Seismic Random Noise Attenuation Using Non‐Local Reference‐Guided Deep Image Prior

Suppression of seismic random noise is one critical step in seismic data processing. In recent years, the outstanding ability of deep learning to denoise seismic data is impressive. The unsupervised deep image prior (DIP) model has achieved promising denoising results without training labels. However, during training, these models first learn the effective seismic events in the noisy data, and then pick up the random noise afterwards, i.e. overfitting. Thus, the practicability of DIP hinges on good early stopping (ES) that catches the potentially noise-free seismic data. In this respect, most DIP studies only demonstrate potential of the models by showing the peak performance accessing the ground truth as reference, but provide no clue about how to operationally catch near-peak output without the ground truth. In this paper, we investigate the ES strategy in seismic data denoising using DIP method, which consistently detects the performance of reconstruction sequence by observing its running variance (VAR). The adopted ES method incurs low computational overhead. Numerical tests on 2D/3D synthetic and field data demonstrate that compared with other stopping criteria, the ES method exhibits superiority in suppressing random noise and preserves the effective signals better.

The presence of random noise in field data significantly reduces the precision of subsequent seismic processing steps. As a result, random noise suppression is essential to improve the quality of field data. Because most traditional algorithms characterize seismic data linearly, the denoising accuracy is still open to be improved. As an unsupervised deep-learning method, the deep image prior (DIP) algorithm can characterize seismic data nonlinearly. The DIP uses randomly generated noise as input and noisy seismic data as desired output for random noise attenuation over several rounds of training epochs. However, determining the optimal training epoch for obtaining the final denoised result of unlabeled noisy data remains a challenge. To terminate the DIP training in time and obtain the denoised result, we design an improved quality control criterion (IQCC) based on adjacent estimations of seismic signal. To further improve the denoising accuracy, a recursive strategy is developed that uses the previous desired output as the new input and the previous denoised result as the new desired output. To obtain the optimal denoised results using the suggested recursive algorithm, a convergence condition also is established. Numerous examples of synthetic prestack and poststack data demonstrate the effectiveness of the designed IQCC and our recursive strategy with a convergence condition in protecting the effective signal, especially when compared with the curvelet thresholding algorithm and the original DIP. Furthermore, the denoising accuracy is on par with that of the supervised learning algorithm, demonstrating the adaptability of our recursive DIP under the convergence condition. Its superiority is further supported by field poststack seismic data processing, which uses the local similarity for performance assessments.

Seismic random noise is one of the main factors that degrade the quality of seismic data. Therefore, seismic random noise attenuation should be performed appropriately through several stages during seismic data processing, and this requires sufficient experience and knowledge because the proper hyperparameters need to be determined based on the features of the noise in the target seismic data. Recently, machine learning–based seismic noise attenuation has been widely studied because it provides suitable results by learning noise features from noisy data, unlike conventional physics‐based approaches. There are many important factors in machine learning, and, here, we focus on the loss functions of machine learning in terms of seismic random noise attenuation. The most widely used loss function is l2, but we train a model with various kinds of single and multiple loss functions and attenuate seismic random noise. We analyse the efficiency of loss functions by comparing the noise‐attenuated results of synthetic and field seismic data qualitatively and quantitatively. Our analysis indicates that the multiple loss function with the l1 norm can be a proper choice for random noise suppression of seismic data.

Patch classification based EPLL with mixed GMM for nonstationary seismic random noise attenuation

Seismic random noise attenuation and signal-preserving by multiple directional time-frequency peak filtering

Seismic random noise attenuation based on adaptive time–frequency peak filtering

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

Local spatiotemporal time–frequency peak filtering method for seismic random noise reduction

Seismic field data are usually contaminated by random or complex noise, which seriously affect the quality of seismic data contaminating seismic imaging and seismic interpretation. Improving the signal-to-noise ratio (SNR) of seismic data has always been a key step in seismic data processing. Deep learning approaches have been successfully applied to suppress seismic random noise. The training examples are essential in deep learning methods, especially for the geophysical problems, where the complete training data are not easy to be acquired due to high cost of acquisition. In this work, we propose a natural images pre-trained deep learning method to suppress seismic random noise through insight of the transfer learning. Our network contains pre-trained and post-trained networks: the former is trained by natural images to obtain the preliminary denoising results, while the latter is trained by a small amount of seismic images to fine-tune the denoising effects by semi-supervised learning to enhance the continuity of geological structures. The results of four types of synthetic seismic data and six field data demonstrate that our network has great performance in seismic random noise suppression in terms of both quantitative metrics and intuitive effects.

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

The ability of deep image prior (DIP) to recover high-quality images from incomplete or corrupted measurements has made it popular in inverse problems in image restoration and medical imaging, including magnetic resonance imaging (MRI). However, conventional DIP suffers from severe overfitting and spectral bias effects. In this work, we first provide an analysis of how DIP recovers information from undersampled imaging measurements by analyzing the training dynamics of the underlying networks in the kernel regime for different architectures. This study sheds light on important underlying properties for DIP-based recovery. Current research suggests that incorporating a reference image as network input can enhance DIP's performance in image reconstruction compared to using random inputs. However, obtaining suitable reference images requires supervision and raises practical difficulties. In an attempt to overcome this obstacle, we further introduce a self-driven reconstruction process that concurrently optimizes both the network weights and the input while eliminating the need for training data. Our method incorporates a novel denoiser regularization term which enables robust and stable joint estimation of both the network input and reconstructed image. We demonstrate that our self-guided method surpasses both the original DIP and modern supervised methods in terms of MR image reconstruction performance and outperforms previous DIP-based schemes for image inpainting.

