random noise and preserve the effective signal components. Comparisons with time–frequency peak filtering and$f{-}x$filtering further verify its better performance.

The time-frequency peak filtering (TFPF) is an effective tool in random-noise attenuation and has been applied to seismic record denoising in recent years. The window length (WL) of the time-frequency distribution (TFD) is the key to the conventional TFPF technology. A fixed WL is not optimal for both the low- and high-frequency components at the same time; an adaptive WL results in serious distortion of the reflected waveform. In this letter, we discuss a modified TFPF along the radial-trace direction and prove its advantage in TFD window selection. Experiments on both synthetic models and field data show that the radial-trace TFPF result is no longer much influenced by the WL as the conventional TFPF. Furthermore, it can provide better performance in both random-noise attenuation and reflected signal preservation with a fixed WL.

A main target of seismic data processing is to remove the surface waves and improve the quality of seismic records. Here, we propose a Co-Core Trace (CCT) transform filtering based on the Trace transform from image processing and apply it to seismic surface wave attenuation. The CCT transform is designed according to the distribution and propagation of the surface waves. In the CCT transform domain, the energies of surface waves are significantly enhanced and could be filtered out with a relative threshold, while the reflection events are saved due to the conspicuous disparity. Experiments on both synthetic model and field data demonstrate that the proposed algorithm performs well both in surface wave attenuation and reflected signal preservation, besides presenting advantages over some conventional methods.

The time-frequency peak filtering (TFPF) technology is applied for recovering seismic events without loss of valid information. By using frequency modulation signal encoding and taking peak of Wigner-Ville distribution (WVD) of encoded analytic signal, valid reflect signals constructing seismic events are estimated. To reduce the deterministic bias of TFPF resulted from nonlinearity of seismic reflect signal, the pseudo WVD (PWVD) TFPF is utilized. The reduced bias window length is derived by analyzing bias from experimental resulting. Testing of this method on synthetic seismic data and common shot point recordings indicates that TFPF technique significantly enhances signals from noisy seismic data and improves the continuity of seismic events by filtering out most of the additive noise. The resulting shows the clean recovery of seismic events in noise level down to a signal-to-noise ratio of-2.4dB.