Geophysical Inversion via Hierarchical Bayesian Deep Learning with Statistical Sampling

References

1. Abril‐Pla, O., V.Andreani, C.Carroll, et al. 2023. “PyMC: A Modern, and Comprehensive Probabilistic Programming Framework in Python.” PeerJ Computer Science9: e1516.
   [Google Scholar]
2. Bao, L. L., J. S.Zhang, C. X.Zhang, et al. 2023. “A Reliable Bayesian Neural Network for the Prediction of Reservoir Thickness With Quantified Uncertainty.” Computers & Geosciences178: 105409.
   [Google Scholar]
3. Blundell, C., J.Cornebise, K.Kavukcuoglu, and D.Wierstra. 2015. “Weight Uncertainty in Neural Networks.” In Proceedings of the 32nd International Conference on Machine Learning. ACM Publication.
4. Bodin, T., M.Sambridge, H.Tkalčić, et al. 2012. “Transdimensional Inversion of Receiver Functions and Surface Wave Dispersion.” Journal of Geophysical Research: Solid Earth117: B02301. https://doi.org/10.1029/2011JB008560.
   [Google Scholar]
5. Brown, S., W. L.Rodi, M.Seracini, et al. 2022. “Bayesian Neural Networks for Geothermal Resource Assessment: Prediction With Uncertainty.” arXiv Preprint arXiv: 2209.15543.
6. Colombo, D., E.Turkoglu, W.Li, and D.Rovetta. 2021a. “Coupled Physics‐Deep Learning Inversion.” Computers and Geosciences157: 104917.
   [Google Scholar]
7. Colombo, D., E.Turkoglu, W.Li, E.Sandoval‐Curiel, and D.Rovetta. 2021b. “Physics‐Driven Deep‐Learning Inversion With Application to Transient Electromagnetics.” Geophysics86, no. 3: E209–E224.
   [Google Scholar]
8. Colombo, D., E.Turkoglu, E.Sandoval‐Curiel, and T.Alyousuf. 2024. “Self‐Supervised, Active Learning Seismic Full‐Waveform Inversion.” Geophysics89, no. 2: U31–U52.
   [Google Scholar]
9. Constable, S. C., R. L.Parker, and C. G.Constable. 1987. “Occam's Inversion: A Practical Algorithm for Generating Smooth Models From Electromagnetic Sounding Data.” Geophysics52, no. 3: 289–300.
   [Google Scholar]
10. Feng, R., N.Balling, D.Grana, J. S.Dramsch, and T. M.Hansen. 2021a. “Bayesian Convolutional Neural Networks for Seismic Facies Classification.” IEEE Transactions on Geoscience and Remote Sensing59, no. 10: 8933–8940.
    [Google Scholar]
11. Feng, R., D.Grana, and N.Balling. 2021b. “Variational Inference in Bayesian Neural Network for Well‐Log Prediction.” Geophysics86, no. 3: M91–M99.
    [Google Scholar]
12. Feng, R., D.Grana, and K.Mosegaard. 2025. “Geostatistical Facies Simulation Based on Training Image Using Generative Networks and Gradual Deformation.” Mathematical Geosciences57: 1021–1044. https://doi.org/10.1007/s11004‐024‐10169‐y.
    [Google Scholar]
13. Feng, R., K.Mosegaard, D.Grana, T.Mukerji, and T. M.Hansen. 2024. “Stochastic Facies Inversion With Prior Sampling by Conditional Generative Adversarial Networks Based on Training Image.” Mathematical Geosciences56, no. 4: 665–690.
    [Google Scholar]
14. Feng, R., and S.Nasser. 2024. “A Deep Learning‐Based Surrogate Model for Trans‐Dimensional Inversion of Discrete Fracture Networks.” Journal of Hydrology638: 131524.
    [Google Scholar]
15. Gal, Y., and Z.Ghahramani. 2016. “Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning.” In Proceedings of the 33rd International Conference on Machine Learning. ACM Publication.
16. Gal, Y., J.Hron, and A.Kendall. 2017. “Concrete Dropout.” arXiv Preprint arXiv: 1705.07832.
17. Gelman, A.2006. “Multilevel (Hierarchical) Modelling: What It Can and CannotNot Do.” Technometrics48, no. 3: 432–435.
    [Google Scholar]
18. Gelman, A., J. B.Carlin, H. S.Stern, D. B.Dunson, A.Vehtari, and D. B.Rubin. 2013. Bayesian Data Analysis. CRC Press.
    [Google Scholar]
19. Gelman, A., and J.Hill. 2006. Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.
    [Google Scholar]
20. Gelman, A., D.Simpson, and M.Betancourt. 2017. “The Prior Can Often Only be Understood in the Context of the Likelihood.” Entropy19, no. 10: 555.
