1887
Volume 69, Issue 2
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

We propose an algorithm for seismic trace interpolation using generative adversarial networks, a type of deep neural network. The method extracts feature vectors from the training data using self‐learning and does not require any pre‐processing to create the training labels. The algorithm also does not make any prior explicit assumptions about linearity of seismic events or sparsity of the data, which are often required in the traditional interpolation methods. We create the training labels by removing traces from different receiver indices of the original datasets to simulate the effect of missing traces. We adopt the framework of the generative adversarial networks to train the network and add additional loss functions to regularize the model. Numerical examples using land and marine field datasets demonstrate the validity and effectiveness of the proposed approach. With minimal computational burden and proper training, the proposed method can be applied to three‐dimensional seismic datasets to achieve accurate interpolation results.

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/content/journals/10.1111/1365-2478.13055
2021-01-16
2024-04-25
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References

  1. Abma, R. and Kabir, N. (2006) 3D interpolation of irregular data with a POCS algorithm. Geophysics, 71(6), E91–E97.
    [Google Scholar]
  2. Benaim, S. and Wolf, L. (2017) One‐sided unsupervised domain mapping. In Advances in Neural Information Processing Systems, pages 752–762.
    [Google Scholar]
  3. Brougois, A., Bourget, M., Lailly, P., Poulet, M., Ricarte, P. and Versteeg, R. (1990) Marmousi, model and data. In EAEG Workshop‐Practical Aspects of Seismic Data Inversion.
  4. Candes, E., Demanet, L., Donoho, D. and Ying, L. (2006) Fast discrete curvelet transforms. Multiscale Modeling & Simulation, 5(3), 861–899.
    [Google Scholar]
  5. Chen, Y., Bai, M., Guan, Z., Zhang, Q., Zhang, M. and Wang, H. (2019) Five‐dimensional seismic data reconstruction using the optimally damped rank‐reduction method. Geophysical Journal International, 218(1), 224–246.
    [Google Scholar]
  6. Chen, Y., Zhang, D., Jin, Z., Chen, X., Zu, S., Huang, W. and Gan, S. (2016) Simultaneous denoising and reconstruction of 5D seismic data via damped rank‐reduction method. Geophysical Journal International, 206, 1695–1717.
    [Google Scholar]
  7. Claerbout, J. F. and Fomel, S. (2008) Image estimation by example: geophysical soundings image construction: multidimensional autoregression. http://sepwww.stanford.edu/sep/pro.
    [Google Scholar]
  8. Crawley, S. (2000) Seismic trace interpolation with nonstationary prediction‐error filters. PhD thesis, Stanford University.
  9. Crawley, S., Clapp, R. and Claerbout, J. (1999) Interpolation with smoothly nonstationary prediction‐error filters. In SEG Technical Program Expanded Abstracts 1999, pp. 1154–1157. Society of Exploration Geophysicists.
    [Google Scholar]
  10. Creswell, A., White, T., Dumoulin, V., Arulkumaran, K., Sengupta, B. and Bharath, A. A. (2018) Generative adversarial networks: an overview. IEEE Signal Processing Magazine, 35(1), 53–65.
    [Google Scholar]
  11. Fomel, S. (2002) Applications of plane‐wave destruction filters. Geophysics, 67(6), 1946–1960.
    [Google Scholar]
  12. Fomel, S. (2003) Seismic reflection data interpolation with differential offset and shot continuation. Geophysics, 68(2), 733–744.
    [Google Scholar]
  13. Fomel, S., Sava, P., Vlad, I., Liu, Y. and Bashkardin, V. (2013) Madagascar: Open‐source software project for multidimensional data analysis and reproducible computational experiments. Journal of Open Research Software, 1(1), e8.
    [Google Scholar]
  14. Gao, J., Stanton, A. and Sacchi, M. D. (2015) Parallel matrix factorization algorithm and its application to 5d seismic reconstruction and denoising. Geophysics, 80(6), V173–V187.
    [Google Scholar]
  15. Goodfellow, I. (2016) Nips 2016 tutorial: generative adversarial networks. arXiv preprint. arXiv:1701.00160.
  16. Goodfellow, I., Pouget‐Abadie, J., Mirza, M., Xu, B., Warde‐Farley, D., Ozair, S., Courville, A. and Bengio, Y. (2014) Generative adversarial nets. In Advances in Neural Information Processing Systems, pp. 2672–2680.
    [Google Scholar]
  17. Guitton, A. and Claerbout, J. (2010) An algorithm for interpolation in the pyramid domain. Geophysical Prospecting, 58(6), 965–976.
