Skip to main content

Advertisement

SpringerLink
Log in

Automatic reconstruction method of 3D geological models based on deep convolutional generative adversarial networks

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

Abstract

How to reconstruct a credible three-dimensional (3D) geological model from very limited survey data, e.g. boreholes, outcrop, and two-dimensional (2D) images, is challenging in the field of 3D geological modeling. Against the limitations of the huge computational consumption and complex parameterization of geostatistics-based stochastic simulation methods, we propose an automatic reconstruction method of 3D geological models based on deep convolutional generative adversarial network (DCGAN). In this work, 2D geological sections are used as conditioning data to generate 3D geological models automatically. Various realizations can be reproduced under a same DCGAN model established through deep network training. A U-Net structure is used to enhance the fitting effect of the DCGAN model. In addition, joint loss functions are exploited to increase the similarity between 3D realizations and reference models. Three synthetic datasets were used to verify the capability of the method presented in this paper. Experimental results show that the proposed 3D automatic reconstruction method based on DCGAN can capture the features, trends and spatial patterns of geological structures well. The output models obey the used conditioning data. The complex heterogeneous structures are reconstructed more accurately and quickly by using the proposed method.

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

Data availability

The test data used in this work were collected from open datasets, with appropriate citations given in this paper. They are available on request from the corresponding author (chenqiyu403@163.com).

References

  1. Arjovsky, M., Chintala, S., Bottou, L.: Wasserstein generative adversarial networks. In: International conference on machine learning. PMLR, pp. 214–223 (2017)

  2. Arpat, G.B., Caers, J.: Conditional simulation with patterns. Math. Geol. 39(2), 177–203 (2007)

    Google Scholar 

  3. Bai, T., Tahmasebi, P.: Hybrid geological modeling: combining machine learning and multiple-point statistics. Comput. Geosci. 142, 104519 (2020)

    Google Scholar 

  4. Bynagari, N.B.: GANs trained by a two time-scale update rule converge to a local Nash equilibrium. Asian Journal of Applied Science and Engineering. 8, 25–34 (2019)

    Google Scholar 

  5. Chan, S., Elsheikh, A.H.: Parametrization of stochastic inputs using generative adversarial 21 networks with application in geology. Front. Water. 2, 5 (2020)

    Google Scholar 

  6. Chen, L.C., Papandreou, G., Kokkinos, I., Murphy, K., Yuille, A.L.: Deeplab: semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected crfs. IEEE Trans. Pattern Anal. Mach. Intell. 40(4), 834–848 (2017)

    Google Scholar 

  7. Chen, Q., Liu, G., Ma, X., Li, X., He, Z.: 3D stochastic modeling framework for quaternary sediments using multiple-point statistics: a case study in Minjiang estuary area, Southeast China. Comput. Geosci. 136, 104404 (2020)

    Google Scholar 

  8. Chen, Q., Liu, G., Ma, X., Zhang, J., Zhang, X.: Conditional multiple-point geostatistical simulation for unevenly distributed sample data. Stoch. Env. Res. Risk A. 33(4), 973–987 (2019)

    Google Scholar 

  9. Chen, Q., Mariethoz, G., Liu, G., Comunian, A., Ma, X.: Locality-based 3-D multiple-point statistics reconstruction using 2-D geological cross sections. Hydrol. Earth Syst. Sci. 22(12), 6547–6566 (2018)

    Google Scholar 

  10. Chen, T., Cheng, M.M., Tan, P., Shamir, A., Hu, S.M.: Sketch2photo: internet image montage. ACM Trans. Graph. 28(5), 1–10 (2009)

    Google Scholar 

  11. Chen, X., Wan, D.: GPU accelerated MPS method for large-scale 3-D violent free surface flows. Ocean Eng. 171, 677–694 (2019)

    Google Scholar 

  12. Cui, Z., Chen, Q., Liu, G., Ma, X., Que, X.: Multiple-point geostatistical simulation based on conditional conduction probability. Stoch. Env. Res. Risk A. 35, 1355–1368 (2021a)

