Skip to main content
SpringerLink
Log in

Geological Facies modeling based on progressive growing of generative adversarial networks (GANs)

  • Original Paper
  • Published:
Computational Geosciences Aims and scope Submit manuscript

Abstract

Geological facies modeling has long been studied to predict subsurface resources. In recent years, generative adversarial networks (GANs) have been used as a new method for geological facies modeling with surprisingly good results. However, in conventional GANs, all layers are trained concurrently, and the scales of the geological features are not considered. In this study, we propose to train GANs for facies modeling based on a new training process, namely progressive growing of GANs or a progressive training process. In the progressive training process, GANs are trained layer by layer, and geological features are learned from coarse scales to fine scales. We also train a GAN in the conventional training process, and compare the conventionally trained generator with the progressively trained generator based on visual inspection, multi-scale sliced Wasserstein distance (MS-SWD), multi-dimensional scaling (MDS) plot visualization, facies proportion, variogram, and channel sinuosity, width, and length metrics. The MS-SWD reveals realism and diversity of the generated facies models, and is combined with MDS to visualize the relationship between the distributions of the generated and training facies models. The conventionally and progressively trained generators both have very good performances on all metrics. The progressively trained generator behaves especially better than the conventionally trained generator on the MS-SWD, MDS plots, and the necessary training time. The training time for the progressively trained generator can be as small as 39% of that for the conventionally trained generator. This study demonstrates the superiority of the progressive training process over the conventional one in geological facies modeling, and provides a better option for future GAN-related researches.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Pyrcz, M.J., Deutsch, C. V.: Geoestatistical Reservoir Modeling. (2014)

  2. Mariethoz, G., Caers, J.: Multiple-Point Geostatistics: Stochastic Modeling with Training Images. (2014)

  3. Zuo, C., Yin, Z., Pan, Z., MacKie, E.J., Caers, J.: A tree-based direct sampling method for stochastic surface and subsurface hydrological modeling. Water Resour. Res. 56, (2020). https://doi.org/10.1029/2019WR026130

  4. Yan, N., Mountney, N.P., Colombera, L., Dorrell, R.M.: A 3D forward stratigraphic model of fluvial meander-bend evolution for prediction of point-bar lithofacies architecture. Comput. Geosci. 105, 65–80 (2017). https://doi.org/10.1016/j.cageo.2017.04.012

    Article  Google Scholar 

  5. Tahmasebi, P., Kamrava, S., Bai, T., Sahimi, M.: Machine Learning in Geo- and Environmental Sciences: from Small to Large Scale, (2020)

  6. Avalos, S., Ortiz, J.M.: Recursive convolutional neural networks in a multiple-point statistics framework. Comput. Geosci. 141, 104522 (2020). https://doi.org/10.1016/j.cageo.2020.104522

    Article  Google Scholar 

  7. Ian Goodfellow, Yoshua Bengio, A.C.: Deep Learning. (2015)

  8. Gan, Z., Henao, R., Carlson, D., Carin, L.: Learning Deep Sigmoid Belief Networks with Data Augmentation. In: Journal of Machine Learning Research (2015)

  9. Larochelle, H., Murray, I.: The Neural Autoregressive Distribution Estimator. In: Proceedings of the 14th International Conference on Artificial Intelligence and Statistics (AISTATS 2011) (2011)

  10. Van Den Oord, A., Kalchbrenner, N., Vinyals, O., Espeholt, L., Graves, A., Kavukcuoglu, K.: Conditional Image Generation with PixelCNN Decoders. In: Advances in Neural Information Processing Systems (2016)

  11. Rezende, D.J., Mohamed, S., Wierstra, D.: Stochastic backpropagation and approximate inference in deep generative models. In: 31st Int;ernational Conference on Machine Learning, ICML 2014 (2014)

  12. Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., Bengio, Y.: Generative Adversarial Networks. In: Advances in Neural Information Processing Systems 27 (2014)

  13. Radford, A., Metz, L., Chintala, S.: Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks. arXiv e-prints. arXiv:1511.06434 (2015)

  14. Arjovsky, M., Chintala, S., Bottou, L.: Wasserstein GAN. arXiv e-prints. arXiv:1701.07875 (2017)

  15. Gulrajani, I., Ahmed, F., Arjovsky, M., Dumoulin, V., Courville, A.: Improved Training of Wasserstein GANs. arXiv e-prints. arXiv:1704.00028 (2017)

  16. Zhu, J.Y., Park, T., Isola, P., Efros, A.A.: Unpaired Image-to-Image Translation Using Cycle-Consistent Adversarial Networks. In: Proceedings of the IEEE International Conference on Computer Vision (2017)

