Seismic Denoising Research Articles

Seismic Foundation Model (SFM): a next generation deep learning model in geophysics

While computer science has seen remarkable advancements in foundation models, they remain underexplored in geoscience. Addressing this gap, we introduce a workflow to develop geophysical foundation models, including data preparation, model pre-training, and adaption to downstream tasks. From 192 globally collected 3-D seismic volumes, we create a carefully curated dataset of 2,286,422 2-D seismic images. Fully using these unlabeled images, we employ the self-supervised learning to pre-train a Transformer-based Seismic Foundation Model (SFM) for producing all-purpose seismic features that work across various tasks and surveys. Through experiments on seismic facies classification, geobody identification, interpolation, denoising, and inversion, our pre-trained model demonstrates versatility, generalization, scalability, and superior performance over baseline models. In conclusion, we provide a foundation model and vast dataset to advance AI in geophysics, addressing challenges (poor generalization, lacking labels, and repetitive training for task-specified models) of applying AI in geophysics and paving the way for future innovations in geoscience.

Quadratic Unet for seismic random noise attenuation

In the field of seismic data processing, seismic denoising is essential to improve the quality of seismic data. Various deep learning methods have been proposed, showing promising performance for seismic denoising. However, most deep learning methods are based on lin ear neurons, resulting in limited expressive ability for complex seismic signals. To enhance denoising capability using non-linear neurons, we propose a supervised quadratic U-shaped network (QUnet) for seismic random noise attenuation. The quadratic neurons in QUnet are represented by a second-order polynomial of input data and weighted parameters. Nu merical synthetic seismic data experiments show that the proposed QUnet method achieves higher signal-to-noise ratio results and preserves the continuity of reflectors more effectively. We have also tested the effectiveness of QUnet on both prestack field data and post-stack seismic data. The detailed structures and weak signals of seismic data are better preserved by our proposed QUnet method.

Three-dimensional seismic denoising based on deep convolutional dictionary learning

Three-dimensional seismic denoising based on deep convolutional dictionary learning

Seismic Random Noise Attenuation Using DARE U-Net

Seismic data processing plays a pivotal role in extracting valuable subsurface information for various geophysical applications. However, seismic records often suffer from inherent random noise, which obscures meaningful geological features and reduces the reliability of interpretations. In recent years, deep learning methodologies have shown promising results in performing noise attenuation tasks on seismic data. In this research, we propose modifications to the standard U-Net structure by integrating dense and residual connections, which serve as the foundation of our approach named the dense and residual (DARE U-Net) network. Dense connections enhance the receptive field and ensure that information from different scales is considered during the denoising process. Our model implements local residual connections between layers within the encoder, which allows earlier layers to directly connect with deep layers. This promotes the flow of information, allowing the network to utilize filtered and unfiltered input. The combined network mechanisms preserve the spatial information loss during the contraction process so that the decoder can locate the features more accurately by retaining the high-resolution features, enabling precise location in seismic image denoising. We evaluate this adapted architecture by applying synthetic and real data sets and calculating the peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM). The effectiveness of this method is well noted.

An adaptive parameter-free seismic data denoising approach by combining general cross-validation thresholding and pixel connectivity in synchrosqueezed domain

High signal-to-noise ratio (SNR) seismic waveform data are conductive to various studies in seismology. Seismic denoising aims to enhance SNR by eliminating additive noise through signal processing while preserving important features of the seismic signal. Conventional parametric seismic denoising methods often require selecting appropriate parameters to achieve optimal results, which may be limiting when dealing with various types and scales of seismic data. Here, we develop an adaptive parameter-free denoising method by combining general cross-validation (GCV) thresholding and pixel connectivity in synchrosqueezed (SS) domain. In this denoising framework, the synchrosqueezed continuous wavelet transform (SS-CWT) is first applied to obtain a high-resolution time–frequency representation. Then, the GCV approach, which allows for choosing the (nearly) optimal threshold without relying on any prior knowledge about the noise level, is employed to attenuate most of the low-energy noise. After that, the relatively isolated high-energy residual noise remaining in the SS-CWT spectrum is removed using pixel connectivity thresholding. Finally, the inverse SS-CWT is applied to the thresholded spectrum to obtain the denoised seismic record. As the thresholds for GCV and pixel connectivity are derived from the spectrum characteristics of the data being analyzed, the proposed denoising approach is highly adaptive and parameter-free. We demonstrate the effectiveness and versatility of the proposed denoising framework using synthetic data and real seismic data from diverse monitoring scenarios, including land, ocean, and emerging distributed acoustic sensing (DAS). The results indicate that the method is a stable and efficient tool for seismic data denoising.Graphical

