Transposed arrangement strategy-based deep learning for seismic data crossline interpolation

Abstract

Towed-streamer marine seismic acquisition systems generally have a dense receiver spacing in the inline receiver direction within common-shot gathers (along-streamer), while the streamer spacing is relatively sparse in the crossline receiver direction within common-shot gathers (cross-streamer). This disparity can lead to spatial aliasing issues in the crossline receiver direction within common-shot gathers and result in resolution degradation during the processing of 3D seismic data. To address this issue and enhance resolution, data interpolation in the crossline receiver direction within common-shot gathers is essential. Various supervised learning-based interpolation methods have been developed to this end. However, the absence of true data in the crossline receiver direction within common-shot gathers poses challenges for training supervised learning models with actual field data. To overcome this, we have developed a novel approach called the “transposed arrangement strategy” for a deep learning-based reconstruction model for crossline interpolation. This method involves training the model with 3D input and labels patched from existing field data, and then applying the trained model with transposed 3D input to reconstruct data in the crossline receiver direction within common-shot gathers. During this process, the 3D U-Net and U-Net+ models were utilized, demonstrating their superiority through comparisons with traditional interpolation methods.

Keywords

Data processing / Signal processing / Deep learning / Crossline interpolation / Transposed arrangement strategy / 3D U-Net+

Funding

Part of the findings of this study were presented at the 2023 Fall Joint Conference and the 9th  International Symposium on Mine Reclamation, held at Pyeongchang on November 03, 2023.

References

[1] Ikelle LT, Amundsen L. Introduction to Petroleum Seismology. Society of Exploration Geophysicists; 2005. doi:10.1190/1.9781560803447.ch1

[2] Keys R. Cubic convolution interpolation for digital image processing. IEEE Trans. Acoust. 1981; 29(6):1153-1160. doi:10.1109/TASSP.1981.1163711

[3] Ronen J. Wave-equation trace interpolation. Geophysics. 1987; 52(7):973-984. doi:10.1190/1.1442366

[4] Fomel S. Seismic reflection data interpolation with differential offset and shot continuation. Geophysics. 2003; 68(2):733-744. doi:10.1190/1.1567243

[5] Spitz S. Seismic trace interpolation in the F-X domain. Geophysics. 1991; 56(6):785-794. doi:10.1190/1.1443096

[6] Spitz S. Pattern recognition, spatial predictability, and subtraction of multiple events. Geophysics. 1999; 64(2): 431-436. doi:10.1190/1.1438154

[7] Bregman L. The method of successive projection for finding a common point of convex sets (theorems for determining common point of convex sets by method of successive projection). Sov Math. 1965; 6:688-692.

[8] Herrmann FJ, Hennenfent G. Non-parametric seismic data recovery with curvelet frames. Geophys J Int. 2008; 173(1):233-248. doi:10.1111/j.1365-246X.2007.03698.x

[9] Naghizadeh M, Sacchi MD. Multistep autoregressive reconstruction of seismic records. Geophysics. 2007; 72(6):V111-V118. doi:10.1190/1.2771685

[10] Trickett S, Burroughs L, Milton A, Walton L, Dack R. Rank-Reduction-Based Trace Interpolation. In: Conference: SEG Technical Program Expanded Abstracts 2010; 2010. p. 3829-3833. doi:10.1190/1.3513645

[11] Gao J, Sacchi MD, Chen X. A fast reduced rank interpolation method for prestack seismic volumes that depend on four spatial dimensions. Geophysics. 2013; 78(1):V21-V30. doi:10.1190/geo2012-0038.1

[12] Ma J. Three-dimensional irregular seismic data reconstruction via low-rank matrix completion. Geophys. 2013; 78(5):V181-V192. doi:10.1190/geo2012-0465.1

[13] Abma R, Kabir N. 3D interpolation of irregular data with a POCS algorithm. Geophysics. 2006; 71(6):E91-E97. doi:10.1190/1.2356088