  17. Karras, T., Aila, T., Laine, S., Lehtinen, J.: Progressive Growing of GANs for Improved Quality, Stability, and Variation. arXiv e-prints. arXiv:1710.10196 (2017)

  18. Karras, T., Laine, S., Aila, T.: A Style-Based Generator Architecture for Generative Adversarial Networks. arXiv e-prints. arXiv:1812.04948 (2018)

  19. Dumoulin, V., Belghazi, I., Poole, B., Mastropietro, O., Lamb, A., Arjovsky, M., Courville, A.: Adversarially Learned Inference. arXiv e-prints. arXiv:1606.00704 (2016)

  20. Van Den Oord, A., Dieleman, S., Zen, H., Simonyan, K., Vinyals, O., Graves, A., Kalchbrenner, N., Senior, A., Kavukcuoglu, K.: WaveNet: A Generative Model for Raw Audio. arXiv e-prints. arXiv:1609.03499 (2016)

  21. Ledig, C., Theis, L., Huszar, F., Caballero, J., Cunningham, A., Acosta, A., Aitken, A., Tejani, A., Totz, J., Wang, Z., Shi, W.: Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network. arXiv e-prints. arXiv:1609.04802 (2016)

  22. Reed, S., Akata, Z., Yan, X., Logeswaran, L., Schiele, B., Lee, H.: Generative Adversarial Text to Image Synthesis. arXiv e-prints. arXiv:1605.05396 (2016)

  23. Isola, P., Zhu, J.-Y., Zhou, T., Efros, A.A.: Image-to-Image Translation with Conditional Adversarial Networks. arXiv e-prints. arXiv:1611.07004 (2016)

  24. 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

    Article  Google Scholar 

  25. Mosser, L., Dubrule, O., Blunt, M.J.: Reconstruction of three-dimensional porous media using generative adversarial neural networks. Phys. Rev. E. 96, (2017). https://doi.org/10.1103/PhysRevE.96.043309

  26. Mosser, L., Dubrule, O., Blunt, M.J.: Stochastic reconstruction of an Oolitic limestone by generative adversarial networks. Transp. Porous Media. 125, 81–103 (2018). https://doi.org/10.1007/s11242-018-1039-9

    Article  Google Scholar 

  27. Chan, S., Elsheikh, A.H.: Parametrization and generation of geological models with generative adversarial networks, (2017)

  28. Wu, J., Zhang, C., Xue, T., Freeman, W.T., Tenenbaum, J.B.: Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling. arXiv e-prints. arXiv:1610.07584 (2016)

  29. Zhang, T.F., Tilke, P., Dupont, E., Zhu, L.C., Liang, L., Bailey, W.: Generating geologically realistic 3D reservoir facies models using deep learning of sedimentary architecture with generative adversarial networks. Pet. Sci. 16, 541–549 (2019). https://doi.org/10.1007/s12182-019-0328-4

    Article  Google Scholar 

  30. Mogren, O.: C-RNN-GAN: Continuous recurrent neural networks with adversarial training. arXiv e-prints. arXiv:1611.09904 (2016)

  31. Ma, L., Jia, X., Sun, Q., Schiele, B., Tuytelaars, T., Van Gool, L.: Pose Guided Person Image Generation. arXiv e-prints. arXiv:1705.09368 (2017)

  32. Zhang, H., Xu, T., Li, H., Zhang, S., Wang, X., Huang, X., Metaxas, D.: StackGAN: Text to Photo-realistic Image Synthesis with Stacked Generative Adversarial Networks. arXiv e-prints. arXiv:1612.03242 (2016)

  33. Lucic, M., Kurach, K., Michalski, M., Gelly, S., Bousquet, O.: Are GANs Created Equal? A Large-Scale Study. arXiv e-prints. arXiv:1711.10337 (2017)

  34. Tran, T.T.: Improving variogram reproduction on dense simulation grids. Comput. Geosci. 20, 1161–1168 (1994). https://doi.org/10.1016/0098-3004(94)90069-8

    Article  Google Scholar 

  35. Strebelle, S.: Conditional simulation of complex geological structures using multiple-point statistics. Math. Geol. 34, 1–21 (2002). https://doi.org/10.1023/A:1014009426274

    Article  Google Scholar 

  36. Liu, Y.: Using the Snesim program for multiple-point statistical simulation. Comput. Geosci. 32, 1544–1563 (2006). https://doi.org/10.1016/j.cageo.2006.02.008

    Article  Google Scholar 

  37. Arpat, G.B., Caers, J.: Conditional simulation with patterns. Math. Geol. 39, 177–203 (2007). https://doi.org/10.1007/s11004-006-9075-3