Dealiased seismic data interpolation by dynamic matching

Interpolation is a critical step in seismic data processing. Gaps in seismic traces can lead to severe spatial aliasing phenomena in the corresponding f- k spectra. The aliasing caused by regularly spaced gaps has similar f- k spectra as those of the actual data. Existing dealiasing interpolation algorithms generally assume that seismic events are linear and cannot handle nonstationary events. To address this shortcoming, we develop a novel dealiased seismic data interpolation approach using dynamic matching. First, we match two adjacent seismic traces using the local affine regional dynamic time-warping algorithm. Subsequently, we calculate the local slope between two seismic traces. Finally, we perform linear interpolation on the regularly missing seismic data using local slope information. Our approach is tested on synthetic and field seismic data sets. The interpolation results indicate that our approach has a better antialiasing ability and computational efficiency than the traditional Spitz and seislet-based approaches. In addition, this method can be applied to interpolate irregularly sampled seismic data and for simultaneous seismic data interpolation and denoising.

Cold Diffusion Model for Seismic Denoising

AbstractSeismic waves contain information about the earthquake source, the geologic structure they traverse, and many forms of noise. Separating the noise from the earthquake is a difficult task because optimal parameters for filtering noise typically vary with time and, if chosen inappropriately, may strongly alter the original seismic waveform. Diffusion models based on Deep Learning have demonstrated remarkable capabilities in restoring images and audio signals. However, those models assume a Gaussian distribution of noise, which is not the case for typical seismic noise. Motivated by the effectiveness of “cold” diffusion models in speech enhancement, medical anomaly detection, and image restoration, we present a cold variant for seismic data restoration. We describe the first Cold Diffusion Model for Seismic Denoising (CDiffSD), including key design aspects, model architecture, and noise handling. Using metrics to quantify the performance of CDiffSD models compared to previous works, we demonstrate that it provides a new standard in performance. CDiffSD significantly improved the Signal to Noise Ratio by about 18% compared to previous models. It also enhanced Cross‐correlation by 6%, showing a better match between denoised and original signals. Moreover, testing revealed a 50% increase in the recall of P‐wave picks for seismic picking. Our work show that CDiffSD outperforms existing benchmarks, further underscoring its effectiveness in seismic data denoising and analysis. Additionally, the versatility of this model suggests its potential applicability across a range of tasks and domains, such as GNSS, Lab Acoustic Emission, and Distributed Acoustic Sensing data, offering promising avenues for further utilization.

Unsupervised deep-learning framework for 5D seismic denoising and interpolation

We develop an unsupervised framework to reconstruct missing data from noisy and incomplete five-dimensional (5D) seismic data. Our method comprises two main components: a deep-learning network and the projection onto the convex sets (POCS) method. The model works iteratively, passing the data between the two components and splitting the data into a group of patches. The developed deep-learning model is inspired by the transformer architecture, wherein the extracted patches are flattened, and an embedded layer (fully connected layer) is used to transform the 1D flattened vector into the feature latent space. Afterward, an attention network is used to highlight the important information within these features, which improves the denoising performance of the deep-learning model. Furthermore, we use several skip connections between the fully connected layers to enhance the learning capability of the network. Next, the output of the POCS algorithm is considered the input of the deep-learning model for the following iteration. The developed model iteratively works in an unsupervised scheme wherein labeled data are not required. A performance comparison with benchmark methods using several synthetic and field examples shows that our method outperforms the traditional methods.

Application of 2D Variational Mode Decomposition Method in Seismic Signal Denoising

Seismic data are typical nonlinear and nonstationary data. In the acquisition and processing of seismic data, many factors interfere with it. Seismic data contain both effective waves and random noises, seriously affecting the quality of seismic data and not conducive to the goal of fine interpretation of subsequent seismic data. Therefore, studying new seismic data denoising methods is beneficial for improving the quality of seismic data and plays a very important role in subsequent seismic data interpretation. In this paper, the principle of variational mode decomposition (VMD) and 2D-VMD is introduced in detail, and the seismic profile with a simple signal and fault model is denoised. Compared to traditional empirical mode decomposition (EMD), the 2D-VMD method has the best seismic data denoising effect. The test results of the synthesised signal show that the 2D-VMD method has a signal-to-noise ratio of 47.14 dB after denoising, which is higher than the signal-to-noise ratio after EMD and VMD denoising, indicating that it has a better denoising effect. The VMD and 2D-VMD methods are applied to the denoising of actual seismic data. The application results show that the 2D-VMD method can effectively improve the quality of the seismic data, enhance the continuity and reliability of the seismic data, and is conducive to the fine interpretation of subsequent seismic data.

