Erratic Noise Research Articles

Robust seismic data denoising via self-supervised deep learning

Seismic data denoising is a critical component of seismic data processing, yet effectively removing erratic noise, characterized by its non-Gaussian distribution and high amplitude, remains a substantial challenge for conventional methods and deep-learning (DL) algorithms. Supervised learning frameworks typically outperform others, but they require pairs of noisy data sets alongside corresponding clean ground truth, which is impractical for real-world seismic data sets. In contrast, unsupervised learning (UL) methods, which do not rely on ground truth during training, often fall short in performance when compared with their supervised or traditional denoising counterparts. Moreover, current unsupervised DL methods fail to address the specific challenges posed by erratic seismic noise adequately. This paper introduces a novel zero-shot unsupervised DL framework designed specifically to mitigate random and erratic noise, with a particular emphasis on blended noise. Drawing inspiration from Noise2Noise (N2N) and data augmentation principles, we develop a robust self-supervised denoising network called robust Noiser2Noiser. Our approach eliminates the need for paired noisy and clean data sets as required by supervised methods or paired noisy data sets as in N2N. Instead, our framework relies solely on the original noisy seismic data set. Our methodology generates two independent recorrupted data sets from the original noisy data set, using one as the input and the other as the training target. Subsequently, we use a DL-based denoiser, denoising convolutional neural network, for training purposes. To address various types of random and erratic noise, the original noisy data set is recorrupted with the same noise type. Detailed explanations for generating training input and target data for blended data are provided. We apply our network to synthetic and real marine data examples, demonstrating significantly improved noise attenuation performance compared with traditional denoising methods and state-of-the-art UL Codes are available on https://github.com/Ji-seismic/N2N_deblending .

SelfMixed: Self-supervised mixed noise attenuation for distributed acoustic sensing data

Distributed acoustic sensing (DAS) is an emerging data acquisition technique known for its high sensing density, cost effectiveness, and environmental friendliness, making it a technology with significant future application potential in many fields. However, DAS signals are often contaminated by various types of noise, such as high-frequency, high-amplitude erratic, and horizontal noise, making their processing challenging. Therefore, it is crucial to leverage the physical characteristics of these diverse types of noise in DAS data and effectively attenuate them. In this work, we develop SelfMixed, a novel self-supervised learning method for mixed noise suppression of DAS data. We fully exploit the physical characteristics of different types of noise in DAS data and introduce a physical characteristic-based training strategy. Specifically, we use the [Formula: see text] norm to characterize random noise, the [Formula: see text] norm for erratic noise, and horizontal smoothness and vertical nonsmoothness for horizontal noise. In addition, we use a blind-spot-based training strategy for DAS denoising, relying solely on observed noisy data. To more effectively attenuate horizontal noise, we also introduce a Fourier transform-based parameterization method. By combining self-supervised deep priors with the physical characteristics of mixed DAS noise, our method effectively attenuates complex mixed noise in field DAS data. Extensive experiments on synthetic and field data from various geographic scenarios validate the superiority of SelfMixed over seven state-of-the-art DAS denoising approaches.

Robust multidimensional reconstruction via group sparsity with Radon operators

Seismic data processing, specifically tasks like denoising and interpolation, often hinges on sparse solutions of linear systems. Group sparsity plays an essential role in this context by enhancing sparse inversion. It introduces more refined constraints, which preserve the inherent relationships within seismic data. To this end, we propose a robust orthogonal matching pursuit algorithm, combined with Radon operators in the frequency-slowness [Formula: see text] domain, to tackle the strong group sparsity problem. This approach is vital for interpolating seismic data and attenuating erratic noise simultaneously. Our algorithm takes advantage of group sparsity by selecting the dominant slowness group in each iteration and fitting Radon coefficients with a robust [Formula: see text] norm using the alternating direction method of multipliers (ADMM) solver. Its ability to resist erratic noise, along with its superior performance in applications such as simultaneous source deblending and reconstruction of noisy onshore data sets, underscores the importance of group sparsity. Synthetic and real comparative analyses further demonstrate that strong group sparsity inversion consistently outperforms corresponding traditional methods without the group sparsity constraint. These comparisons emphasize the necessity of integrating group sparsity in these applications, thereby indicating its indispensable role in optimizing seismic data processing.