    Article  Google Scholar 

  38. He, K., Zhang, X., Ren, S., Sun, J.: Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification. In: IEEE International Conference on Computer Vision. pp. 1026–1034 (2015)

  39. Kingma, D., Ba, J.: Adam: a method for stochastic optimization. arXiv Prepr. arXiv1412.6980. (2014). https://doi.org/10.1109/ICCE.2017.7889386

  40. Borji, A.: Pros and Cons of GAN Evaluation Measures. arXiv e-prints. arXiv:1802.03446 (2018)

  41. Wang, Z., Simoncelli, E.P., Bovik, A.C.: Multiscale structural similarity for image quality assessment. In: The Thrity-Seventh Asilomar Conference on Signals, Systems & Computers, 2003. pp. 1398–1402 (2003)

  42. Mosser, L., Dubrule, O., Blunt, M.J.: Stochastic seismic waveform inversion using generative adversarial networks as a geological prior. Math. Geosci. 52, 53–79 (2020). https://doi.org/10.1007/s11004-019-09832-6

    Article  Google Scholar 

  43. Zhong, Z., Sun, A.Y., Jeong, H.: Predicting CO 2 plume migration in heterogeneous formations using conditional deep convolutional generative adversarial network. Water Resour. Res. 55, 5830–5851 (2019). https://doi.org/10.1029/2018wr024592

    Article  Google Scholar 

  44. Burt, P.J., Adelson, E.H.: Readings in Computer Vision: Issues, Problems, Principles, and Paradigms. Presented at the (1987)

  45. Rabin, J., Peyré, G., Delon, J., Bernot, M.: Wasserstein barycenter and its application to texture mixing. In: Bruckstein, A.M., ter Haar Romeny, B.M., Bronstein, A.M., and Bronstein, M.M. (eds.) Scale Space and Variational Methods in Computer Vision. pp. 435–446. Springer Berlin Heidelberg, Berlin, Heidelberg (2012)

  46. Scheidt, C., Caers, J.: Representing spatial uncertainty using distances and kernels. Math. Geosci. 41, 397–419 (2009). https://doi.org/10.1007/s11004-008-9186-0

    Article  Google Scholar 

  47. Azevedo, L., Paneiro, G., Santos, A., Soares, A.: Generative adversarial network as a stochastic subsurface model reconstruction. Comput. Geosci. 24, 1673–1692 (2020). https://doi.org/10.1007/s10596-020-09978-x

    Article  Google Scholar 

  48. Laloy, E., Hérault, R., Jacques, D., Linde, N.: Training-image based Geostatistical inversion using a spatial generative adversarial neural network. Water Resour. Res. 54, 381–406 (2018). https://doi.org/10.1002/2017WR022148

    Article  Google Scholar 

  49. Nesvold, E., Mukerji, T.: Geomodeling Using Generative Adversarial Networks and a Database of Satellite Imagery of Modern River Deltas. In: Petroleum Geostatistics (2019)

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China (42072146). We acknowledge the sponsors of the Stanford Center for Earth Resources Forecasting (SCERF) and support from Prof. Steve Graham, the Dean of the Stanford School of Earth, Energy and Environmental Sciences. Some of the computing for this project was performed on the Sherlock cluster at Stanford University. We would like to thank Stanford University and the Stanford Research Computing Center for providing computational resources and support that contributed to these research results. Codes, data, and some results of this work are available at the GitHub site (https://github.com/SuihongSong/GeoModeling_Unconditional_ProGAN).

Author information

Authors and Affiliations

  1. State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum (Beijing), Beijing, 102249, China

    Suihong Song & Jiagen Hou

  2. College of Geoscience, China University of Petroleum (Beijing), Beijing, 102249, China

    Suihong Song & Jiagen Hou

  3. Stanford University, 367 Panama St, Stanford, CA, 94305, USA

    Suihong Song & Tapan Mukerji

Authors
  1. Suihong Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tapan Mukerji
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jiagen Hou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiagen Hou.

Additional information

Publisher’s note

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

Key Points

• Progressive growing of GANs is used for geological facies modeling, where geological features are learned from large scales to fine scales.

• Multi-scale sliced Wasserstein distance, multi-dimensional scaling plot, facies proportion, variogram, and channel sinuosity, width, and length are proposed as metrics to evaluate GANs.

• Progressive growing of GANs behaves better than conventional training processes in many metrics including computation time.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Song, S., Mukerji, T. & Hou, J. Geological Facies modeling based on progressive growing of generative adversarial networks (GANs). Comput Geosci 25, 1251–1273 (2021). https://doi.org/10.1007/s10596-021-10059-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10596-021-10059-w

Keywords

Search

Navigation