Seismic data denoising with two-step prediction strategy based on Neural Network

Seismic data denoising (SDD) plays an important role in obtaining high-quality data for subsequent seismic imaging and inversion. However, traditional SDD methods still present several disadvantages such as parameter selection difficulties, high computational costs, and a strong dependence on the experience of processing personnel. Deep learning (DL)-based SDD methods can overcome these issues to a certain extent, having the advantages of high computational efficiency and negligible dependency on the experience of processing personnel. However, existing DL-based SDD methods typically adopt a specific single-network architecture, which can be further improved in terms of training efficiency and denoising quality. In this paper, we propose a two-step prediction denoising method based on the combination of two identical or different network architectures for improving the accuracy and efficiency of DL-based SDD methods. Compared with existing SDD methods, the two-step prediction denoising method is more capable of extracting feature information at multiple scales because multiple network architectures are combined in a single denoising task, thus improving the training efficiency and denoising accuracy. In this study, we implemented the two-step prediction denoising method using an improved denoising convolutional neural network (DnCNN) and a nested U-shaped fully convolutional network (U-Net++). Several synthetic numerical examples based on three different types of noise were denoised, with the results indicating that the proposed method effectively improves the accuracy and efficiency of the DL-based SDD method. Finally, a test using field data was performed to demonstrate the real-world applicability of the novel two-step prediction denoising method.

Seismic signal denoising using Swin-Conv-UNet

In recent years, a notable surge has occurred in the adoption of deep neural networks for addressing the challenges of seismic signal denoising. However, many existing methodologies are constrained by simplistic noise assumptions and exhibit limited generalisation capabilities, particularly when confronted with field seismic signals. Consequently, the need for a robust denoising solution tailored to the complexities of field seismic signals remains unresolved. To address this gap and effectively enhance the signal-to-noise ratio (SNR), we proposed a novel denoising approach. Central to our methodology is the incorporation of a custom-designed network structure that leverages the unique characteristics of seismic signals. Specifically, we introduced the swin-link-conv block, which amalgamates the modelling capabilities of the swin transformer block with the adaptive properties of the residual connection layer. This innovative building block was seamlessly integrated into the UNet architecture, which is a widely acclaimed framework for seismic signal processing. The resulting network architecture was a christened seismic swin-conv UNet (SSC-UNet). Extensive experiments conducted on both synthetic and field seismic signals underscore the efficacy of the proposed network structure. The SSC-UNet methodology achieved state-of-the-art denoising performance, demonstrating superior accuracy in removing additive white Gaussian noise (AWGN). This success not only validates the generalisation capabilities of SSC-UNet but also underscores its viability as a robust solution for field seismic signal denoising applications.

A method for denoising active source seismic data via Fourier transform and spectrum reconstruction

Denoising is a critical step in signal processing. We develop a method for random noise reduction in active source seismic data using spectrum reconstruction. Two methods are developed for modifying the observed data’s amplitude spectrum: one substitutes it with the source wavelet’s amplitude spectrum, whereas the other involves multiplying the source wavelet’s amplitude spectrum with the observed data’s amplitude spectrum. By reconstructing the modified amplitude spectrum while preserving the observed data’s phase spectrum, noise suppression is achieved. Extensive testing with theoretical models, synthetic shot gathers, and field data indicate a notable improvement in the signal-to-noise ratio (S/N) compared with the traditional band-pass filtering method. This method proves particularly effective for enhancing the S/N in the context of active source wide-angle seismic data used in offshore structural studies, eliminating the need for data segmentation based on offset, and thereby improving processing efficiency. Our method relies solely on a single complete cycle of the source wavelet, making it a purely data-driven solution. It has broad applications in processing active source or controlled source data with consistent source wavelets, including but not limited to seismic exploration, acoustic detection, and signal denoising in various ground-penetrating radars used on Mars, the moon, and earth.

Sparse Regularization Based on Orthogonal Tensor Dictionary Learning for Inverse Problems