Protecting the weak signals in distributed acoustic sensing data processing using local orthogonalization: The FORGE data example

The development of the distributed acoustic sensing (DAS) technique enables us to record seismic data at a significantly improved spatial sampling rate at meter scales, which offers new opportunities for high-resolution subsurface imaging. However, DAS recordings are often characterized by a low signal-to-noise ratio (S/N) due to the presence of data noise, significantly degrading the reliability of imaging and interpretation. Current DAS data noise reduction methods remain insufficient in simultaneously preserving weak signals and eliminating various types of noise. Particularly when dealing with DAS data that are contaminated by four types of noise (i.e., high-frequency noise, high-amplitude erratic noise, horizontal noise, and random background noise), it becomes challenging to attenuate the strong noise while maintaining fine-scale features. To address these issues, we develop an integrated local orthogonalization (LO) method that can remove a mixture of different types of noise while protecting the useful signal. Our LO method effectively eliminates the aforementioned noise by concatenating multiple denoising operators including a band-pass filter, a structure-oriented, spatially varying median filter, a dip filter in the frequency-wavenumber domain, and a curvelet filter. Next, the local orthogonalization weighting operator is applied to extract signal energy from the removed noise section. We demonstrate the robustness of our LO method on various challenging DAS data sets from the Frontier Observatory for Research in Geothermal Energy geothermal field. The denoising results demonstrate that our LO method can successfully minimize the levels of different types of noise while preserving the energy of weak signals.

Unsupervised Learning With Waveform Multibranch Attention Mechanism for Erratic Noise Attenuation

Unsupervised Learning With Waveform Multibranch Attention Mechanism for Erratic Noise Attenuation

Deep learning for noise attenuation from the ocean bottom node 4C data

AbstractThe source vessel noise is a very common noise type in offshore seismic surveys. The state‐of‐art deep learning‐based methods provide an end‐to‐end framework for seismic data denoising. The denoising performance of a pretrained network is, however, highly dependent on the completeness of the training set. When training a denoising network with only field data, especially for attenuating erratic noise, it is hard to obtain a noise‐free data as the training target for the network. Transfer learning, by combining the synthetic and field data, is an alternative solution for improving the generalization capabilities of the network, although being able to model such erratic noise represents also a challenge. Although the denoising results by traditional methods are not accurate enough for creating a complete training set, the features in residual noise by subtracting the denoised data from noisy data are enough for the network to learn. Considering the aforementioned factors, we develop a deep learning‐based workflow for the attenuation of the erratic source vessel noise from ocean bottom node 4C data. Instead of using denoising results directly, we use the conventional methods to extract noise and add them to the high signal‐to‐ratio region of the field data. The created noisy dataset is different from the original noisy data in noise regions; thus, the pretrained network can also be used for predicting the same original data. The denoising results of synthetic and field data all show that even the network is trained on a noisy labelled dataset, we still can obtain high signal‐to‐noise ratio denoising result. Besides, when compare with the results by filtering‐based methods, our proposed method can attenuate the vessel noise more effectively and preserve the near offsets reflections.

A comparative analysis of moving average filter and Kalman filter for large diesel engine test cell back-pressure control

Diesel engine combustion releases many harmful components, thus there are continuous efforts into improving the efficiency of these engines and reducing the harmful gasses and particulates to meet the emission authorities targets. To develop and sell new engine-related products, these engines are required to run and to be audited in diesel engine test cells. A critical measurement for benchmark testing is the exhaust back-pressure, which is the resultant exhaust flow from the engine and a product of the air and fuel consumed. The back-pressure is controlled by restricting the flow of the exhaust using a butterfly valve and this pressure must be set to the defined limits to ensure engine compliance. Setting this limit takes time and consumes large volumes of fuel, which causes additional emissions. Therefore, a feedback control solution to regulate this back-pressure is desirable. In current practice, a moving average filter is used on two commercial standard engine softwares – SGS CyFlex® and AVL Puma 2® Data Acquisition and Control Systems to provide a useful signal for feedback control. Considering the presence of erratic noise associated with the back-pressure measurement, a Kalman Filter with tunable measurement uncertainty and process noise gains is also considered. By modifying the script in SGS CyFlex® and AVL PUMA 2®, a Kalman Filter is implemented for the first time on diesel engine test cells and a comparative analysis between the performance of the two filters is provided. Both filters effectively reduce the noise of the system, with the Kalman Filter showing a closer tracking to the desired system response. This demonstrates the potential of applying the Kalman Filter to provide the feedback signal for improved back-pressure control that could reduce the fuel consumption during testing, thereby makes testing process more economical and environment friendly. The script and results presented in this work will open up the opportunities of applying Kalman filtering method’s in various engine testing functions, which will have broader impact in the current industrial practice.