    Google Scholar 

  13. Cui, Z., Chen, Q., Liu, G., Mariethoz, G., Ma, X.: Hybrid parallel framework for multiple-point geostatistics on Tianhe-2: a robust solution for large-scale simulation. Comput. Geosci. 157, 104923 (2021b)

    Google Scholar 

  14. Demir, U., Unal, G.: Patch-based image inpainting with generative adversarial networks. arXiv preprint arXiv:1803.07422 (2018)

  15. Deutsch, C.V., Tran, T.T.: FLUVSIM: a program for object-based stochastic modeling of fluvial depositional systems. Comput. Geosci. 28(4), 525–535 (2002)

    Google Scholar 

  16. Dramsch, J.S.: 70 years of machine learning in geoscience in review. Adv. Geophys. 61, 1–55 (2020)

    Google Scholar 

  17. Dubey, A.K., Jain, V.: Comparative study of convolution neural network’s relu and leaky-relu activation functions. In:Applications of Computing, Automation and Wireless Systems in Electrical Engineering. Springer, Singapore, pp. 873–880 (2019)

  18. Dupont, E., Zhang, T., Tilke, P., Liang, L., Bailey, W.: Generating realistic geology conditioned on physical measurements with generative adversarial networks. arXiv preprint arXiv:1802.03065 (2018)

  19. Fang, W., Zhang, F., Sheng, V.S., Ding, Y.: A method for improving CNN-based image recognition using DCGAN. Computers, Materials and Continua. 57(1), 167–178 (2018)

    Google Scholar 

  20. Feng, J., He, X., Teng, Q., Ren, C., Chen, H., Li, Y.: Reconstruction of porous media from extremely limited information using conditional generative adversarial networks. Phys. Rev. E. 100(3), 033308 (2019)

    Google Scholar 

  21. Feng, J., Teng, Q., Li, B., He, X., Chen, H., Li, Y.: An end-to-end three-dimensional reconstruction framework of porous media from a single two-dimensional image based on deep learning. Comput. Methods Appl. Mech. Eng. 368, 113043 (2020)

    Google Scholar 

  22. Gan, Z., Henao, R., Carlson, D., Carin, L.: Learning deep sigmoid belief networks with data augmentation. In: Artificial Intelligence and Statistics. PMLR, pp. 268–276 (2015)

  23. Gao, M., He, X., Teng, Q., Zuo, C., Chen, D.: Reconstruction of three-dimensional porous media from a single two-dimensional image using three-step sampling. Phys. Rev. E. 91(1), 013308 (2015)

    Google Scholar 

  24. Gatys, L., Ecker, A.S., Bethge, M.: Texture synthesis using convolutional neural networks. Adv. Neural Inf. Proces. Syst. 28, 262–270 (2015)

    Google Scholar 

  25. Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., Bengio, Y.: Generative adversarial nets. In: Advances in neural information processing systems. pp. 2672–2680 (2014)

  26. Goodfellow, I., Bengio, Y., Courville, A.: Deep learning. MIT Press. (2016)

  27. Guardiano, F.B., Srivastava, R.M.: Multivariate geostatistics: beyond bivariate moments. In: Geostatistics Troia’92. Springer, Dordrecht, pp. 133–144 (1993)

  28. Guo, J., Li, Y., Jessell, M., Giraud, J., Li, C., Wu, L., Li, F., Liu, S.: 3D geological structure inversion from Noddy-generated magnetic data using deep learning methods. Comput. Geosci. 149, 104701 (2021)

    Google Scholar 

  29. Hermans, T., Nguyen, F., Caers, J.: Uncertainty in training image-based inversion of hydraulic head data constrained to ERT data: workflow and case study. Water Resour. Res. 51(7), 5332–5352 (2015)

    Google Scholar 

  30. Hori, C., Gotoh, H., Ikari, H., Khayyer, A.: GPU-acceleration for moving particle semi-implicit method. Comput. Fluids. 51(1), 174–183 (2011)

    Google Scholar 

  31. Ioffe, S., Szegedy, C.: Batch normalization: Accelerating deep network training by reducing internal covariate shift. In: International conference on machine learning. PMLR, pp. 448–456 (2015)

  32. Isola, P., Zhu, J.Y., Zhou, T., Efros, A.A.: Image-to-image translation with conditional adversarial networks. In: Proceedings of the IEEE conference on computer vision and pattern recognition. pp. 1125–1134 (2017)

