Advertisement

Machine Learning Using U-Net Convolutional Neural Networks for the Imaging of Sparse Seismic Data

Abstract

Machine learning using convolutional neural networks (CNNs) is investigated for the imaging of sparsely sampled seismic reflection data. A limitation of traditional imaging methods is that they often require seismic data with sufficient spatial sampling. Using CNNs for imaging, even if the spatial sampling of the data is sparse, good imaging results can still be obtained. Therefore, CNNs applied to seismic imaging have the potential of producing improved imaging results when spatial sampling of the data is sparse. The imaged model can then be used to generate more densely sampled data and in this way be used to interpolate either regularly or irregularly sampled data. Although there are many approaches for the interpolation of seismic data, here seismic imaging is performed directly with sparse seismic data once the CNN model has been trained. The CNN model is found to be relatively robust to small variations from the training dataset. For greater deviations, a larger training dataset would likely be required. If the CNN is trained with a sufficient amount of data, it has the potential of imaging more complex seismic profiles.

This is a preview of subscription content, log in to check access.

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

References

  1. Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro, C. et al. (2016). TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems. arXiv:1603.04467 [cs.DC]. Accessed 25 June 2019.

  2. Araya-Polo, M., Jennings, J., Adler, A., & Dahlke, T. (2018). Deep-learning tomography. The Leading. Edge,37(1), 58–66.

  3. Bengio, Y., Lamblin, P., Popovici, D., Larochelle, H. (2007). Greedy layer-wise training of deep networks. In J.D. Cowan, G. Tesauro, J. Alspector (Eds.), Advances in Neural Information Processing Systems, vol.19 (NIPS), (pp. 153–160). MIT Press.

  4. Bergen, K.J., Johnson, P.A., Hoop, M.V. de, Beroza, G.C. (2019). Machine learning for data-driven discovery in solid Earth geoscience. Science, 363(6433), eaau0323.

  5. Bhandare, A., Bhide, M., Gokhale, P., & Chandavarkar, R. (2016). Applications of convolutional neural networks. International Journal of Computer Science and Information Technologies,7(5), 2206–2215.

  6. Chellapilla, K., Puri, S., Simard, P. (2006). High performance convolutional neural networks for document processing. In Tenth International Workshop on Frontiers in Handwriting Recognition, Université de Rennes 1, La Baule, France, October 23–26 2006 (inria-00112631).

  7. Chen, Y., Chen, X., Wang, Y., & Zu, S. (2019). The interpolation of sparse geophysical data. Surveys in Geophysics,40(1), 73–105.

  8. Chollet, F. (2015). Keras. https://github.com/fchollet/keras. Accessed 1 Jun 2019.

  9. Clark, C., Storkey, A. (2015). Training deep convolutional neural networks to play go. In 32nd International Conference on Machine Learning, vol. 37 (pp. 1766–1774). Lille (06–11 Jul 2015).

  10. Di, H., Wang, Z., AlRegib, G. (2018). Deep convolutional neural networks for seismic salt-body delineation. AAPG 2018 Annual Convention and Exhibition. Salt Lake City (20–23 May 2018).

  11. Dice, L. R. (1945). Measures of the amount of ecologic association between species. Ecology,26(3), 297–302.

  12. Duchi, J., Hazan, E., & Singer, Y. (2011). Adaptive subgradient methods for online learning and stochastic optimization. Journal of Machine Learning Research,12, 2121–2159.

  13. Esteva, A., Kuprel, B., Novoa, R. A., Ko, J., Swetter, S. M., Blau, H. M., et al. (2017). Dermatologist-level classification of skin cancer with deep neural networks. Nature,542, 115–118.

  14. Fukushima, K., & Miyake, S. (1982). Neocognitron: A Self-Organizing Neural Network Model for a Mechanism of Visual Pattern Recognition. In S. Amari & M. A. Arbib (Eds.), Competition and Cooperation in Neural Nets. Lecture Notes in Biomathematics (Vol. 45, pp. 267–285). Berlin: Springer.

  15. Han, J., & Moraga, C. (1995). The influence of the sigmoid function parameters on the speed of backpropagation learning. In J. Mira & F. Sandoval (Eds.), International Workshop on Artificial Neural Networks. Lecture Notes in Computer Science (Vol. 930, pp. 195–201). Berlin: Springer.

  16. Hinton, G. E., Osindero, S., & Teh, Y.-W. (2006). A fast learning algorithm for deep belief nets. Neural Computation,18(7), 1527–1554.

  17. Hinton, G., Srivastava, N., Swersky, K. (2012). Neural networks for machine learning Lecture 6a Overview of mini-batch gradient descent. https://www.cs.toronto.edu/~hinton/coursera/lecture6/lec6.pdf. Accessed 3 May 2019.