Denoising of Distributed Acoustic Sensing Seismic Data Using an Integrated Framework

Abstract Distributed acoustic sensing (DAS) is an emerging technology that offers great potential in the high-resolution multi-scale seismic investigation due to its dense spatial coverage and cost-effectiveness. However, DAS data notoriously suffer from the low signal-to-noise ratio (SNR) due to various types of strong noise, for example, high-frequency noise, high-amplitude erratic noise, vertical or horizontal noise. Here, we propose a novel denoising framework by cascading several individual denoising methods that are designed for suppressing specific types of noise. First, to suppress the high-frequency noise, we apply a bandpass filter, which is implemented by recursive infinite impulse response filtering in the time domain. Second, to suppress the erratic noise, we apply a structure-oriented median filter that arises from the reflection seismology field. Finally, to suppress the vertical or horizontal noise, we apply a carefully designed dip filter in the frequency–wavenumber domain. The overall effect of these cascaded denoising steps is that the DAS data can be dramatically improved in terms of SNR. We introduce in detail the implementations of each step in the proposed denoising framework and analyze their respective contribution toward the final improvement. We demonstrate the effectiveness of the proposed denoising framework through the open-access Frontier Observatory for Research in Geothermal Energy (FORGE) geothermal DAS dataset and provide the reproducible processing workflows for all the DAS subsets containing the catalog earthquake and microseismic events.

Retrieving useful signals from highly corrupted erratic noise using robust residual dictionary learning

Seismic denoising will inevitably cause signal leakage, which is seen as coherent signal energy in the removed noise profile. Most traditional methods either ignore the signal leakage while maintaining clean denoised data or adjust parameters to decrease the signal leakage while causing more residual noise in the denoised data. The local signal-and-noise orthogonalization method can help retrieve the leaked signals without bringing significant residual noise. However, when seismic data contain erratic noise, the local orthogonalization method does not work properly because of the unstable inversion when solving the local orthogonalization weight due to the large-amplitude erratic noise. We propose a robust dictionary learning and sparse coding algorithm to retrieve the leaked signals. In this robust method, we substitute the L2-norm regularized sparse coding model with a Huber-norm sparse coding model, which is solved iteratively via a robust algorithm. The dictionary atoms used to retrieve the leaked signals are first learned from the initial estimate of signals and then updated during the robust iterations. Synthetic and field data examples containing erratic noise are used to demonstrate the effectiveness of the proposed method.

Erratic and random noise attenuation using adaptive local orthogonalization

The local orthogonalization (LO) approach has been broadly applied to attenuate random noise and deal with the signal-leakage problem induced using the traditional denoising schemes. First, this approach removes noise and applies the LO weight (LOW) operator to the originally estimated signal. Then, the signal leakage is predicted and subsequently recovered from the original noise component. Finally, the original denoised component and the recovered signal are mixed to output the denoised seismic signal. However, this approach has limits when the seismic data include random and erratic noise. We find that this shortcoming is mainly caused by the weakness of the traditional denoising operators (e.g., curvelet and f- x deconvolution methods), which are insufficient to adapt themselves to the originally denoised signal and noise sections for the LOW process. Therefore, we aim to attenuate random and erratic noise using an adaptive LO method. By mixing the hard thresholding (HT) operator and the exponential moving-average (EMA) filter, we have developed a novel operator, which we call the HTEMA operator. Then, by introducing this novel operator into the curvelet method framework, we adapt the initially denoised signal and noise sections for the LOW process. The proposed operator is applied to the frequency domain curvelet coefficients provided by the inverse transform. Then, we use the LOW operator to compensate for the damage of useful signals. The proposed approach is not limited to the curvelet method but can be applied to other traditional denoising methods. We estimate the noise attenuation performance by the visual inspections, local similarity maps, and the signal-to-noise ratio. Synthetic and field data examples indicate the effectiveness of the proposed method in applications to erratic and random noise attenuation compared with the curvelet, f- x deconvolution, and the LO methods.

Robust fast dictionary learning for seismic noise attenuation

ABSTRACTDictionary learning has been intensively applied to process multi‐channel seismic data due to its adaptively learned basis atoms that are data driven. Traditionally, dictionary learning is mostly used to attenuate random noise in the literature since the dictionary update operation is not sensitive to Gaussian noise. However, when dictionary learning is applied to seismic data containing strong erratic noise, which does not follow the Gaussian distribution, its performance greatly deteriorates. In this paper, we propose a novel robust dictionary learning method for dealing with both random and erratic noise. We formulate the dictionary‐learning‐sbased denoising problem as an iterative process. During each iteration, we gradually diminish the effect of the erratic noise and make the denoising problem more Gaussian type. Considering the computational overburden of the classic K‐singular value decomposition algorithm due to many iterations, we substitute the K‐singular value decomposition algorithm with an efficient algorithm, which does not require the singular value decomposition operation. We apply the proposed method to several synthetic and field datasets and obtain good performance, which demonstrates its potential for wide application.

