Unsupervised Seismic Random Noise Suppression Based on Local Similarity and Replacement Strategy

The sparse representation of a seismic signal plays a significant role to suppress random noise in the seismic data. Dictionary learning (DL) is an effective tool to find a suitable sparse representation of a seismic signal. As an unsupervised DL, non-negative matrix factorization (NMF) has been widely used for attenuating random noise in seismic data during recent years. However, due to the nonconvexity of the NMF, most of the NMF methods might suffer from bad local minima, especially for seismic data with heavy noise. To solve this issue, we propose a workflow to suppress seismic random noise in the time-space domain, named self-paced nonnegative dictionary learning (SPNDL). The SPNDL is implemented by incorporating the self-paced learning (SPL) method with the NMF. Inspired by the learning way of humans and animals, the SPL selects the training samples automatically from easy to complex. Based on the SPL theory, a valid seismic data can be recovered by training the sample points with the high signal-to-noise ratio (SNR) values, and then gradually including the sample points with the low SNR values into NMF training. Our proposed SPNDL solves the bad local minima issue and obtains a robust denoised result. The potential of the proposed SPNDL method is demonstrated by both examples of a synthetic data and a field data.

The suppression of random noise in seismic data is an essential step in the processing of seismic signals. However, as the exploration environment is becoming more and more complicated, the energy of valid signals is weaker and the signal to noise (SNR) of seismic data is much lower which bring great difficulty to seismic data processing and interpretation. In this paper, we propose a new seismic random noise suppression approach based on the non-subsampled contourlet transform (NSCT). Firstly, the noisy seismic data is decomposed into different sub-bands of frequency and orientation responses using NSCT. Then, we use an appropriate thresholding operator to denoise the sub-bands of NSCT coefficients. Finally, we perform the inverse NSCT transform on the denoised NSCT components to reconstruct the denoised seismic data. We use synthetic data examples to demonstrate the superior performance of the proposed approach over the wavelet transform based threshold denoising method.

Seismic data processing plays a key role in the field of geophysics. The collected seismic data are inevitably contaminated by various types of noise, which makes the effective signals difficult to be accurately discriminated. A fundamental issue is how to improve the signal-to-noise ratio of seismic data. Due to the complex characteristics of noise and signals, it is a challenge for the denoising model to suppress noise and recover weak signals. To suppress random noise in seismic data, we propose a multi-scale deformable convolution neural network denoising model based on U-Net, named MSDC-Unet. The MSDC-Unet mainly contains modules of deformable convolution and dilated convolution. The deformable convolution can change the shape of the convolution kernel to adjust the shape of seismic signals to fit different features, while the dilated convolution with different dilation rates is used to extract feature information at different scales. Furthermore, we combine Charbonnier loss and structure similarity index measure (SSIM) to better characterize geological structures of seismic data. Several examples of synthetic and field seismic data demonstrate that the proposed method is effective in the comprehensive results in terms of quantitative metrics and visual effect of denoising, compared with two traditional denoising methods and two deep convolutional neural network denoising models.

Summary The random noise in seismic data seriously limits the extraction of information related to underground geological structure and lithology parameters. How to remove such noise sufficiently while keeping the fidelity of original seismic data is an important issue in the seismic data processing. In the poststack seismic profile, the most obvious feature is the structural feature and non-stationary feature. Inspired by it, we propose an improved non-local means (NLM) method with adaptive search window (ASWNLM). This method includes determining the direction of the search window by a correlation algorithm and the height of the search window by the instantaneous center frequency. Tests on synthetic data and real post-stack data prove our method can remove random noise as much as possible while preserving signal detail well even without a proper filtering parameter h.

Suppressing random noise and improving the signal-to-noise ratio of seismic data are of great significance for subsequent high-precision processing. As one of the most popular denoising methods, the algorithms based on deep learning usually utilize the network’s poor generalization ability for denoising processing. As a result, such methods usually face the problem of high training set construction costs and high computational costs. In addition, the widely used network UNet’s processing of multiscale features is limited to its U-shaped processing path. Therefore, we proposed a denoising method based on unsupervised learning, including a new denoising strategy based on spatial correlation, the corresponding training method, and a new network M-ResUNet. The training method allows networks to be trained directly on the test area and conducts independent training and processing for subtest areas with different geological characteristics. This not only effectively solves the problems caused by the method using generalization ability for denoising but also improves the denoising accuracy to a certain extent. In addition, M-ResUNet breaks through the limitation of the U-shaped processing path and effectively improves the training effect by controlling the bias degree of the network output to features with different scales. Compared with the traditional denoising methods and networks, the results’ test on synthetic and field data indicates that the proposed denoising method has superior performance in random noise attenuation, and M-ResUNet is effective.