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.

Using Hilbert transform as a tool for random noise attenuation and it’s application at one of the Iranian south east oilfields.<br>Seismic data always consist of a signal and a noise component. What has to be considered as noise<br>depends on the application? However, as a general defnition we can say that any recorded energy<br>which interferes with the desired signal can be considered as noise. The noise can be classifed as<br>background noise (for instance wind, swell, noise from nearby production, or interference from nearby<br>seismic acquisition), source-generated noise (for instance direct and scattered waves or multiples), and<br>instrument noise and can show up as coherent or incoherent energy in seismic gathers. This diversity<br>of noise types with different characteristics makes separation of signal and noise a challenging process.<br>In recent years, several authors have developed effective methods of eliminating random noise<br>(incoherent energy). For example, Gülünay (2000) used the noncausal prediction filter for randomnoise<br>attenuation; Ristau and Moon (2001) compared several adaptive filters, which they applied in an<br>attempt to reduce random noise in geophysical data; and Karsli et al. (2006) applied complex-trace<br>analysis to eismic data for random noise suppression, recommending it for low-fold seismic data. Also<br>Some transform methods were used to eliminate seismic random noise, e.g., seislet transform (Fomel,<br>2006; Fomel and Liu, 2008), and curvelet transform (Neelamani et al., 2008).<br>We use a procedure, complex-trace transformation (CTT) that uses complex-trace envelope and<br>normalized phase traces to improve the temporal resolution and to increase S/N of stacked seismic<br>data. We follow the technique offered by Shtivelman et al. (1986) and Karsli et al. (2006) who showed<br>that analysis of seismic data in complex geologic environments should be based on both group and phase correlation.<br>In this study, we suggest further applications of the method for resolution improvement and randomnoise<br>suppression, which have not been considered by Shtivelman et al. (1986) and Karsli et al.<br>(2006). The applicability of the method for temporal resolution improvement in presence of<br>interference effects and random noise is also discussed with examples of synthetic and field seismic<br>data from one of the Iranian south east oil fiels where the Hilbert transform denoising method has<br>successfully attenuated the noise and allowed for improved imaging.

The attenuation of seismic field noise using self-supervised deep learning has gained attention due to its label-free training process. However, common self-supervised methods are limited by the pixelwise independence assumption, which does not align with field seismic noise characteristics, and suffer from signal leakage due to receptive fields containing inherent blind spots or traces. In this paper, we propose a self-supervised random noise attenuation method based on the non-pixelwise independence assumption. By considering the spatial correlation map of field noise, we extend the blind spot to a generalized blind neighborhood, ensuring that the prediction pixel is not influenced by neighboring pixels with noise correlation greater than zero. The blind neighborhood size controls how much spatial correlation is disrupted, allowing our method to handle random noise with varying spatial correlation. Since larger blind neighborhoods may lead to signal loss, we introduce an automatic trade-off between noise correlation disruption and signal preservation during training. Experiments on real seismic noise attenuation (including random and tracewise coherent noise) demonstrate the superiority of our method in destroying the spatial coherence of noise and preventing useful signal leakage.

Supervised image denoising methods based on deep neural networks require a large amount of noisy-clean or noisy image pairs for network training. Thus, their performance drops drastically when the given noisy image is significantly different from the training data. Recently, several unsupervised learning models have been proposed to reduce the dependence on training data. Although unsupervised methods only require noisy images for learning, their denoising effect is relatively weak compared with supervised methods. This paper proposes a two-stage unsupervised deep learning framework based on deep image prior (DIP) to enhance the image denoising performance. First, a two-target DIP learning strategy is proposed to impose a learning restriction on the DIP optimization process. A cleaner preliminary image, together with the given noisy image, was used as the learning target of the two-target DIP learning process. We then demonstrate that adding an extra learning target with better image quality in the DIP learning process is capable of constraining the search space of the optimization process and improving the denoising performance. Furthermore, we observe that given the same network input and the same learning target, the DIP optimization process cannot generate the same denoised images. This indicates that the denoised results are uncertain, although they are similar in image quality and are complemented by local details. To utilize the uncertainty of the DIP, we employ a supervised denoising method to preprocess the given noisy image and propose an up- and down-sampling strategy to produce multiple sampled instances of the preprocessed image. These sampled instances were then fed into multiple two-target DIP learning processes to generate multiple denoised instances with different image details. Finally, we propose an unsupervised fusion network that fuses multiple denoised instances into one denoised image to further improve the denoising effect. We evaluated the proposed method through extensive experiments, including grayscale image denoising, color image denoising, and real-world image denoising. The experimental results demonstrate that the proposed framework outperforms unsupervised methods in all cases, and the denoising performance of the framework is close to or superior to that of supervised denoising methods for synthetic noisy image denoising and significantly outperforms supervised denoising methods for real-world image denoising. In summary, the proposed method is essentially a hybrid method that combines both supervised and unsupervised learning to improve denoising performance. Adopting a supervised method to generate preprocessed denoised images can utilize the external prior and help constrict the search space of the DIP, whereas using an unsupervised method to produce intermediate denoised instances can utilize the internal prior and provide adaptability to various noisy images of a real scene.