In geosciences, generative adversarial networks have been successfully applied to generate multiple realizations of rock properties from geological priors described by training images, within probabilistic seismic inversion and history matching methods. Here, the use of generative adversarial networks is proposed not as a model generator but as a model reconstruction technique for subsurface models where we do have access to sparse measurements of the subsurface properties of interest. We use sets of geostatistical realizations as training datasets combined with observed experimental data. These networks are applied to reconstruct nonstationary sedimentary channels and continuous elastic properties, such as P-wave propagation velocity, in the presence and absence of conditioning data. The reconstruction examples shown herein can be considered a post-processing step applied after seismic inversion and performed at those locations where the convergence of the inversion is low, and therefore, the inverted models are associated with high uncertainty. The application examples show the suitability of generative adversarial networks in learning the spatial structure of the data from sets of geostatistical realizations. The generated models reproduce the first- and second-order statistical moments and the spatial covariance matrix of the training dataset.
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Arjovsky, M., Bottou, L.: Towards principled methods for training generative adversarial networks. (2017). arXiv:1701.04862v1 [stat.ML]
Arjovsky, M., Chintala, S., Bottou, L.: Wasserstein generative adversarial networks. Proceedings of the 34th international conference on machine learning. PMLR. 70, 214–223 (2017)
Arpat, G., Caers, J.: Conditional simulation with patterns. Math. Geol. 39(2), 177–203 (2007). https://doi.org/10.1007/s11004-006-9075-3
Azevedo, L., Soares, A.: Geostatistical Methods for Reservoir Geophysics. Springer International Publishing (2017)
Barnett, S.A.: Convergence Problems with Generative Adversarial Networks. A dissertation presented for CCD Dissertations on a Mathematical Topic. Mathematical Institute. University of Oxford (2018). arXiv:1806.11382 [cs.LG]
Bjorck, J., Gomes, C., Selman, B., Weinerger, K.Q.: Understanding batch normalization. (2018). arXiv:1806.02375[cs.AI]
Bosch, M., Mukerji, T., Gonzalez, E.F.: Seismic inversion for reservoir properties combining statistical rock physics and geostatistics: a review. Geophysics. 75(5), 75A165 (2010). https://doi.org/10.1190/1.3478209
Caterini, A.L., Chang, D.E.: A novel representation of neural networks. (2016). arXiv:1610.01549v2 [stat.ML]
Caterini, A.L., Chang, D.E.: A geometric framework for convolutional neural networks. (2016). arXiv:1608.04374v2 [stat.ML]
Chan, S., Elsheikh, A.H.: Parametrization and generation of geological models with generative adversarial networks. (2017). arXiv: 1708,01810v1 [stat.ML]
Chan, S., Elsheikh, A.H.: Parametric generation of conditional geological realizations using generative neural networks. Comput. Geosci. 23, 925–952 (2019)
Cox, T.F., Cox, M.A.A.: Multidimensional Scaling. Chapman & Hall (1994)
Creswell, A., White, T., Dumoulin, V., Arulkumaran, K., Sengupta, B., Bharath, A.: Generative adversarial networks: an overview. IEEE Signal Process. Mag. 35(1), 53–65 (2018). https://doi.org/10.1109/MSP.2017.2765202
Daly, C., Caers, J.: Multi-point geostatistics—and introductory overview. First Break. 28(9), 39–47 (2010). https://doi.org/10.3997/1365-2397.2010020
Deutsch, C., Journel, A.G.: GSLIB: Geostatistical Software Library and Users’ Guide. Oxford University Press (1998)
Doyen P (2007) Seismic Reservoir Characterization: an Earth Modeling Perspective. EAGE
Dubrule, O.: Geostatistics for Seismic Data Integration in Earth Models. SEG/EAGE Distinguished Instructor Short Course Number 6, Tulsa (2003)
Dupont, E, Zhang, T, Tilke, P, Liang, L, Bailey, W. (2018). Generating realistic geology conditioned on physical measurements with generative adversarial networks. arXiv preprint arXiv:1802.03065