    [Google Scholar]
  18. Gülünay, N. (2003) Seismic trace interpolation in the Fourier transform domain. Geophysics, 68(1), 355–369.
    [Google Scholar]
  19. Hennenfent, G. and Herrmann, F. J. (2008) Simply denoise: Wavefield reconstruction via jittered undersampling. Geophysics, 73(3), V19–V28.
    [Google Scholar]
  20. Herrmann, F. J., Siahkoohi, A. and Rizzuti, G. (2019) Learned imaging with constraints and uncertainty quantification. arXiv preprint. arXiv:1909.06473.
  21. Hou, S., Zhang, F., Li, X., Zhao, Q. and Dai, H. (2018) Simultaneous multi‐component seismic denoising and reconstruction via k‐svd. Journal of Geophysics and Engineering, 15(3), 681–695.
    [Google Scholar]
  22. Jia, Y. and Ma, J. (2017) What can machine learning do for seismic data processing? an interpolation application. Geophysics, 82(3), V163–V177.
    [Google Scholar]
  23. Kaur, H., Pham, N. and Fomel, S. (2019a) Estimating the inverse hessian for amplitude correction of migrated images using deep learning. In SEG Technical Program Expanded Abstracts 2019, pp. 2278–2282. Society of Exploration Geophysicists.
    [Google Scholar]
  24. Kaur, H., Pham, N. and Fomel, S. (2019b) Seismic data interpolation using cyclegan. In SEG Technical Program Expanded Abstracts 2019, pp. 2202–2206. Society of Exploration Geophysicists.
    [Google Scholar]
  25. Kaur, H., Pham, N. and Fomel, S. (2020) Improving resolution of migrated images by approximating the inverse Hessian using deep learning. Geophysics, 85(4), 1–62.
    [Google Scholar]
  26. Kim, T., Cha, M., Kim, H., Lee, J. K. and Kim, J. (2017) Learning to discover cross‐domain relations with generative adversarial networks. arXiv preprint. arXiv:1703.05192.
  27. Li, Q. and Luo, Y. (2019) Using GAN priors for ultrahigh resolution seismic inversion. In SEG International Exposition and Annual Meeting. Society of Exploration Geophysicists.
    [Google Scholar]
  28. Lin, Z., Khetan, A., Fanti, G. and Oh, S. (2017) Pacgan: the power of two samples in generative adversarial networks. arXiv preprint. arXiv:1712.04086.
  29. Liu, L., Plonka, G. and Ma, J. (2017) Seismic data interpolation and denoising by learning a tensor tight frame. Inverse Problems, 33(10), 105011.
    [Google Scholar]
  30. Liu, Y. and Fomel, S. (2011) Seismic data interpolation beyond aliasing using regularized nonstationary autoregression. Geophysics, 76(5), V69–V77.
    [Google Scholar]
  31. Mahmood, A., Bennamoun, M., An, S., Sohel, F., Boussaid, F., Hovey, R., Kendrick, G. and Fisher, R. B. (2017) Deep learning for coral classification. In Handbook of Neural Computation, pp. 383–401. Elsevier.
    [Google Scholar]
  32. Mandelli, S., Lipari, V., Bestagini, P. and Tubaro, S. (2019) Interpolation and denoising of seismic data using convolutional neural networks. arXiv preprint. arXiv:1901.07927.
  33. Mosser, L., Dubrule, O. and Blunt, M. J. (2020) Stochastic seismic waveform inversion using generative adversarial networks as a geological prior. Mathematical Geosciences, 52(1), 53–79.
    [Google Scholar]
  34. Naghizadeh, M. (2012) Seismic data interpolation and denoising in the frequency‐wavenumber domain. Geophysics, 77(2), V71–V80.
    [Google Scholar]
  35. Naghizadeh, M. and Sacchi, M. D. (2007) Multistep autoregressive reconstruction of seismic records. Geophysics, 72(6), V111–V118.
    [Google Scholar]
  36. Naghizadeh, M. and Sacchi, M. D. (2008) f‐x adaptive seismic‐trace interpolation. Geophysics, 74(1), V9–V16.
    [Google Scholar]
  37. Naghizadeh, M. and Sacchi, M. D. (2010) Beyond alias hierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data. Geophysics, 75(6), WB189–WB202.
    [Google Scholar]
  38. Oliveira, D. A., Ferreira, R. S., Silva, R. and Brazil, E. V. (2018) Interpolating seismic data with conditional generative adversarial networks. IEEE Geoscience and Remote Sensing Letters, 99, 1–5.
