Data-driven subsurface modelling using a Markov random field model

References

• Ackley, D. H., G. E. Hinton, and T. J. Sejnowski. 1985. “A Learning Algorithm for Boltzmann Machines*.” Cognitive Science 9: 147–169. doi:10.1207/s15516709cog0901_7.
   Web of Science ®Google Scholar
• Bárdossy, G., and J. Fodor. 2004. “Probabilistic Approaches for Handling Uncertainties, Chapter 3.” In Evaluation of Uncertainties and Risks in Geology, 13–39. Springer.
   Google Scholar
• Bertalmio, M., A. Bertozzi, and G. Sapiro. 2001. “Navier-Stokes, Fluid Dynamics and Image Video Inpainting.” Proceedings of the IEEE International Conference on Computer Vision and Pattern Recognition (CVPR), 355–362.
   Google Scholar
• Bertalmio, M., G. Sapiro, C. Ballester, and V. Caselles. 2000. Image Inpainting, Proceedings of the ACM SIGGRAPH, 417–424.
   Google Scholar
• Besag, J. 1986. “On the Statistical Analysis of Dirty Pictures.” J. R. Statist. Soc. B 48 (3): 259–302. doi:10.1111/j.2517-6161.1986.tb01412.x.
   Google Scholar
• Bishop, C. M. 2006. Pattern Recognition and Machine Learning. Springer.
   Google Scholar
• Burns, K. L. 1975. “Analysis of Geological Events.” Journal of the International Association for Mathematical Geology 7: 295–321. doi:10.1007/BF02081703.
   Google Scholar
• Cami, B., S. Javankhoshdel, K. K. Phoon, and J. Ching. 2020. “Scale of Fluctuation for Spatially Varying Soils: Estimation Methods and Values. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems.” Part A: Civil Engineering 6 (4): 03120002.
   Google Scholar
• Ching, J., and Y. C. Chen. 2007. “Transitional Markov Chain Monte Carlo Method for Bayesian Model Updating, Model Class Selection, and Model Averaging.” Journal of Engineering Mechanics 133 (7): 816–832. doi:10.1061/(ASCE)0733-9399(2007)133:7(816).
   Web of Science ®Google Scholar
• Deng, Z. P., D. Q. Li, X. H. Qi, Z. J. Cao, and K. K. Phoon. 2017. “Reliability Evaluation of Slope Considering Geological Uncertainty and Inherent Variability of Soil Parameters.” Computers and Geotechnics 92: 121–131. doi:10.1016/j.compgeo.2017.07.020.
   Web of Science ®Google Scholar
• Diens, I. 1974. “General Formulation of the Correlation Problem and Its Solution in Two Special Situations.” Mathematical Geology 6: 73–81. doi:10.1007/BF02111928.
   Google Scholar
• Diens, I., and C. J. Mann. 1977. “Mathematical Formalization of Stratigraphic Terminology.” Mathematical Geology 9: 587–603. doi:10.1007/BF02067215.
   Google Scholar
• Dubes, R. C., and A. K. Jain. 1989. “Random Field Models in Image Analysis.” Journal of Applied Statistics 16 (2): 131–164. doi:10.1080/02664768900000014.
   Google Scholar
• Elfeki, A., and M. Dekking. 2001. “A Markov Chain Model for Subsurface Characterization: Theory and Application.” Mathematical Geology 33 (5): 569–589. doi:10.1023/A:1011044812133.
   Google Scholar
• Elkateb, T., R. Chalaturnyk, and P. Robertson. 2003. “An Overview of Soil Heterogeneity: Quantification and Implications on Geotechnical Field Problems.” Canadian Geotechnical Journal 40: 1–15. doi:10.1139/t02-090.
   Web of Science ®Google Scholar
• Geman, S., and D. Geman. 1987. “Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images.” IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI-6 (6): 564–741. doi:10.1016/B978-0-08-051581-6.50057-X.
   Google Scholar
• Gong, W., C. Zhao, C. H. Juang, H. Tang, H. Wang, and X. Hu. 2020. “Stratigraphic Uncertainty Modelling with Random Field Approach.” Computers and Geotechnics 125: 103681. doi:10.1016/j.compgeo.2020.103681.
   Web of Science ®Google Scholar
• Greig, D. M., B. T. Porteous, and A. H. Seheult. 1989. “Exact Maximum A Posteriori Estimation for Binary Images.” Journal of the Royal Statistical Society. Series B (Methodological 51 (2): 271–279. doi:10.1111/j.2517-6161.1989.tb01764.x.