In seismic data processing, data recovery including reconstruction of the missing trace and removal of noise from the recorded data are the key steps in improving the signal-to-noise ratio (SNR). The reconstruction of seismic data and removal of noise becomes a sparse optimization problem that can be solved by using sparse regularization. Sparse regularization is a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed inverses feasible. It deals with ill-posedness by replacing an ill-posed inverse problem with a well-posed problem that has a solution close to the true solution. In the last 2 decades, interest has shifted from linear toward nonlinear regularization methods even for linear inverse problems. In inverse problems, regularizations serve as stabilizing the solution of ill-posed inverse problems and give a solution that adequately fits measurements without producing unjustifiably complex artifacts. In this paper, we present a novel sparse regularization based on a tensor-based dictionary method for inverse problems (seismic data interpolation and denoising). This regularization avoids the vectorization step for sparse representation of seismic data during the reconstruction process. The key step in sparsifying signals is the choice of sparsity-promoting dictionary learning. The learning-based approach can adaptively sparsify datasets but has high computational complexity and involves no prior-constraint pattern information for the dataset. Many existing dictionary learning methods would be computationally infeasible for the high dimensional seismic data processing. These methods also destroy the essential information as well as it reduces the discriminability and expressibility of the signal, since they deal with vectorization. In this paper, the orthogonal tensor dictionary learning that learns a dictionary from the input data by employing orthogonality and separability is proposed as sparse regularization for the inverse problems. The performance of the proposed method was validated in seismic data interpolation and denoising individually as well as simultaneously. Numerical examples of synthetic and real seismic datasets demonstrate the validity of the proposed method. The SNR of the recovered data confirms that the proposed method is the most effective method than K-singular value decomposition and orthogonal dictionary learning methods.

Explainable artificial intelligence‐driven mask design for self‐supervised seismic denoising

AbstractThe presence of coherent noise in seismic data leads to errors and uncertainties, and as such it is paramount to suppress noise as early and efficiently as possible. Self‐supervised denoising circumvents the common requirement of deep learning procedures of having noisy‐clean training pairs. However, self‐supervised coherent noise suppression methods require extensive knowledge of the noise statistics. We propose the use of explainable artificial intelligence approaches to ‘see inside the black box’ that is the denoising network and use the gained knowledge to replace the need for any prior knowledge of the noise itself. This is achieved in practice by leveraging bias‐free networks and the direct linear link between input and output provided by the associated Jacobian matrix; we show that a simple averaging of the Jacobian contributions over a number of randomly selected input pixels provides an indication of the most effective mask to suppress noise present in the data. The proposed method, therefore, becomes a fully automated denoising procedure requiring no clean training labels or prior knowledge. Realistic synthetic examples with noise signals of varying complexities, ranging from simple time‐correlated noise to complex pseudo‐rig noise propagating at the velocity of the ocean, are used to validate the proposed approach. Its automated nature is highlighted further by an application to two field data sets. Without any substantial pre‐processing or any knowledge of the acquisition environment, the automatically identified blind masks are shown to perform well in suppressing both trace‐wise noise in common shot gathers from the Volve marine data set and coloured noise in post‐stack seismic images from a land seismic survey.

Compressed sensing with log-sum heuristic recover for seismic denoising

The compressed sensing (CS) method, commonly utilized for restructuring sparse signals, has been extensively used to attenuate the random noise in seismic data. An important basis of CS-based methods is the sparsity of sparse coefficients. In this method, the sparse coefficient vector is acquired by minimizing the l1 norm as a substitute for the l0 norm. Many efforts have been made to minimize the lp norm (0 < p < 1) to obtain a more desirable sparse coefficient representation. Despite the improved performance that is achieved by minimizing the lp norm with 0 < p < 1, the related sparse coefficient vector is still suboptimal since the parameter p is greater than 0 rather than infinitely approaching 0 p→0+. Therefore, the CS method with the limit p→0+ is proposed to enhance the sparse performance and thus generate better denoised results in this paper. Our proposed method is referred to as the CS-LHR method because the solving process for minimizing p→0+ is the log-sum heuristic recovery (LHR). Furthermore, to improve the computational efficiency, we incorporate the majorization-minimization (MM) algorithm in this CS-LHR method. Experimental results of synthetic and real seismic records demonstrate the remarkable performance of CS-LHR in random noise suppression.

STUGAN: An Integrated Swin Transformer-Based Generative Adversarial Networks for Seismic Data Reconstruction and Denoising

STUGAN: An Integrated Swin Transformer-Based Generative Adversarial Networks for Seismic Data Reconstruction and Denoising

Dictionary Learning for Single-Channel Passive Seismic Denoising

Abstract Passive seismic denoising is mostly performed using a simple band-pass filter, which can be problematic when signal and noise share the same frequency band. More advanced passive seismic denoising methods take advantage of fixed-basis transforms, for example, the wavelet, to remove noise. Here, we present an open-source package for data-driven denoising based on adaptively learning sparse transform. Contrary to the fixed-basis transforms, the proposed method belongs to the adaptive-basis transforms. We learn the 1D features embedded in the passive seismic data from all the available waveform data sets without requiring spatial coherency in a data-driven way. Thus, the new method is flexible to apply in any passive seismic monitoring project because of its data-driven and single-channel nature when implemented. Considering the computationally expensive K-singular-value-decomposition (KSVD) in the traditional dictionary learning framework, we suggest applying a fast SVD-free dictionary learning method that can be readily applicable to process massive seismic data during passive seismic monitoring. The proposed method is applied to two synthetic data examples and three real passive seismic data sets to demonstrate its effectiveness in improving the signal-to-noise ratio, and its potential in applications like arrival picking. The open-source reproducible package can be found in the Data and Resources section.