Erratic Noise Attenuation Using Double Sparsity Dictionary Learning Method

In seismic data processing, attenuation of erratic noise is a challenging task due to the unknown noise distribution. Erratic noise consists of high amplitude peaks and conventional sparse transforms based on least-square (LS) approach that is not appropriate for erratic noise attenuation. An alternative approach, where the data with erratic noise are transformed into pseudodata and then denoised based on fast discrete curvelet transform with structure-oriented space-varying median filtering, is performed and achieves better attenuation. However, the fast discrete curvelet transform with a fixed basis lacks the adaptivity for various data patterns of seismic data. Hence, in this article, we propose a double sparsity dictionary learning (DSDL) method which performs denoising and also preserves the original features of seismic data. The proposed method combines the strength of the analytical transform and adaptive transform to attenuate both random noise and erratic noise in data. The performance of proposed DSDL method is studied on synthetic datasets and field datasets. The numerical results demonstrate that the proposed method gives a better signal-to-noise ratio (SNR), a lower mean-squared error, and energy values for the denoised data in comparison to the existing methods.

Attention-Based Neural Network for Erratic Noise Attenuation From Seismic Data With a Shuffled Noise Training Data Generation Strategy

The supervised neural network-based method provides an effective way for seismic data denoising. The noise level of seismic erratic noise, i.e. outlier, varies from traces, time windows and shot gathers. The networks with popular structures may damage reflections because the network cannot learn the exact location of the noises. In order to accommodate the characteristics of erratic noise, we propose using an attention-based network which focuses more on noisy regions. The network outputs an attention map which shows the spatial distribution probability of erratic noise and a raw-noise which may have leakage reflections. To train the network with two kinds of outputs, we use two different loss function to optimize the network. The erratic noises in the specified area can be extracted by multiplying the attention map and the raw-noise, and the reflections in areas without noise are preserved. For generating the training set, we proposed a shuffled noise strategy which starts from the inaccurate denoised data with conventional method. Only the noisy data is available in the whole denoising workflow. The network can learn the noise features effectively with the shuffle noise strategy and can achieve better denoising effect than that based on conventional method. Besides, the denoising capability of the network can be controlled manually by filtering the attention map with probability, and the denoising effect can be further improved through recovering the leaked signals. Synthetic and field data examples show that the proposed method has potential for field erratic noise attenuation.

Unsupervised Erratic Seismic Noise Attenuation With Robust Deep Convolutional Autoencoders

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

Seismic erratic noise attenuation using unsupervised anomaly detection

ABSTRACTThis study introduces a new attribute to identify seismic erratic noise, i.e. outlier, in the context of unsupervised anomaly detection and is defined as local outlier probabilities. The local outlier probabilities calculate scores of degrees of isolation, i.e. outlier‐ness, for each object in a data set, which represents how far an object is deviated from its surrounding objects. Since the local outlier probabilities combines a density‐based outlier detection method with a statistically oriented scheme, its scoring system provides regularized outlier‐ness, which is an outlier probability, to be used for making a binary decision to do inclusion or exclusion of an object; such a decision only requires a simple and straightforward threshold on a probability. Based on the binary decision that flags outliers versus non‐outliers, local outlier probabilities‐denoising workflows are developed by combining multiple steps to complete an application of the local outlier probabilities to attenuate seismic erratic noise. Higher stability and improved robustness in the detection and rejection of seismic erratic noise have been achieved by implementing moving windows and decision tree‐based processes. To avoid loss of useful signal energy, signal enhancement applications are additionally suggested. Numerical experiments on synthetic data investigate the applicability of the proposed algorithms to seismic erratic noise attenuation. Field data examples demonstrate the feasibility of a local outlier probabilities‐denoising application as an effective tool in seismic denoising portfolio.

An lp-space matching pursuit algorithm and its application to robust seismic data denoising via time-domain Radon transforms

Sparse solutions of linear systems of equations are essential in many applications of seismic data processing. These systems arise in many denoising algorithms, such as those that use Radon transforms. We have developed a robust matching pursuit (RMP) algorithm for the retrieval of sparse Radon domain coefficients. The algorithm is robust to outliers and, hence, is applicable for seismic data deblending. The classic matching pursuit (MP) algorithm is often adopted to approximate data by a small number of basis functions. It performs effectively for data contaminated with well-behaved, typically Gaussian, random noise. However, MP tends to identify the wrong basis functions when the data are contaminated by erratic noise such as source interference encountered in common-receiver and common-channel gathers of simultaneous source surveys. Incorporating an [Formula: see text] space inner product into the MP algorithm significantly increases its robustness to erratic signals. Deblending experiments with synthetic and field data examples indicate a significant signal-to-noise ratio improvement when one adopts a Radon denoiser computed via our RMP solver. We determine in detail the steps required to implement our [Formula: see text] space RMP algorithm when the basis functions are not given in an explicit form, as is the case with the time-domain Radon transform.

