Abstract
Deep learning (DL) techniques have recently attracted considerable attention in the field of seismic data denoising. However, most DL-based seismic denoising models require a considerable number of paired noisy–clean samples for training, which limits their application in practice. In this paper, a novel self-supervised DL scheme for noise attenuation in reflection seismic data is proposed based on the Neighbor2Neighbor strategy. The proposed method adopts a U-shaped convolutional network as the main network and incorporates regularization loss during training to improve the stability of network training, thereby constructing an end-to-end self-learning process for seismic data denoising. Specifically, a neighborhood subsampling workflow is built on single noisy seismic data to generate paired noisy images for training. Next, an unsupervised evaluation metric, grounded solely in noisy data, is adopted to quantitatively evaluate the performance of the denoising algorithm without labeled data. The application to synthetic datasets suggests that the proposed method achieves better denoising results than traditional (e.g., f−x deconvolution and wavelet analysis) and self-supervised methods, and rivals a widely used supervised DL model, the denoising convolution neural network. In real application to seismic data denoising without noise-free labels, the proposed method more effectively suppresses migration artifacts and random noise while better preserving the signal integrity compared to other methods. These improvements demonstrate that the proposed method is an independent, novel, and powerful data-driven DL scheme suitable for real seismic data denoising.
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References
Abma R, Claerbout J (1995) Lateral prediction for noise attenuation by t − x and f − x techniques. Geophysics 60:1887–1896. https://doi.org/10.1190/1.1443920
Alkhalifah T, Wang H, Ovcharenko O (2021) MLReal: bridging the gap between training on synthetic data and real data applications in machine learning. Eur Assoc Geosci Eng 2021:1–5
Bianco MJ, Gerstoft P, Olsen KB, Lin F-C (2019) High-resolution seismic tomography of Long Beach, CA using machine learning. Sci Rep 9:14987. https://doi.org/10.1038/s41598-019-50381-z
Birnie C, Alkhalifah T (2022) Leveraging domain adaptation for efficient seismic denoising. In: Energy in data conference, Austin, TX, 20–23 February 2022. Energy in Data, pp 11–15
Birnie C, Ravasi M, Liu S, Alkhalifah T (2021) The potential of self-supervised networks for random noise suppression in seismic data. Artif Intell Geosci 2:47–59. https://doi.org/10.1016/j.aiig.2021.11.001
Chen G, Zhang H (2021) Wavelets in geosciences. In: Daya Sagar BS, Cheng Q, McKinley J, Agterberg F (eds) Encyclopedia of Mathematical geosciences. Springer, Cham, pp 1–11
Chen G, Cheng Q, Puetz S (2023) Data-driven discovery in geosciences: opportunities and challenges. Math Geosci 55:287–293. https://doi.org/10.1007/s11004-023-10054-0
Donoho DL (1995) De-noising by soft-thresholding. IEEE Trans Inf Theory 41:613–627. https://doi.org/10.1109/18.382009
Dragomiretskiy K, Zosso D (2014) Variational mode decomposition. IEEE Trans Signal Process 62:531–544. https://doi.org/10.1109/TSP.2013.2288675
Gulunay N (1986) FXDECON and complex wiener prediction filter. In: SEG technical program expanded abstracts 1986. Society of Exploration Geophysicists, pp 279–281
Herrmann FJ, Wang D, Hennenfent G, Moghaddam PP (2008) Curvelet-based seismic data processing: a multiscale and nonlinear approach. Geophysics 73:1–5. https://doi.org/10.1190/1.2799517
Hu L, Zheng X, Duan Y, Yan X, Hu Y, Zhang X (2019) First-arrival picking with a U-net convolutional network. Geophysics 84:45–57. https://doi.org/10.1190/geo2018-0688.1