Seismic reflection data are used by geologists to identify the best site for oil and gas explorations. The raw seismic image cannot be directly used for explorations because the noises may hinder the primary reflections and result in misinterpretations. In the proposed research work, the denoising method with adaptive dictionary learning is attempted to attenuate the coherent and random noises which affect the seismic reflections. In this method, Karhunen Loeve Transform (KLT) is combined with K-means Singular Value Decomposition (KSVD) to improve the Signal to Noise Ratio (SNR) of the seismic data. The combination of fixed transform using KLT and learning-based dictionary using KSVD remove the redundant data while retaining the necessary data for further interpretations. KLT is applied on the whole seismic image to decorrelate the coefficients and retain the primary reflections. The horizontal events in the seismic image are preserved as they represent the eigen images with large energy. The KSVD is applied to the KLT resultant data, which denoises the patch of data while simultaneously updating the dictionary. The noise is eliminated using local sparsity of the image where mutually overlapping small image blocks are learned to yield the self-adaptive redundant dictionary. It is then used to obtain the sparse representation of the image blocks by eliminating noise. The algorithm is tested for both synthetic and field seismic images, and the results indicate a better reduction of random and coherent noise with the acceptable execution time compared to other denoising algorithms used. The KLT combined with KSVD method decorrelate the seismic data from noise by preserving the primary reflections and discarding the redundant noise.

In seismic data processing, denoising is crucial for identifying the Earth’s subsurface structure. Erratic noise in seismic data is challenging because of its high amplitude and non-Gaussian distribution characteristics. Dictionary learning with KSVD requires a longer computational time due to its iterative nature at various stages. To address this, we propose a robust denoising DHHL method that utilises mini-batch dictionary learning, the quantum Harrow–Hassidim–Lloyd (HHL) algorithm, and quantum singular value transformation (QSVT) to attenuate random and erratic noise in seismic data. The HHL algorithm provides a significant estimate of the sparse coefficient. The HHL provides a theoretically efficient method for sparse coding with favorable asymptotic scaling, improving the potential scalability of the method. Mini-batch dictionary learning constructs hierarchical dictionaries, thereby enhancing the capture of signal features in seismic data. QSVT enables the direct transformation of singular values, leading to faster convergence and more accurate sparse representations for dictionary updating. Here, we use minimisation loss using ℓ<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</sub> to provide group sparsity and preserve the signal features. The proposed DHHL method was applied to both synthetic and field datasets. The efficiency of the DHHL method was assessed using evaluation metrics such as the signal-to-noise ratio (SNR), mean squared error (MSE), and local similarity map. The quantitative and visual results indicate that the DHHL method achieved a higher SNR, minimised the MSE with less signal leakage, and reduced the computational time by accelerating sparse coding.

Many seismic denoising algorithms are easily trapped in the dilemma of signal leaking and noise remaining. But between the two situations, more complex and common situations happens that both signal leaking and noise remaining exist. We have presented a denoising framework for random seismic noise attenuation to mitigate the dilemma and achieve a better denoising performance. The framework consists of a denoising autoencoder (DAE) and data generator. The DAE attenuates random noise without ground truth and works with a vectoring patching technique to reduce time complexity. In the data generator, local correlation is first developed to nonlinear local correlation to detect and extract the signal leakage with noise components suppressed. Then, the extracted signal leakage is compensated back to the DAE output in a supersaturated way to generate a new record. After that, DAE is used again to suppress the remaining noise in the new record. The supersaturated compensation of the first signal leakage counteracts the signal leakage of the second DAE noise attenuation. Formally, the proposed framework can be implemented like a nonlinear geological inversion by thinking of the data generator as the forward operator. Four 2D/3D synthetic and field examples test the performance of the proposed framework. Experiments demonstrate that the proposed method is effective in random noise attenuation and signal leakage compensation, and thus significantly mitigates the mentioned dilemma.

We have developed convolutional sparse coding (CSC) to attenuate noise in seismic data. CSC gives a data-driven set of basis functions whose coefficients form a sparse distribution. The noise attenuation method by CSC can be divided into the training and denoising phases. Seismic data with a relatively high signal-to-noise ratio are chosen for training to get the learned basis functions. Then, we use all (or a subset) of the basis functions to attenuate the random or coherent noise in the seismic data. Numerical experiments on synthetic data show that CSC can learn a set of shifted invariant filters, which can reduce the redundancy of learned filters in the traditional sparse-coding denoising method. CSC achieves good denoising performance when training with the noisy data and better performance when training on a similar but noiseless data set. The numerical results from the field data test indicate that CSC can effectively suppress seismic noise in complex field data. By excluding filters with coherent noise features, our method can further attenuate coherent noise and separate ground roll.