  33. Jessell, M., Pakyuz-Charrier, E., Lindsay, M., Giraud, J., de Kemp, E., Arribas, A.M., Mauk, J.L.: Assessing and mitigating uncertainty in three-dimensional geologic models in contrasting geologic scenarios. Metals, Minerals, and Society. 21, 63–74 (2018)

    Google Scholar 

  34. Jessell, M., Guo, J., Li, Y., Lindsay, M., Scalzo, R., Giraud, J., Pirot, G., Cripps, E., Ogarko, V.: Into the Noddyverse: a massive data store of 3D geological models for machine learning and inversion applications. Earth System Science Data. 14(1), 381–392 (2022)

    Google Scholar 

  35. Karpatne, A., Ebert-Uphoff, I., Ravela, S., Babaie, H.A., Kumar, V.: Machine learning for the geosciences: challenges and opportunities. IEEE Trans. Knowl. Data Eng. 31(8), 1544–1554 (2018)

    Google Scholar 

  36. Kingma, D.P., Welling, M.: An introduction to variational autoencoders. Foundations and Trends® in Machine Learning, 12(4), 307–392 (2019)

  37. 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)

    Google Scholar 

  38. Li, L., Srinivasan, S., Zhou, H., Gomez-Hernandez, J.J.: Two-point or multiple-point statistics? A comparison between the ensemble Kalman filtering and the ensemble pattern matching inverse methods. Adv. Water Resour. 86, 297–310 (2015)

    Google Scholar 

  39. Linde, N., Renard, P., Mukerji, T., Caers, J.: Geological realism in hydrogeological and geophysical inverse modeling: a review. Adv. Water Resour. 86, 86–101 (2015)

    Google Scholar 

  40. Liu, Q., Liu, W., Yao, J., Liu, Y., Pan, M.: An improved method of reservoir facies modeling based on generative adversarial networks. Energies. 14(13), 3873 (2021)

    Google Scholar 

  41. Mariethoz, G., Caers, J.: Multiple-point geostatistics: stochastic modeling with training images. John Wiley & Sons. (2014)

  42. Mariethoz, G., Renard, P., Straubhaar, J.: The direct sampling method to perform multiple-point geostatistical simulations. Water Resour. Res. 46(11), W11536 (2010)

    Google Scholar 

  43. Miyato, T., Kataoka, T., Koyama, M., Yoshida, Y.: Spectral normalization for generative adversarial networks. arXiv preprint arXiv:1802.05957 (2018)

  44. Mosser, L., Dubrule, O., Blunt, M.J.: Reconstruction of three-dimensional porous media using generative adversarial neural networks. Phys. Rev. 96(4), 043309 (2017)

    Google Scholar 

  45. Nicolas, A., Mello, A.W., Sun, Y., Johnson, D.R., Sangid, M.D.: Reconstruction methods and analysis of subsurface uncertainty for anisotropic microstructures. Mater. Sci. Eng. A. 760, 76–87 (2019)

    Google Scholar 

  46. Nussbaumer, R., Mariethoz, G., Gloaguen, E., Holloger, K.: Which path to choose in sequential Gaussian simulation. Math. Geosci. 50(1), 97–12 (2018)

    Google Scholar 

  47. Oliver, M.A., Webster, R.: Kriging: a method of interpolation for geographical information systems. International Journal of Geographical Information System. 4(3), 313–332 (1990)

    Google Scholar 

  48. Oord, A., Kalchbrenner, N., Vinyals, O., Espeholt, L., Graves, A., Kavukcuoglu, K.: Conditional image generation with pixelCNN decoders. In: Proceedings of the 30th International Conference on Neural Information Processing Systems, pp. 4797–4805 (2016)

  49. Pyrcz, M.J., Deutsch, C.V.: Geoestatistical Reservoir Modeling. Oxford University Press, Oxford (2014)

  50. Rao, D.Y., Wu, X.J., Li, H., Kittler, J., Xu, T.Y.: UMFA: a photorealistic style transfer method based on U-net and multi-layer feature aggregation. Journal of Electronic Imaging. 30(5), 053013 (2021)

