Seismic erratic noise, characterized by large isolated events following non-Gaussian distributions, significantly degrades seismic data quality by masking useful signals. Methods based on conventional priors remain essential but face inherent challenges as they struggle to balance noise attenuation and signal preservation. Supervised deep learning approaches are constrained by the scarcity of high-quality labeled training pairs, while existing unsupervised techniques often suffer from suboptimal accuracy and high computational cost. To address these limitations, we propose an unsupervised deep learning framework based on implicit neural representation (INR) for erratic noise suppression in seismic data. The proposed method employs Fourier feature mapping to encode the spatial coordinates of noisy seismic data, which are then processed by a lightweight multilayer perceptron (MLP). The MLP is optimized using a robust Huber loss function to learn a continuous representation of the underlying seismic wavefield, effectively attenuating erratic noise while preserving valuable signal components. The Fourier feature mapping enhances the MLP’s ability to capture high-frequency signal details, while the Huber loss adaptively weights residuals based on amplitude, enabling precise noise suppression. Experimental results on synthetic and field datasets demonstrate its superior performance in suppressing noise while preserving signal fidelity.

How to represent a seismic wavefield? Traditionally, while seismic wavefields are conceptualized continuously, acquisition geometries capture seismic data discretely using 2-D spatial coordinates. Motivated by recent advances in neural radiance fields for 3-D reconstruction through implicit neural representation, we introduce implicit seismic representation (ISR) for 5-D seismic data interpolation. This approach processes seismic data coordinates as inputs and outputs amplitude values at those coordinates with multilayer perceptrons (MLPs). Due to the continuous nature of the coordinates, ISR can achieve representations at any desired resolution and is easily scalable to a 5-D representation. To achieve a continuous representation of seismic data, we employ a self-supervised learning strategy to train the ISR on observed data. The trained network is then capable of interpolating missing seismic traces by querying every coordinate of the missing data. Our approach’s effectiveness is validated through synthetic and field data experiments, showcasing superior reconstruction abilities. Our findings highlight the potential of the implicit neural representation framework to achieve precise parametrization of continuous seismic wavefields, marking a significant advancement in seismic data processing and analysis.

Seismic swell noise, often observed in marine seismic data, is characterized by high amplitude and low frequencies. This noise significantly hides useful signals, underscoring the importance of attenuating it in the processing pipeline for marine seismic data. To date, most deep learning methods proposed for swell noise suppression have focused on supervised paradigms, which require a large dataset of paired noisy and clean data to gain insights into signal features and swell noise statistics at the training phase. In field data processing, however, obtaining generalizable training data often proves to be challenging. The inherent complexity and variability of the real world often make it difficult to acquire unbiased, noise-free datasets in the context of marine seismic data processing. To address this problem, we present a self-supervised deep learning method for suppressing swell noise even in the absence of access to clean seismic training data. First, we propose a strategy for the synthetic swell noise generation based on the amplitude, frequency, and coherence features of noisy traces. We implement the noisy-as-clean (NAC) strategy, wherein either the original noisy seismic data or its reorganized variant acts as the network’s target. Simultaneously, the network receives the observed noisy seismic data combined with simulated swell noise as its input. By leveraging these “noisy-noisy” pairs, we train a DnCNN network. Experimental evaluations conducted on both synthetic and field data demonstrate that, through the integration of swell noise simulation and the NAC strategy, the trained network consistently achieves superior denoising performance.

Seismic deblending is an ill-posed inverse problem that involves counteracting the effect of a blending matrix derived from the shots position and firing time. In this letter, we propose a seismic deblending method based on so-called deep preconditioners. A convolutional Autoencoder (AE) is first trained in a patch-wise fashion to learn an effective sparse representation of the common receiver gathers (CRGs) we aim to reconstruct. Then, the decoder branch of the trained AE is used as a nonlinear preconditioner for the deblending problem. Particularly, to avoid the explicit creation of a training dataset, we suggest to use the common shot gathers (CSGs) of the blended dataset itself to train the AE network, as they are not affected by incoherent blending noise. Numerical examples on synthetic and field datasets demonstrate the effectiveness of the proposed method in comparison with significantly comparable techniques: a dictionary-learning based deblending method; an end-to-end deblending convolution neutral network (CNN).

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-$a$posterioriprobability (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.

Deblending can extract good quality seismic data from blended seismic data. Generally, the deblending methods can be categorized as model- and data-driven methods. The model-driven deblending methods usually suffer from a massive computational burden, while the data-driven ones need to implement a forward blending process to construct training samples for network training. To solve these issues, we develop a plug and play (PnP) method that integrates a trained convolutional neural network (CNN) Gaussian denoiser as the prior for seismic intelligent deblending. Specifically, we propose to use acquired blended common shot gathers (CSGs) as training dataset for the CNN Gaussian denoiser training to avoid constructing or collecting any extra data. According to the theory and dedicated designed experiments, this training mode can greatly improve network performance. Then, the trained CNN Gaussian denoiser is plugged into the alternating direction method of multiplier (ADMM) algorithm to solve the deblending problem. Furthermore, based on the${l}_{{\mathrm{2}}} $norm data fidelity term and the special structure of the network architecture, the PnP-ADMM method converges to a fixed point. Experiments on synthetic and field data demonstrate that the presented PnP method with blended CSGs trained deep CNN Gaussian denoiser has superior deblending performances over the dictionary learning and discriminative deblending CNN methods.