Method for seismic signal denoising based on generalized S-transform and nonlinear complex diffusion

This paper aims to improve the problem of seismic signal enhancement and noise filtering by utilizing the generalized S-transform (GST) and nonlinear complex diffusion (NCD) methods. GST and its inverse transform (IGST) can decompose the original seismic signal into several sub-component signals in terms of the instantaneous frequencies to discern the distribution of various frequencies in the entire signal. The imaginary value generated by the NCD process, which can be used as the directional structure indicator to suppress the noise and enhance the effective signal. Therefore, we present a denoise method of seismic signal based on generalized S-transform and nonlinear complex diffusion (GSNCD). GSNCD, is a decomposition, denoise, and reconstruction method, with three key features: (1) A new GST transform is proposed under the GST framework, which uses the characteristic of the higher frequency resolution in high frequency and the higher time resolution in low frequency to decompose the signal into sub-component signals as different frequencies, and the sub-component signals are used to determine the structural tensor of seismic signal; (2) a fixed diffusion coefficient of complex diffusion is improved to adjust the adaptive iteration step size; (3) the sub-component seismic signals are calculated to avoid filtering deviation caused by fixed inclination angle. Finally, we reconstruct the processed sub-component signals into a complete signal. The simulations and real example fully verify the effectiveness of GSNCD in seismic signal denoising, with particular improvements in the attenuation at the data edge. In the ground motion signal test, the signal-to-noise ratio (SNR) after denoising by GSNCD increased from −2.50 dB to 13.83 dB. In two scenarios tests of exploration signals, the SNR of GSNCD is 12.09 dB and 11.19 dB, respectively, demonstrating better relative error and stability compared to other denoise methods such as Wavelet, empirical mode decomposition (EMD), adaptive NCD (ANCD), damped rank-reduction (DRR) and structural filtering method applied in the low-SNR seismic signal.

Two-dimensional complex wavelet transform for linear noise attenuation and image decomposition

Abstract For developing a high-fidelity, high-resolution seismic denoising method, we use the two-dimensional complex wavelet transform (2D CWT) to analyze noise and signals. By investigating a surface wave's features and evaluating factors affecting the fidelity of the method, the best practice for the wavelet transform-based denoising has been established. First, static and normal moveout correction are applied on shot gathers. Then, 2D CWT is used to attenuate linear noises. The results demonstrate that the proposed method and practice significantly attenuate noises and preserve the signal's amplitudes and frequency band. In addition to denoising, we also apply the 2D CWT to decompose a seismic image into multiscale images with different resolutions. Multiscale decomposed images derive more detailed information for subsurface structures and fault networks. The decomposed images depict sharper structures and reveal detailed features of faults more significantly than the original images.

Deep learning seismic damage assessment with embedded signal denoising considering three-dimensional time–frequency feature correlation

Fast and accurate seismic damage assessment is crucial for timely post-earthquake evaluation and rescue. In seismic damage assessment, the correlation between ground motions in three directions during the time–frequency transform and the appropriate denoising thresholds during signal data preprocessing pose challenges for traditional methods. We propose a novel deep learning framework, DRSNet (deep residual shrinkage network), which incorporates the CNN structure of ResNet and a soft-threshold denoising module for simultaneous seismic signal denoising and damage assessment. To consider the feature correlation in time–frequency transform of seismic signals, they are first decomposed synchronously with noise-assisted multivariate empirical mode decomposition (NAMEMD) into multi-dimensional intrinsic mode functions (MIMF), and MIMFs are then transformed into seismic time–frequency maps using a non-parametric time–frequency analysis with scalable time windows and the Duhamel integral form. The subsidence and the subsidence rate of the dam are computed with finite element analysis and considered to assess seismic damage. The time–frequency maps and the finite element analysis results are used as input and output data to train DRSNet with no need for preprocessing seismic signal noise. The proposed model has been applied to a large-scale hydropower dam and achieved an average precision of 94.52% for predicting the seismic damage levels, which outperforms ResNet and ResNeSt by 3.09% and 2.62%, respectively. Thorough comparison and analysis of the model demonstrate its potential for accurate and efficient seismic damage assessment.