Huang N, Shen Z, Long S, Wu M, Shi H, Zheng Q, Yen N, Tung C, Liu H (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc R Soc Lond A 454:903–995. https://doi.org/10.1098/rspa.1998.0193
Huang T, Li S, Jia X, Lu H, Liu J (2022) Neighbor2Neighbor: a self-supervised framework for deep image denoising. IEEE Trans on Image Process 31:4023–4038. https://doi.org/10.1109/TIP.2022.3176533
Krull A, Buchholz T-O, Jug F (2019) Noise2Void-learning denoising from single noisy images. In: 2019 IEEE/CVF conference on computer vision and pattern recognition (CVPR). IEEE, Long Beach, pp 2124–2132
Kaur H, Fomel S, Pham N (2020) Seismic ground-roll noise attenuation using deep learning. Geophys Prospect 68:2064–2077. https://doi.org/10.1111/1365-2478.12985
Kutyniok G, Lim W-Q, Reisenhofer R (2016) ShearLab 3D: faithful digital shearlet transforms based on compactly supported shearlets. ACM Trans Math Softw 42:1–42. https://doi.org/10.1145/2740960
Lee D, Aune E, Langet N, Eidsvik J (2023) Ensemble and self-supervised learning for improved classification of seismic signals from the Åknes Rockslope. Math Geosci 55:377–400. https://doi.org/10.1007/s11004-022-10037-7
Lehtinen J, Munkberg J, Hasselgren J, Laine S, Karras T, Aittala M, Aila T (2018) Noise2Noise: learning image restoration without clean data. https://doi.org/10.48550/arXiv.1803.04189
Li Q, Gao J (2013) Contourlet based seismic reflection data non-local noise suppression. J Appl Geophys 95:16–22. https://doi.org/10.1016/j.jappgeo.2013.05.002
Li Y, Wang Y, Wu N (2021) Noise suppression method based on multi-scale dilated convolution network in desert seismic data. Comput Geosci 156:104910. https://doi.org/10.1016/j.cageo.2021.104910
Li, He P, Feng P, Guo X, Wu W, Yu H (2022) Spectral2Spectral: image-spectral similarity assisted spectral CT deep reconstruction without reference. https://doi.org/10.48550/arXiv.2210.01125
Liu W, Cao S, Chen Y (2016) Applications of variational mode decomposition in seismic time-frequency analysis. Geophysics 81:365–378. https://doi.org/10.1190/geo2015-0489.1
Liu N, Wang J, Gao J, Chang S, Lou Y (2022) Similarity-informed self-learning and its application on seismic image denoising. IEEE Trans Geosci Remote Sens 60:1–13. https://doi.org/10.1109/TGRS.2022.3210217
Liu S, Birnie C, Alkhalifah T (2022b) Coherent noise suppression via a self-supervised blind-trace deep learning scheme. https://doi.org/10.48550/arXiv.2206.00301
Luiken N, Ravasi M, Birnie CE (2022) A hybrid approach to seismic deblending: when physics meets self-supervision. https://doi.org/10.48550/arXiv.2205.15395
Maleky A, Kousha S, Brown MS, Brubaker MA (2022) Noise2NoiseFlow: realistic camera noise modeling without clean images, pp 17632–17641
Mandelli S, Lipari V, Bestagini P, Tubaro S (2019) Interpolation and denoising of seismic data using convolutional neural networks. https://doi.org/10.48550/arXiv.1901.07927
Marcos-Morales A, Leibovich M, Mohan S, Vincent JL, Haluai P, Tan M, Crozier P, Fernandez-Granda C (2022) Evaluating unsupervised denoising requires unsupervised metrics. https://doi.org/10.48550/arXiv.2210.05553
Mosser L, Dubrule O, Blunt MJ (2020) Stochastic seismic waveform inversion using generative adversarial networks as a geological prior. Math Geosci 52:53–79. https://doi.org/10.1007/s11004-019-09832-6
Qian F, Guo W, Liu Z, Yu H, Zhang G, Hu G (2022) Unsupervised erratic seismic noise attenuation with robust deep convolutional autoencoders. IEEE Trans Geosci Remote Sens 60:1–16. https://doi.org/10.1109/TGRS.2022.3158389