[14] Gan S, Wang S, Chen Y, Zhang Y, Jin Z. Dealiased seismic data interpolation using seislet transform with low-frequency constraint. IEEE Geosci Remote Sens Lett. 2015; 12(10): 2150-2154. doi:10.1109/LGRS.2015.2453119

[15] Liu W, Cao S, Gan S, Chen Y, Zu S, Jin Z. One-step slope estimation for dealiased seismic data reconstruction via iterative seislet thresholding. IEEE Geosci Remote Sens Lett. 2016; 13(10):1462-1466. doi:10.1109/LGRS.2016.2591939

[16] Jia Y, Ma J. What can machine learning do for seismic data processing? An interpolation application. Geophysics. 2017; 82:163-177. doi:10.1190/geo2016-0300.1

[17] Oliveira DAB, Ferreira RS, Silva R, Brazil EV. Interpolating seismic data with conditional generative adversarial networks. IEEE Geosci Remote Sens Lett. 2018; 15:1952-1956. doi:10.1109/LGRS.2018.2866199

[18] Wang B, Zhang N, Lu W, Geng J, Huang X. Intelligent missing shots’ reconstruction using the spatial reciprocity of green’s function based on deep learning. IEEE Trans Geosci Remote Sens. 2020; 58:1587-1597. doi:10.1109/TGRS.2019.2947085

[19] Park J, Choi J, Seol SJ, Byun J, Kim Y. A method for adequate selection of training data sets to reconstruct seismic data using a convolutional U-Net. Geophysics. 2021; 86:375-388. doi:10.1190/geo2019-0708.1

[20] Park J, Yeeh Z, Seol SJ, et al. Seismic data interpolation using attention-based deep learning. Eur Assoc Geosci Eng. 2022; 2022:1-5. doi:10.3997/2214-4609.202210245

[21] Yu J, Wu B. Attention and hybrid loss guided deep learning for consecutively missing seismic data reconstruction. IEEE Trans Geosci Remote Sens. 2021; 60:1-8. doi:10.1109/TGRS.2021.3068279

[22] Li X, Wu B, Zhu X, Yang H. Consecutively missing seismic data interpolation based on coordinate attention unet. IEEE Geosci Remote Sens Lett. 2022; 19:1-5. doi:10.1109/LGRS.2021.3128511

[23] Lou Y, Wu L, Liu L, et al. Irregularly sampled seismic data interpolation via wavelet-based convolutional block attention deep learning. Artif Intellig Geosci. 2022; 3:192-202. doi:10.1016/j.aiig.2022.12.001

[24] Dodda VC, Kuruguntla L, Mandpura AK, Elumalai K. Simultaneous seismic data denoising and reconstruction with attention-based wavelet-convolutional neural network. IEEE Trans Geosci Remote Sens. 2023; 61:1-14. doi:10.1109/TGRS.2023.3267037

[25] Tian Y, Fu L, Fang W, Li T. FR-UNet: A feature restoration-based UNet for seismic data consecutively missing trace interpolation. IEEE Trans Geosci Remote Sens. 2025; 63:1-10. doi:10.1109/TGRS.2025.3531934

[26] Kaur H, Pham N, Fomel S. Seismic data interpolation using CycleGAN. SEG Tech Prog Expand Abstracts. 2019; 38:5407. doi:10.1190/segam2019-3207424.1

[27] Chang DK, Yang WY, Yong XS, Li S. Seismic data interpolation with conditional generative adversarial network in time and frequency domain. SEG Tech Prog Expand Abstracts. 2019; 38:2589-2593. doi:10.1190/segam2019-3210118.1

[28] Deng F, Wang S, Wang X, Fang P. Seismic data reconstruction based on conditional constraint diffusion model. IEEE Geosci Remote Sens Lett. 2024; 21:1-5. doi:10.1109/LGRS.2024.3371675

[29] Kong F, Picetti F, Lipari V, Bestagini P, Tang X, Tubaro S. Deep prior-based unsupervised reconstruction of irregularly sampled seismic data. IEEE Geosci Remote Sens Lett. 2022; 19:1-5. doi:10.1109/LGRS.2020.3044455