    Google Scholar 

  51. Renard, P., Mariethoz, G.: Special issue on 20 years of multiple-point statistics: part 1. Math. Geosci. 46(2), 129–131 (2014)

    Google Scholar 

  52. Ronneberger, O., Fischer, P., Brox, T.: U-net: Convolutional networks for biomedical image segmentation. In: International Conference on Medical image computing and computer-assisted intervention. Springer, pp. 234–241 (2015)

  53. Song, S., Mukerji, T., Hou, J.: Geological facies modeling based on progressive growing of generative adversarial networks (GANs). Comput. Geosci. 25(3), 1251–1273 (2021)

    Google Scholar 

  54. Strebelle, S.: Conditional simulation of complex geological structures using multiple-point statistics. Math. Geol. 34(1), 1–21 (2002)

    Google Scholar 

  55. Tahmasebi, P., Hezarkhani, A., Sahimi, M.: Multiple-point geostatistical modeling based on the cross-correlation functions. Comput. Geosci. 16(3), 779–797 (2012)

    Google Scholar 

  56. Tahmasebi, P., Sahimi, M., Caers, J.: MS-CCSIM: accelerating pattern-based geostatistical simulation of categorical variables using a multi-scale search in Fourier space. Comput. Geosci. 67, 75–88 (2014)

    Google Scholar 

  57. Tahmasebi, P., Kamrava, S., Bai, T., Sahimi, M.: Machine learning in geo-and environmental sciences: from small to large scale. Adv. Water Resour. 142, 103619 (2020)

    Google Scholar 

  58. Van der Baan, M., Jutten, C.: Neural networks in geophysical applications. Geophysics. 65(4), 1032–1047 (2000)

    Google Scholar 

  59. Wellmann, F., Caumon, G.: 3-D structural geological models: concepts, methods, and uncertainties. Advances in Geophysics. Elsevier. 59, 1–121 (2018)

    Google Scholar 

  60. Yang, L., Hou, W., Cui, C., Cui, J.: GOSIM: a multi-scale iterative multiple-point statistics algorithm with global optimization. Comput. Geosci. 89, 57–70 (2016)

    Google Scholar 

  61. Zhang, T., Ji, X., Zhang, A.: Reconstruction of fluvial reservoirs using multiple-stage concurrent generative adversarial networks. Comput. Geosci. 25, 1983–2004 (2021). https://doi.org/10.1007/s10596-021-10086-7

    Article  Google Scholar 

  62. Zheng, S., Song, Y., Leung, T., Goodfellow, I.: Improving the robustness of deep neural networks via stability training. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 4480–4488 (2016)

  63. Zuo, R., Xiong, Y., Wang, J., Carranza, E.J.M.: Deep learning and its application in 7 geochemical mapping. Earth Sci. Rev. 192, 1–14 (2019)

    Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (41902304, 42172333, U1711267).

Code availability

The source code developed by using Python is made open and accessible on GitHub: https://github.com/GS-3DMG/DCGAN-Reconstruction.

Author information

Authors and Affiliations

  1. School of Computer Science, China University of Geosciences, Wuhan, 430074, China

    Zixiao Yang, Qiyu Chen, Zhesi Cui, Gang Liu & Yiping Tian

  2. Hubei Key Laboratory of Intelligent Geo-Information Processing, China University of Geosciences, Wuhan, 430074, China

    Zixiao Yang, Qiyu Chen, Zhesi Cui, Gang Liu & Yiping Tian

  3. State Key Laboratory of Biogeology and Environmental Geology, China University of Geosciences, Wuhan, 430074, China

    Qiyu Chen & Gang Liu

  4. College of Science, China University of Petroleum, Beijing, 102249, China

    Shaoqun Dong

Authors
  1. Zixiao Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qiyu Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhesi Cui
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Gang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Shaoqun Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Yiping Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qiyu Chen.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

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

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, Z., Chen, Q., Cui, Z. et al. Automatic reconstruction method of 3D geological models based on deep convolutional generative adversarial networks. Comput Geosci 26, 1135–1150 (2022). https://doi.org/10.1007/s10596-022-10152-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10596-022-10152-8

Keywords

Search

Navigation