Ferreirinha, T., Nunes, R., Azevedo, L., Soares, A., Pratas, F., Tomás, P., Roma, N.: Acceleration of stochastic seismic inversion in OpenCL-based heterogeneous platforms. Comput Geosci. 26–36 (2015). https://doi.org/10.1016/j.cageo.2015.02.005
Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., Bengio, Y.: Generative adversarial networks. In: The twenty-eight annual conference on neural information processing systems (NIPS), Montréal, Canada (2014)
Grana, D., Della Rossa, E.: Probabilistic petrophysical-properties estimation integrating statistical rock physics with seismic inversion. Geophysics. 75(3), O21–O37 (2010). https://doi.org/10.1190/1.3386676
Gulrajani, I., Ahmed, F., Arjovsky, M. Dumoulin, V., Courville, A. (2017) Improved training of Wasserstein GANs. arXiv:1704.00028 [stat.ML]
Laloy, E., Hérault, R., Lee, J., Jacques, D., Linde, N.: Inversion using a new low-dimensional representation of complex binary geological media based on a deep neural network. Adv. Water Resour. 110, 387–405 (2017). https://doi.org/10.1016/j.advwatres.2017.09.029
Laloy, E., Hérault, R., Lee, J., Jacques, D., Linde, N.: Training-image based geostatistical inversion using a spatial generative adversarial neural network. Water Resour. Res. 54(1), 381–406 (2017). https://doi.org/10.1002/2017WR022148
Mariethoz, G., Caers, J.: Multiple-Point Geostatistics: Stochastic Modelling with Training Images, 376 pp. Wiley-Blackwell, Hoboken (2014)
Mariethoz, G., Renard, P., Straubhaar, J.: The direct sampling method to perform multiple-point geostatistical simulations. Water Resour. Res. 46(11), 1–14 (2010). https://doi.org/10.1029/2008WR007621
Mosser, L., Dubrule, O., Blunt, M.J.: Reconstruction of three-dimensional porous media using generative adversarial neural networks. Phys. Rev. E. 96, 043309 (2017). https://doi.org/10.1103/PhysRevE.96.043309
Mosser L, Kimman W, Dramsch J, Purves S, De la Fuente A, Ganssle G (2018) Rapid seismic domain transfer: seismic velocity inversion and modeling using deep generative neural networks. 80th EAGE conference and exhibition 2018. https://doi.org/10.3997/2214-4609.201800734
Mosser, L, Dubrule, O, Blunt, MJ (2018) Conditioning of three-dimensional generative adversarial networks for pore and reservoir-scale models. arXiv preprint arXiv:1802.05622
Radford A, Metz L, Chintala A (2016) Unsupervised representation learning with deep convolutional generative adversarial networks. arXiv: 1511.06434v2 [cs.LG]
Scheidt, C., Caers, J.: Representing spatial uncertainty using distances and kernels. Math. Geosci. 41, 397–419 (2009)
Soares, A.: Direct sequential simulation and cosimulation. Math. Geol. 33(8), 911–926 (2001). https://doi.org/10.1023/A:1012246006212
Springenberg J T, Dosovitskiy A, Brox T, Riedmiller M (2015) Striving for simplicity: the all convolutional net. arXiv:1412.6806v3 [cs.LG]
Strebelle, S.: Conditional simulation of complex geological structures using multiple-point statistics. Math. Geol. 34(1), 1–21 (2002). https://doi.org/10.1023/A:1014009426274
Tarantola, A.: Inverse Problem Theory. SIAM (2005)
Villani, C.: Optimal Transport: Old and New. Springer, Berlin (2009) ISBN 978-3-540-71049-3
Yeh, R.A., Chen, C., Lim, T.Y., Schwing, A.G., Hasegawa-Johnson, M., Do, M.N.: Semantic image inpainting with deep generative models. 2017 IEEE conference on computer vision and pattern recognition (CVPR). p. 6882–6890 (2017). https://doi.org/10.1109/CVPR.2017.728
The authors gratefully acknowledge the support of the CERENA (strategic project FCT-FCT-UIDB/04028/2020). The authors acknowledge Arjovsky, M., Chintala, S., and Bottou, L. for making available the WGAN algorithm (https://github.com/martinarjovsky/WassersteinGAN) and Mosser, L., Dubrule, O., and Blunt, M.J. for the geogan conde (https://github.com/LukasMosser/geogan). The authors acknowledge the fruitful discussions with the two anonymous reviewers.
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Azevedo, L., Paneiro, G., Santos, A. et al. Generative adversarial network as a stochastic subsurface model reconstruction. Comput Geosci (2020). https://doi.org/10.1007/s10596-020-09978-x
- Generative adversarial network
- Stochastic modeling
- Model reconstruction