[30] Jin Z, Li X, Yang H, Wu B, Zhu X. Depthwise separable convolution Unet for 3D seismic data interpolation. Front Earth Sci. 2023; 10:1-18. doi:10.3389/feart.2022.1005505

[31] Chang D, Yang W, Young X, et al. Seismic data interpolation using dual-domain conditional generative adversarial networks. IEEE Geosci Remote Sens Lett. 2020; 18:1856-1860. doi:10.1109/LGRS.2020.3008478

[32] Dou Y, Li K, Duan H, et al. MDA GAN: Adversarial-learning-based 3-D seismic data interpolation and reconstruction for complex missing. IEEE Trans Geosci Remote Sens. 2023; 61:1-14. doi:10.48550/arXiv.2204.03197

[33] Yu J, Yoon D. Crossline reconstruction of 3D seismic data using 3D cWGAN: A comparative study on sleipner seismic survey data. Appl Sci. 2023; 13:5999. doi:10.3390/app13105999

[34] Ding M, Zhou Y, Chi Y. Self-attention generative adversarial network interpolating and denoising seismic signals simultaneously. Remote Sens. 2024; 16:305. doi:10.3390/rs16020305

[35] Wang S, Deng F, Jiang P, Gong Z, Wei X, Wang Y. SeisFusion: Constrained diffusion model with input guidance for 3-D seismic data interpolation and reconstruction. IEEE Trans Geosci Remote Sens. 2024; 62:1-15. doi:10.48550/arXiv.2403.11482

[36] Qian F, Liu Z, Wang Y, Liao S, Pan S, Hu G. DTAE: Deep tensor autoencoder for 3-D seismic data interpolation. IEEE Trans Geosci Remote Sens. 2021; 60:1-19. doi:10.1109/TGRS.2021.3075968

[37] Larsen Greiner TA, Hlebnikov V, Lie JE, et al. Cross-streamer wavefield reconstruction through wavelet domain learning. Geophysics. 2020; 85:457-471. doi:10.1190/geo2019-0771.1

[38] Yeeh Z, Yoon D, Byun J. Cross-streamer wavefield reconstruction of a towed streamer system using bidirectional LSTM networks with a traces-to-trace approach. IEEE Geosci Remote Sens Lett. 2023; 20:1-5. doi:10.1109/LGRS.2023.3312712

[39] Chen Y, Yu S, Lin R. Self-supervised transfer learning POCS-net for seismic data interpolation. IEEE Trans Geosci Remote Sens. 2024; 62:1-18. doi:10.1109/TGRS.2024.3494723

[40] Wang S, Wu X, Chen J. Dip-informed neural network for self-supervised anti-aliasing seismic data interpolation. IEEE Trans Geosci Remote Sens. 2024; 62:1-4. doi:10.1109/TGRS.2024.3359247

[41] Goyes-Peñafiel P, Kamilov US, Arguello H. CDDIP: Constrain diffusion-driven deep image prior for seismic data reconstruction. IEEE Geosci Remote Sens Lett. 2025; 22:1-5. doi:10.48550/arXiv.2407.17402

[42] Souza WE, Cerqueira AG, Porsani MJ. First-break prediction in 3-D land seismic data using the dynamic time warping algorithm. Geophys J Int. 2024; 237:402-418. doi:10.1093/gji/ggae048

[43] Ronneberger O, Fischer P, Brox T. U-net:Convolutional networks for biomedical image segmentation. In: Medical Image Computing and Computer-Assisted Intervention (MICCAI). Cham: Springer; 2015. p. 234-241.

[44] Zhou Z, Siddiquee MMR, Tajbakhsh N, Liang J. UNet++: A nested U-Net architecture for medical image segmentation. Deep Learn Med Image Anal Multimodal Learn Clin Decis Support. 2018; 11045:3-11. doi:10.48550/arXiv.1807.10165

[45] Ji J, Choi YG. 3D seismic data processing methodology using public domain software system. Geophys Geophys Explor. 2010; 13:159-168.