Self-adaptive denoising net: Self-supervised learning for seismic migration artifacts and random noise attenuation

Summary We have developed a novel random noise attenuation method for seismic data based on inversion in the frequency-space (f-x) domain. The method regards ‘clean’ seismic data in f-x domain as model parameters, and the noise attenuation is equivalent to inverting these parameters from the noisy data. The prediction error filter (PEF) in the f-x prediction method is used as lateral continuity constraints of the inversion. Since the PEF is calculated from the noisy data, it should be recalculated from the denoised seismic data. The process of calculating signal, then getting a new PEF should be iterated a few times. The choice of trade-off parameters also influences the performance of this method. The proposed method overcame the problem of the generation of spurious events and reduction of the signal amplitudes in the conventional f-x prediction method. Tests on synthetic and field data examples demonstrated that, compared with f-x domain prediction, the proposed method has a better performance in noise attenuation and signal-preserving.

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.

ABSTRACTTensor algebra provides a robust framework for multi‐dimensional seismic data processing. A low‐rank tensor can represent a noise‐free seismic data volume. Additive random noise will increase the rank of the tensor. Hence, tensor rank‐reduction techniques can be used to filter random noise. Our filtering method adopts the Candecomp/Parafac decomposition to approximates a N‐dimensional seismic data volume via the superposition of rank‐one tensors. Similar to the singular value decomposition for matrices, a low‐rank Candecomp/Parafac decomposition can capture the signal and exclude random noise in situations where a low‐rank tensor can represent the ideal noise‐free seismic volume. The alternating least squares method is adopted to compute the Candecomp/Parafac decomposition with a provided target rank. This method involves solving a series of highly over‐determined linear least‐squares subproblems. To improve the efficiency of the alternating least squares algorithm, we uniformly randomly sample equations of the linear least‐squares subproblems to reduce the size of the problem significantly. The computational overhead is further reduced by avoiding unfolding and folding large dense tensors. We investigate the applicability of the randomized Candecomp/Parafac decomposition for incoherent noise attenuation via experiments conducted on a synthetic dataset and field data seismic volumes. We also compare the proposed algorithm (randomized Candecomp/Parafac decomposition) against multi‐dimensional singular spectrum analysis and classical prediction filtering. We conclude the proposed approach can achieve slightly better denoising performance in terms of signal‐to‐noise ratio enhancement than traditional methods, but with a less computational cost.

One of the most crucial challenges in seismic data processing is the reduction of the noise in the data or improving the signal-to-noise ratio. In this study, the 1D undecimated discrete wavelet transform (UDWT) has been acquired to attenuate random noise and ground roll. Wavelet domain ground roll analysis (WDGA) is applied to find the ground roll energy in the wavelet domain. The WDGA will be a substitute method for thresholding in seismic data processing. To compare the effectiveness of the WDGA method, we apply the 1D double density discrete wavelet transform (DDDWT) using soft thresholding in the random noise reduction and ground roll attenuation processes. Seismic signals intersect with ground roll in the time and frequency domains. Random noise and ground roll have many undesirable effects on pre-stack seismic data, and result in an inaccurate velocity analysis for NMO correction. In this paper, the UDWT by using the WDGA technique and DDDWT (using the soft thresholding technique) and the regular Fourier based method as f–k transform will be used and compared for seismic denoising.

Random noise attenuation is an important step in seismic data processing. In this paper, we propose a novel denoising approach based on compressive sensing and the curvelet transform. We formulate the random noise attenuation problem as an L 1 norm regularized optimization problem. We propose to use the curvelet transform as the sparse transform in the optimization problem to regularize the sparse coefficients in order to separate signal and noise and to use the gradient projection for sparse reconstruction (GPSR) algorithm to solve the formulated optimization problem with an easy implementation and a fast convergence. We tested the performance of our proposed approach on both synthetic and field seismic data. Numerical results show that the proposed approach can effectively suppress the distortion near the edge of seismic events during the noise attenuation process and has high computational efficiency compared with the traditional curvelet thresholding and iterative soft thresholding based denoising methods. Besides, compared with f-x deconvolution, the proposed denoising method is capable of eliminating the random noise more effectively while preserving more useful signals.