    [Google Scholar]
  39. Oliveira, D. A., Ferreira, R. S., Silva, R. and Brazil, E. V. (2019) Improving seismic data resolution with deep generative networks. IEEE Geoscience and Remote Sensing Letters, 16, 1929–1933.
    [Google Scholar]
  40. Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L. and Lerer, A. (2017) Automatic differentiation in PyTorch. In 31st Conference on Neural Information Processing Systems (NIPS 2017), Long Beach, CA.
  41. Picetti, F., Lipari, V., Bestagini, P. and Tubaro, S. (2018) A generative adversarial network for seismic imaging applications. In 88th Society of Exploration Geophysicists International Exposition and Annual Meeting, SEG 2018, pp. 2231–2235.
    [Google Scholar]
  42. Poggio, T., Mhaskar, H., Rosasco, L., Miranda, B. and Liao, Q. (2017) Why and when can deep‐but not shallow‐networks avoid the curse of dimensionality: a review. International Journal of Automation and Computing, 14(5), 503–519.
    [Google Scholar]
  43. Porsani, M. J. (1999) Seismic trace interpolation using half‐step prediction filters. Geophysics, 64(5), 1461–1467.
    [Google Scholar]
  44. Richardson, A. (2018) Generative adversarial networks for model order reduction in seismic full‐waveform inversion. arXiv preprint. arXiv:1806.00828.
  45. Ronen, J. (1987) Wave‐equation trace interpolation. Geophysics, 52(7), 973–984.
    [Google Scholar]
  46. Sacchi, M. D. and Ulrych, T. J. (1996) Estimation of the discrete Fourier transform, a linear inversion approach. Geophysics, 61(4), 1128–1136.
    [Google Scholar]
  47. Sacchi, M. D., Ulrych, T. J. and Walker, C. J. (1998) Interpolation and extrapolation using a high‐resolution discrete Fourier transform. IEEE Transactions on Signal Processing, 46(1), 31–38.
    [Google Scholar]
  48. Safran, I. and Shamir, O. (2016) Depth separation in RELU networks for approximating smooth non‐linear functions. arXiv preprint. ,arXiv:1610.09887, 14 pp.
  49. Siahkoohi, A., Kumar, R. and Herrmann, F. (2018) Seismic data reconstruction with generative adversarial networks. In 80th EAGE Conference and Exhibition 2018, pp. 1–5. European Association of Geoscientists & Engineers.
    [Google Scholar]
  50. Siahkoohi, A., Louboutin, M. and Herrmann, F. J. (2019) The importance of transfer learning in seismic modeling and imaging. Geophysics, 84(6), A47–A52.
    [Google Scholar]
  51. Spitz, S. (1991) Seismic trace interpolation in the F‐X domain. Geophysics, 56(6), 785–794.
    [Google Scholar]
  52. Stolt, R. H. (2002) Seismic data mapping and reconstruction. Geophysics, 67(3), 890–908.
    [Google Scholar]
  53. Telgarsky, M. (2015) Representation benefits of deep feedforward networks. arXiv preprint. arXiv:1509.08101.
  54. Turquais, P., Asgedom, E. G., Söllner, W. and Gelius, L. (2018) Parabolic dictionary learning for seismic wavefield reconstruction across the streamers. Geophysics, 83(4), V263–V282.
    [Google Scholar]
  55. Vidal, R., Bruna, J., Giryes, R. and Soatto, S. (2017) Mathematics of deep learning. arXiv preprint. arXiv:1712.04741.
  56. Yi, Z., Zhang, H., Tan, P. and Gong, M. (2017) Dualgan: Unsupervised dual learning for image‐to‐image translation. In Proceedings of the IEEE International Conference on Computer Vision, pp. 2849–2857.
    [Google Scholar]
  57. Yu, S., Ma, J., Zhang, X. and Sacchi, M. D. (2015) Interpolation and denoising of high‐dimensional seismic data by learning a tight frame. Geophysics, 80(5), V119–V132.
    [Google Scholar]
  58. Zhu, J.‐Y., Park, T., Isola, P. and Efros, A. A. (2017) Unpaired image‐to‐image translation using cycle‐consistent adversarial networks. In Proceedings of the IEEE International Conference on Computer Vision, pp. 2223–2232.
    [Google Scholar]
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  • Article Type: Research Article
Keyword(s): Data processing; Interpolation; Neural networks; Signal processing

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