  18. Hubel, D. H., & Wiesel, T. N. (1962). Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex. The Journal of physiology,160(1), 106–154.

  19. Ioffe, S., Szegedy, C. (2015). Batch normalization: Accelerating deep network training by reducing internal covariate shift. arXiv:1502.03167 [cs.LG]. Accessed 25 Jun 2019.

  20. Jia, Y., & Ma, J. (2017). What can machine learning do for seismic data processing? An interpolation application. Geophysics,82(3), V163–V177.

  21. Kingma, D.P., Ba, J. (2014). Adam: A method for stochastic optimization. arXiv:1412.6980 [cs.LG]. Accessed 25 Jul 2019.

  22. LeCun, Y., Bottou, L., Bengio, Y., Haffner, P., & Others., (1998). Gradient-based learning applied to document recognition. Proceedings of the IEEE,86(11), 2278–2324.

  23. LeCun, Y., Bengio, Y., & Hinton, G. (2015). Deep learning. Nature,521, 436–444.

  24. Li, S., Liu, B., Ren, Y., Chen, Y., Yang, S., Wang, Y., Jiang, P. (2019). Deep learning inversion of seismic data. arXiv:1901.07733 [cs.CV]. Accessed 25 Jul 2019.

  25. Maddison, C.J., Huang, A., Sutskever, I., Silver, D. (2014). Move evaluation in go using deep convolutional neural networks. arXiv:1412.6564 [cs.LG]. Accessed 24 Jun 2019.

  26. McCann, M. T., Jin, K. H., & Unser, M. (2017). Convolutional neural networks for inverse problems in imaging: A review. IEEE Signal Processing Magazine,34(6), 85–95.

  27. Perol, T., Gharbi, M., & Denolle, M. (2018). Convolutional neural network for earthquake detection and location. Science Advances,4(2), e1700578.

  28. Ronneberger, O., Fischer, P., & Brox, T. (2015a). Dental X-ray image segmentation using a U-shaped Deep Convolutional network. International Symposium on Biomedical Imaging-ISBI 2015.

  29. Ronneberger, O., Fischer, P., & Brox, T. (2015b). U-Net: Convolutional Networks for Biomedical Image Segmentation. In N. Navab, J. Hornegger, W. Wells, & A. Frangi (Eds.), International Conference on Medical image computing and computer-assisted intervention-MICCAI 2015. Lecture Notes in Computer Science (Vol. 9351, pp. 234–241). Cham: Springer.

  30. Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986). Learning representations by back-propagating errors. Nature,323, 533–536.

  31. TGS Salt Identification Challenge. (2018). https://www.kaggle.com/c/tgs-salt-identification-challenge. Accessed 5 May 2019.

  32. Sørensen, T. J. (1948). A method of establishing groups of equal amplitude in plant sociology based on similarity of species content and its application to analyses of the vegetation on Danish commons. Det Kongelige Danske Videnskabers Selskab Biologiske Skrifter,5, 1–34.

  33. Stockwell, J. W., Jr. (1999). The CWP/SU: seismic Un*x package. Computers & Geosciences,25(4), 415–419.

  34. Waldeland, A. U., Jensen, A. C., Gelius, L.-J., & Schistad Solberg, A. H. (2018). Convolutional neural networks for automated seismic interpretation. The Leading Edge,37(7), 529–537.

  35. Wang, B., Zhang, N., Lu, W., & Wang, J. (2018). Deep-learning-based seismic data interpolation: A preliminary result. Geophysics,84(1), V11–V20.

  36. Yuan, S., Liu, J., Wang, S., Wang, T., & Shi, P. (2018). Seismic waveform classification and first-break picking using convolution neural networks. IEEE Geoscience and Remote Sensing Letters,15(2), 272–276.

  37. Zeiler, M.D. (2012). ADADELTA: an adaptive learning rate method. arXiv:1212.5701 [cs.LG]. Accessed 4 Jun 2019.

Download references

Acknowledgements

The authors would like to thank the Editor and the reviewers for their constructive comments on the manuscript. The authors also thank Abdullah Khan Zehady for providing advice on CNN coding and model testing. This study was partially supported by NSF/EAR 1839322.

Author information

Correspondence to Jiayuan Huang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Huang, J., Nowack, R.L. Machine Learning Using U-Net Convolutional Neural Networks for the Imaging of Sparse Seismic Data. Pure Appl. Geophys. (2020). https://doi.org/10.1007/s00024-019-02412-z

Download citation

Keywords

  • Seismic imaging
  • Machine learning
  • Convolutional neural networks
  • Interpolation of seismic data