Abstract
Migration deconvolution is an image domain approach to least-squares migration, which is considered the state-of-the-art algorithm for obtaining seismic reflectivity models of the earth from seismic acquisition results. Seismic imaging is an active research field with the development over the last few years of several techniques that have mitigated imaging issues. Ongoing research aims to improve image resolution and thus provide a more reliable seismic amplitude for the interpreter. Migration deconvolution can be framed as an inverse problem in the image domain to mitigate image resolution problems and reduce migration artifacts. This paper presents a migration deconvolution method via deep learning based on the Hessian filter least-squares migration (HF-LSM) algorithm. The idea is to use deep learning techniques to model the inverse operator instead of directly estimating the inverse Hessian matrix. A data set is generated from a given velocity model by applying Born modeling to the migrated image, followed by application of the reverse time migration algorithm. The resultant data set is then used to train several neural network models. The networks learn the blurring operator that describes the image degradation due to the effects of acquisition geometry. Three different network topologies were developed to handle this problem: a simple fully convolutional neural network, a U-Net and a generative adversarial network. Our results show that the proposed approach provides images of higher resolution and superior quality than the traditional HF-LSM workflow.
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References
Albluwi, F., Krylov, V.A., & Dahyot, R. (2018). Image deblurring and super-resolution using deep convolutional neural networks. In 2018 IEEE 28th international workshop on machine learning for signal processing (MLSP), IEEE, pp. 1–6.
Aminzadeh, F., Jean, B., & Kunz, T. (1997). 3-D salt and overthrust models. Society of Exploration Geophysicists.
Arjovsky, M., Chintala, S., & Bottou, L. (2017). Wasserstein GAN. arXiv:1701.07875, 1701.07875.
Cavalca, M., Fletcher, R., & Nichols, D. (2018). Image-domain least-squares migration in rapidly-varying media: practical considerations. In First EAGE/SBGf workshop on least-squares migration, European Association of Geoscientists & Engineers, pp. 1–5.
Chavent, G., & Plessix, R. E. (1999). An optimal true-amplitude least-squares prestack depth-migration operator. Geophysics, 64(2), 508–515.
Chevitarese, D., Szwarcman, D., Silva, R.M.D., & Brazil EV. (2018). Seismic facies segmentation using deep learning. AAPG Annual and Exhibition.
Flamary, R. (2017). Astronomical image reconstruction with convolutional neural networks. In 2017 25th European signal processing conference (EUSIPCO), IEEE, pp. 2468–2472.
Fletcher, R.P., Nichols, D., Bloor, R., & Coates, R.T. (2016a). Least-squares migration - data domain versus image domain using point spread functions. The Leading Edge, 35(2), 157–162. https://doi.org/10.1190/tle35020157.1. https://pubs.geoscienceworld.org/tle/article-pdf/35/2/157/3099260/gsedge_35_2_157.pdf).
Fletcher, R. P., Nichols, D., Bloor, R., & Coates, R. T. (2016b). Least-squares migration—data domain versus image domain using point spread functions. The Leading Edge, 35(2), 157–162.
Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., & Bengio, Y. (2014). Generative adversarial nets. In Z. Ghahramani, M. Welling, C. Cortes, N.D. Lawrence, & K.Q. Weinberger (Eds.) Advances in neural information processing systems (vol. 27, pp. 2672–2680). Curran Associates, Inc. http://papers.nips.cc/paper/5423-generative-adversarial-nets.pdf.
Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep learning. MIT Press. http://www.deeplearningbook.org.
Guitton, A. (2004). Amplitude and kinematic corrections of migrated images for nonunitary imaging operators. Geophysics, 69(4), 1017–1024.
Gulrajani, I. Ahmed, F., Arjovsky, M., Dumoulin, V., & Courville, A. (2017). Improved training of wasserstein GANs. arXiv:1704.00028, 1704.00028.
Hu, J., & Schuster, G.T. (1998). Migration deconvolution. In Mathematical methods in geophysical imaging V. International Society for Optics and Photonics, vol. 3453, pp. 118–124.
Huang, J., & Nowack, R.L. (2020). Machine learning using U-net convolutional neural networks for the imaging of sparse seismic data. Pure and Applied Geophysics, pp. 1–16.