A Multispectral Denoising Framework for Seismic Random Noise Attenuation

Random noise attenuation plays an important role in the seismic data processing. The global coherency among different spectral segments is often neglected in the traditional denoising methods, even though the seismic data are naturally broadband in the frequency spectrum. We proposed a multispectral denoising framework (MDF) for seismic random noise attenuation. The MDF contains three key components. First, we use a series of narrow-band filters on the noisy data to construct the multispectral data. Second, we normalize the constructed multispectral data to mitigate the amplitude discrepancy between different spectral slices. Third, we apply the intrinsic tensor sparsity regularization method to denoise the multispectral data. Numerical experiments on synthetic and field data show that the proposed framework can reduce the random noise as well as the erratic noise, and it can achieve improved denoised results, compared with a traditional method (i.e., the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f$ </tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$x$ </tex-math></inline-formula> deconvolution method) and the single-spectral version of the proposed method (i.e., the weighted nuclear norm minimization (WNNM) method). The proposed framework can be applied to both prestack and stacked data and generally well preserve the amplitude of useful signals, compared with the other two methods.

Erratic noise suppression using iterative structure‐oriented space‐varying median filtering with sparsity constraint

ABSTRACTErratic noise often has high amplitudes and a non‐Gaussian distribution. Least‐squares–based approaches therefore are not optimal. This can be handled better with non–least‐squares approaches, for example based on Huber norm which is computationally expensive. An alternative method has been published which involves transforming the data with erratic noise to pseudodata that have Gaussian distributed noise. It can then be attenuated using traditional least‐squares approaches. This alternative method has previously been used in combination with a curvelet transform in an iterative scheme. In this paper, we introduce a median‐filtering step in this iterative scheme. The median filter is applied following the slope direction of the seismic data to maximally preserve the energy of useful signals. The new method can suppress stronger erratic noise compared with the previous iterative method, and can better deal with random noise compared with the single‐step implementation of the median filter. We apply the proposed robust denoising algorithm to a synthetic dataset and two field data examples and demonstrate its advantages over three different noise attenuation algorithms.

A robust method for random noise suppression based on the Radon transform

Linear Radon transform, or slant-stack transform, can be used to obtain an optimally sparse representation of linear seismic events. The linear Radon transform uses a linear kernel function, and can stack the seismic data along several linear trajectories corresponding to specific slopes. The Radon transform can be formulated as a linear operator and the transform coefficients can be inverted via an iterative preconditioned least-squares method. The useful seismic signals are transformed as the sparse coefficients in the transform domain while the random noise are spreading across the transform domain or are not fitted via the Radon operator. It is advantageous to use a L2-norm data misfit to suppress the random noise but ineffective for high-amplitude erratic noise. Here, we propose a robust method to suppress both random and erratic noise based on the linear Radon transform. We iteratively transform the Huber-norm data-misfit regularization into a L2-norm regularization, which is convenient to solve using the preconditioned least-squares method. Both synthetic and field data examples are used to demonstrate the effectiveness of the proposed robust algorithm.

MoG-Based Robust Sparse Representation for Seismic Erratic Noise Suppression

By modeling the noise as Gaussian distribution, quite a lot of methods, such as basis pursuit denoising (BPDN), have demonstrated their great effectiveness in suppressing commonly random seismic noise. However, when it comes to complex seismic erratic noise, which designates non-Gaussian noise that consists of large isolated events with known or unknown distribution, such methods will lead to suboptimal results. In this letter, we present a mixture of Gaussian (MoG)-based robust sparse representation model for seismic erratic noise suppression. Instead of the Gaussian noise modeling, the mixture of Gaussian distribution is used to generally and perfectly fit the extremely complex distribution of seismic erratic noise, apart from the common Gaussian random noise. In addition, the Laplacian distribution is taken as a prior to model the robust and sparse representation of useful signal. In the Bayesian framework, our model can be constructed as a probabilistic maximum- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$a$ </tex-math></inline-formula> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">posteriori</i> probability (MAP) model and all the parameters can be easily estimated by expectation maximization (EM) and linearized Bregman (LB) algorithms. The experimental results on synthetic and real data show that the presented method can significantly suppress the erratic noise and well preserve the useful signal.