    [Google Scholar]
21. Hansen, T. M.2021. “Efficient Probabilistic Inversion Using the Rejection Sampler—Exemplified on Airborne EM Data.” Geophysical Journal International224, no. 1: 543–557.
    [Google Scholar]
22. Hansen, T. M., and C. C.Finlay. 2022. “Use of Machine Learning to Estimate Statistics of the Posterior Distribution in Probabilistic Inverse Problems—An Application to Airborne EM Data.” Journal of Geophysical Research: Solid Earth127: e2022JB024703.
    [Google Scholar]
23. Hoffman, M. D., and A.Gelman. 2014. “The no‐U‐Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo.” Journal of Machine Learning Research15: 1593–1623.
    [Google Scholar]
24. Hüllermeier, E., and W.Waegeman. 2021. “Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods.” Machine Learning110: 457–506.
    [Google Scholar]
25. Jan, A., F.Mahfoudh, G.Draškovic, et al. 2022. “Multitasking Physics‐Informed Neural Network for Drillstring Washout Detection.” In EAGE Extended Abstracts. European Association of Geoscientists & Engineers.
    [Google Scholar]
26. Kendall, A., and Y.Gal. 2017. “What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?” Advances in Neural Information Processing Systems30: 5580–5590.
    [Google Scholar]
27. Kwon, Y., J.Won, B.Kim, and M.Paik. 2020. “Uncertainty Quantification Using Bayesian Neural Networks in Classification: Application to Biomedical Image Segmentation.” Computational Statistics & Data Analysis142: 106816. https://doi.org/10.1016/j.csda.2019.106816.
    [Google Scholar]
28. Li, P., D.Grana, and M.Liu. 2024. “Bayesian Neural Network and Bayesian Physics‐Informed Neural Network via Variational Inference for Seismic Petrophysical Inversion.” Geophysics89: M185–M196.
    [Google Scholar]
29. Lopez‐Alvis, J., E.Laloy, F.Nguyen, and T.Hermans. 2021. “Deep Generative Models in Inversion: The Impact of the Generator's Nonlinearity and Development of a New Approach Based on a Variational Autoencoder.” Computers & Geosciences152: 104762.
    [Google Scholar]
30. Miele, R., S.Levy, N.Linde et al. 2024. “Deep Generative Networks for Multivariate Fullstack Seismic Data Inversion Using Inverse Autoregressive Flows.” Computers & Geosciences188: 105622.
    [Google Scholar]
31. Minsley, B. J.2011. “A Trans‐Dimensional Bayesian Markov Chain Monte Carlo Algorithm for Model Assessment Using Frequency‐Domain Electromagnetic Data.” Geophysical Journal International187, no. 1: 252–272.
    [Google Scholar]
32. Neal, R. M.2011. “MCMC Using Hamiltonian Dynamics.” In Handbook of Markov Chain Monte Carlo. Chapman & Hall/CRC.
    [Google Scholar]
33. Pham, N., and W.Li. 2022. “Physics‐Constrained Deep Learning for Ground Roll Attenuation.” Geophysics87, no. 1: V15–V27.
    [Google Scholar]
34. Raiche, A. P.1983. “Comparison of Apparent Resistivity Functions for Transient Electromagnetic Methods.” Geophysics48, no. 6: 787–789.
    [Google Scholar]
35. Saatchi, Y., and A. G.Wilson. 2017. “Bayesian GAN.” arXiv Preprint arXiv:1705.09558.
36. Su, Y., D.Cao, S.Liu, Z.Hou, and J.Feng. 2023. “Seismic Impedance Inversion Based on Deep Learning With Geophysical Constraints.” Geoenergy Science and Engineering225: 211671.
    [Google Scholar]
37. Tarantola, A.2005. Inverse Problem Theory and Methods for Model Parameter Estimation. SIAM.
    [Google Scholar]
38. Trevor, H., T.Robert, and F.Jerome. 2009. The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer.
    [Google Scholar]
39. Valdenegro‐Toro, M., and D. S.Mori. 2022. “A Deeper Look Into Aleatoric and Epistemic Uncertainty Disentanglement.” arXiv Preprint arXiv: 2204.09308.
40. Wiecki, T. V., I.Sofer, and M. J.Frank. 2013. “HDDM: Hierarchical Bayesian Estimation of the Drift‐Diffusion Model in Python.” Frontiers in Neuroinformatics7: 14.
    [Google Scholar]
41. Wu, S., Q.Huang, and L.Zhao. 2022. “Instantaneous Inversion of Airborne Electromagnetic Data Based on Deep Learning.” Geophysical Research Letters49: e2021GL097165.
    [Google Scholar]