Kaur, H., Pham, N., & Fomel, S. (2019). Estimating the inverse hessian for amplitude correction of migrated images using deep learning. In: SEG Technical Program Expanded Abstracts 2019, Society of Exploration Geophysicists, pp. 2278–2282.
Kaur, H. P., Pham, N., & Fomel, S. (2020). Improving the resolution of migrated images by approximating the inverse Hessian using deep learning. Geophysics, 85(4), WA173–WA183.
Kazei, V., Guo, Q., & Alkhalifah, T. (2020). High-resolution time-lapse FWI with spatio-spectral regularization. In 82nd EAGE annual conference & exhibition, vol. 2020, no. 1, pp. 1–5. https://doi.org/10.3997/2214-4609.202011849.
LeCun, Y., et al. (1989). Generalization and network design strategies. In Connectionism in perspective, vol. 19, Citeseer.
Li, S., Liu, B., Ren, Y., Chen, Y., Yang, S., Wang, Y., & Jiang, P. (2019). Deep learning inversion of seismic data. preprint arXiv:190107733.
Liu, Z., & Schuster, G. (2019). Multilayer sparse LSM: deep neural network. In SEG Technical Program Expanded Abstracts, pp. 2323–2327. https://doi.org/10.1190/segam2019-3215033.1.
Lucas, A., Iliadis, M., Molina, R., & Katsaggelos, A. K. (2018). Using deep neural networks for inverse problems in imaging: beyond analytical methods. IEEE Signal Processing Magazine, 35(1), 20–36.
Mandelli, S., Lipari, V., Bestagini, P., & Tubaro, S. (2019). Interpolation and denoising of seismic data using convolutional neural networks. arXiv:190107927.
McCann, M.T., Jin, K.H., & Unser, M. (2017). A review of convolutional neural networks for inverse problems in imaging. arXiv:171004011.
Nemeth, T., Wu, C., & Schuster, G. T. (1999). Least-squares migration of incomplete reflection data. Geophysics, 64(1), 208–221.
Papyan, V., Romano, Y., Sulam, J., & Elad, M. (2018). Theoretical foundations of deep learning via sparse representations: a multilayer sparse model and its connection to convolutional neural networks. IEEE Signal Processing Magazine, 35(4), 72–89.
Pereira-Dias, B., Bulcão, A., Filho, D.M.S., Santos, L.A., Dias, Rd.M., Loureiro, F.P., & de Souza Duarte, F. (2017). Least-squares migration in the image domain with sparsity constraints: an approach for super-resolution in depth imaging. In 15th International Congress of the Brazilian Geophysical Society & EXPOGEF, Rio de Janeiro, Brazil, 31 July–3 August 2017, Brazilian Geophysical Society, pp. 1213–1218.
Picetti, F., Lipari, V., Bestagini, P., & Tubaro, S. (2019). Seismic image processing through the generative adversarial network. Interpretation, 7(3), SF15–SF26.
Plessix, R. E., & Mulder, W. (2004). Frequency-domain finite-difference amplitude-preserving migration. Geophysical Journal International, 157(3), 975–987.
Ran, X., Xue, L., Zhang, Y., Liu, Z., Sang, X., & He, J. (2019). Rock classification from field image patches analyzed using a deep convolutional neural network. Mathematics, 7(8), 755.
Richardson, A., & Feller, C. (2019). Seismic data denoising and deblending using deep learning. arXiv:190701497.
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.
Schuster, G.T. (1993). Least-squares cross-well migration. In: SEG Technical Program Expanded Abstracts 1993, Society of Exploration Geophysicists, pp. 110–113.
Schuster, G.T. (2017). Seismic inversion. Society of Exploration Geophysicists.
Shi, Y., Wu, X., & Fomel, S. (2018). Automatic salt-body classification using a deep convolutional neural network. In SEG Technical Program Expanded Abstracts 2018, Society of Exploration Geophysicists, pp. 1971–1975.
Stoughton, D., Stefani, J., & Michell, S. (2001). 2D elastic model for wavefield investigations of subsalt objectives, deep water gulf of mexico. In SEG Technical Program Expanded Abstracts 2001, Society of Exploration Geophysicists, pp. 1269–1272.
Wang, P., Gomes, A., Zhang, Z., & Wang, M. (2016). Least-squares RTM: Reality and possibilities for subsalt imaging. In SEG Technical Program Expanded Abstracts 2016, Society of Exploration Geophysicists, pp. 4204–4209.