Qiu B, Zeng S, Meng X, Jiang Z, You Y, Geng M, Li Z, Hu Y, Huang Z, Zhou C, Ren Q, Lu Y (2021) Comparative study of deep neural networks with unsupervised Noise2Noise strategy for noise reduction of optical coherence tomography images. J Biophoton. https://doi.org/10.1002/jbio.202100151
Ronneberger O, Fischer P, Brox T (2015) U-net: convolutional networks for biomedical image segmentation. In: International conference on medical image computing and computer-assisted intervention. Springer, pp 234–241
Saad OM, Chen Y (2020) Deep denoising autoencoder for seismic random noise attenuation. Geophysics 85:V367–V376. https://doi.org/10.1190/geo2019-0468.1
Sebacher B, Toma SA (2022) Bridging deep convolutional autoencoders and ensemble smoothers for improved estimation of channelized reservoirs. Math Geosci 54:903–939. https://doi.org/10.1007/s11004-022-09997-7
Wang D, Chen G (2021) Seismic stratum segmentation using an encoder–decoder convolutional neural network. Math Geosci 53:1355–1374. https://doi.org/10.1007/s11004-020-09916-8
Wang F, Yang B, Wang Y, Wang M (2022a) Learning from noisy data: an unsupervised random denoising method for seismic data using model-based deep learning. IEEE Trans Geosci Remote Sens 60:1–14. https://doi.org/10.1109/TGRS.2022.3165037
Wang X, Sui Y, Wang W, Ma J (2022b) Random noise attenuation by self-supervised learning from single seismic data. Math Geosci 8:1–22. https://doi.org/10.1007/s11004-022-10032-y
Wei X-L, Zhang C-X, Kim S-W, Jing K-L, Wang Y-J, Xu S, Xie Z-Z (2022) Seismic fault detection using convolutional neural networks with focal loss. Comput Geosci 158:104968. https://doi.org/10.1016/j.cageo.2021.104968
Wu X, Liang L, Shi Y, Fomel S (2019) FaultSeg3D: using synthetic data sets to train an end-to-end convolutional neural network for 3D seismic fault segmentation. Geophysics 84:35–45. https://doi.org/10.1190/geo2018-0646.1
Wu B, Meng D, Zhao H (2021) Semi-supervised learning for seismic impedance inversion using generative adversarial networks. Remote Sens 13:909. https://doi.org/10.3390/rs13050909
Wu J, Li Q, Yang G, Li L, Senhadji L, Shu H (2023) Self-supervised speech denoising using only noisy audio signals. Speech Commun 149:63–73. https://doi.org/10.1016/j.specom.2023.03.009
Xu B, Wang N, Chen T, Li M (2015) Empirical evaluation of rectified activations in convolutional network. arXiv.org. https://arxiv.53yu.com/abs/1505.00853v2
Yang L, Chen W, Wang H, Chen Y (2021) Deep learning seismic random noise attenuation via improved residual convolutional neural network. IEEE Trans Geosci Remote Sens 59:7968–7981. https://doi.org/10.1109/TGRS.2021.3053399
Yilmaz Ö (2001) Seismic data analysis: processing, inversion, and interpretation of seismic data. Society of Exploration Geophysicists
Yu S, Ma J, Wang W (2019) Deep learning for denoising. Geophysics 84:333–350. https://doi.org/10.1190/geo2018-0668.1
Zhang K, Zuo W, Chen Y, Meng D, Zhang L (2017) Beyond a Gaussian denoiser: residual learning of deep CNN for image denoising. IEEE Trans Image Process 26:3142–3155. https://doi.org/10.1109/TIP.2017.2662206
Zhang R, Ulrych TJ (2003) Physical wavelet frame denoising. Geophysics 68:225–231. https://doi.org/10.1190/1.1543209
Acknowledgements
This research was jointly supported by the National Natural Science Foundation of China (No. 41972305), MOST Special Fund from the State Key Laboratory of Geological Processes and Mineral Resources (MSFGPMR2022-3), and Mathematical Geoscience Student Award (2021) granted to Detao Wang.
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Wang, D., Chen, G., Chen, J. et al. Seismic Data Denoising Using a Self-Supervised Deep Learning Network. Math Geosci 56, 487–510 (2024). https://doi.org/10.1007/s11004-023-10089-3
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DOI: https://doi.org/10.1007/s11004-023-10089-3