Wei, Z., Hu, H., Hw, Zhou, & Lau, A. (2019). Characterizing rock facies using machine learning algorithm based on a convolutional neural network and data padding strategy. Pure and Applied Geophysics, 176(8), 3593–3605.
Wong, M., Ronen, S., & Biondi, B. (2011). Least-squares reverse time migration/inversion for ocean bottom data: a case study. In SEG Technical Program Expanded Abstracts 2011, Society of Exploration Geophysicists, pp. 2369–2373.
Xiang, P., Wang, L., Cheng, J., Zhang, B., & Wu, J. (2017). A deep network architecture for image inpainting. In 2017 3rd IEEE international conference on computer and communications (ICCC), IEEE, pp. 1851–1856.
Xu, L., Ren, J.S., Liu, C., & Jia, J. (2014). Deep convolutional neural network for image deconvolution. In: Advances in neural information processing systems, pp. 1790–1798.
Yang, F., & Ma, J. (2019). Deep-learning inversion: a next generation seismic velocity-model building method. Geophysics, 84(4), 1–133.
Zhang, Y., Duan, L., & Xie, Y. (2014). A stable and practical implementation of least-squares reverse time migration. Geophysics, 80(1), V23–V31.
Zhu, J.Y., Park, T., Isola, P., & 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.
Acknowledgements
The authors would like to thank PETROBRAS for providing financial support to this project as well for authorizing the publication of the results. We would also like to thank the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) for providing scholarships to the authors. Nvidia Corporation provided the computational resources required for this research.
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Appendices
Appendix 1: Neural Network Topologies
This appendix presents details of the neural network topologies proposed in this work, such as activation functions and the kernel size of each convolutional layer, among others, as shown in the Tables 2, 3 and 4 for the SFCNN, WGAN and U-Net topologies, respectively.
Appendix 2: Parallel Plan Velocity Model Results
This section presents the results obtained for the parallel plan velocity model. See Fig. 3.
a Parallel plan velocity model. b Filtered parallel plan reflectivity model. c The network input (\(m_2\)). d The network target (\(m_1\)). e The HF-LSM result. f The result for SFCNN topology. g The result for U-Net topology. h The result for WGAN topology
Appendix 3: Modified SEG/EAGE Velocity Model Results
This section shows the results obtained for the modified SEG/EAGE velocity model. See Fig. 4.
a SEG/EAGE velocity model. b SEG/EAGE filtered reflectivity model. c The network input (\(m_2\)). d The network target (\(m_1\)). e The HF-LSM result. f The result for SFCNN topology. g The result for U-Net topology. h The result for WGAN topology
Appendix 4: SMAART Pluto Velocity Model Results
This section presents the results obtained for the SMAART Pluto velocity model, with a more detailed discussion of these results given in Sect. 4.3. See Figs. 5, 6, 7, 8, 9 and 10.
a SMAART Pluto velocity model. b Filtered SMAART Pluto reflectivity model. c The network input (\(m_2\)). d The network target (\(m_1\)). e The HF-LSM result. f The result for SFCNN topology. g The result for U-Net topology. h The result for WGAN topology
Wavenumber amplitude spectra from Fig. 6a–e. a Filtered reflectivity model. b The network target, \(\mathbf{m}_1\). c The HF-LSM result. d The result for SFCNN topology. e The result for U-Net topology. f The result for WGAN topology
Normalized mean vertical spectra of the images: filtered reflectivity model, the HF-LSM result, the network target and the results of SFCNN, U-Net and WGAN topology
Curves extracted at a depth of 8991.6 m
a Zoom view of the region where the pseudo-wells are extracted on the filtered reflectivity model. b Pseudo-well comparison at 28 km
Appendix 5: Evaluation Measures for All Velocity Models
Table 5 shows the evaluation measures for all velocity models tested. As we can see from the results, the neural networks achieved better results than the HF-LSM method for both PSNR and SSIM. This shows that the networks were better amplitude-wise and structurally.
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Avila, M.R.V., Osorio, L.N., de Castro Vargas Fernandes, J. et al. Migration Deconvolution via Deep Learning. Pure Appl. Geophys. 178, 1677–1695 (2021). https://doi.org/10.1007/s00024-021-02707-0
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DOI: https://doi.org/10.1007/s00024-021-02707-0