   Web of Science ®Google Scholar
• Griffiths, D. V., J. Huang, and G. A. Fenton. 2012. “Risk Assessment in Geotechnical Engineering: Stability Analysis of Highly Variable Soils”, Geotechnical Engineering State of the Art and Practice: Keynote Lectures GeoCongress 2012 (GSP 226), ASCE, Reston, VA, 78-101. doi:10.1061/9780784412138.0004.
   Google Scholar
• Hinton, G. E., and T. J. Sejnowski. 1986. “Learning and Relearning in Boltzmann Machine, Parallel Distributed Processing: Explorations in the Microstructure of Cognition.” 1(282–317):2.
   Google Scholar
• Hukushima, K., and Y. Iba. 2003. “Population Annealing and Its Application to a Spin Glass.” AIP Conference Proceedings 690: 200–206. doi:10.1063/1.1632130.
   Google Scholar
• Iba, Y. 1991. “Macroscopic Parameter Estimation from Incomplete Data with Metropolis-Type Monte Carlo Algorithm.” Proceedings of the Institute of Statistical Mathematics 39 (1): 1–21. (in Japanese with English abstract).
   Google Scholar
• Ip, R. H. L., and K. Y. K. Wu. 2020. “A Note on Discrete Multivariate Markov Random Field Models.” Statistics and Probability Letters 156: 108588. doi:10.1016/j.spl.2019.108588.
   Web of Science ®Google Scholar
• Juang, C. H., J. Zhang, M. Shen, and J. Hu. 2019. “Probabilistic Methods for Unified Treatment of Geotechnical and Geological Uncertainties in a Geotechnical Analysis.” Engineering Geology 249: 148–161. doi:10.1016/j.enggeo.2018.12.010.
   Web of Science ®Google Scholar
• Kiwata, H. 2012. “Physical Consideration of an Image in Image Restoration Using Bayes’ Formula.” Physica A: Statistical Mechanics and its Applications 391: 2215–2224. doi:10.1016/j.physa.2011.11.025.
   Web of Science ®Google Scholar
• Li, Z., X. Wang, H. Wang, and R. Y. Liang. 2016. “Quantifying Stratigraphic Uncertainties by Stochastic Simulation Techniques Based on Markov Random Field.” Engineering Geology 201: 106–122. doi:10.1016/j.enggeo.2015.12.017.
   Web of Science ®Google Scholar
• Lumb, P. 1966. “The Variability of Natural Soils.” Canadian Geotechnical Journal 3: 74–97. doi:10.1139/t66-009.
   Google Scholar
• Mardia, K. V. 1988. “Multi-dimensional Multivariate Gaussian Markov Random Fields with Application to Image Processing.” Journal of Multivariate Analysis 24: 265–284. doi:10.1016/0047-259X(88)90040-1.
   Web of Science ®Google Scholar
• Metropolis, N., A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller. 1953. “Equation of State Calculations by Fast Computing Machines.” The Journal of Chemical Physics 21: 1087–1092. doi:10.1063/1.1699114.
   Web of Science ®Google Scholar
• Nerberg, T., L. Rosen, A. Baran, and S. Baran. 2002. “On Modeling Discrete Geological Structures as Markov Random Fields.” Mathematical Geology 34 (1): 63–77. doi:10.1023/A:1014079411253.
   Google Scholar
• Phoon, K. K. 2017. “Role of Reliability Calculations in Geotechnical Design.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 11 (1): 4–21. doi:10.1080/17499518.2016.1265653.
   Web of Science ®Google Scholar
• Phoon, K. K., Z. J. Cao, J. Ji, Y. F. Leung, S. Najjar, T. Shuku, C. Tang, Z. Y. Yin, I. Yoshida, and J. Ching. 2022. “Geotechnical Uncertainty, Modeling, and Decision Making.” Soils and Foundations 62 (5): 101189. doi:10.1016/j.sandf.2022.101189.
   Web of Science ®Google Scholar
• Phoon, K. K., J. Ching, and T. Shuku. 2022a. “Challenges in Data-Driven Site Characterization.” Georisk: Assessment & Management of Risk for Engineered Systems & Geohazards 16 (1): 114–126. doi:10.1080/17499518.2021.1896005.
   Google Scholar
• Phoon, K. K., T. Shuku, J. Ching, and I. Yoshida. 2022c. “Benchmark Examples for Data-Driven Site Characterization.” Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 16 (4): 599–621. doi:10.1080/17499518.2022.2025541.
   Google Scholar
• Phoon, K. K., and W. Zhang. 2023. “Future of Machine Learning in Geotechnics.” Georisk: Assessment & Management of Risk for Engineered Systems & Geohazards: 1–16. doi:10.1080/17499518.2022.2087884.
   Google Scholar
• Qi, X. H., D. Q. Li, K. K. Phoon, Z. J. Cao, and X. S. Tang. 2016. “Simulation of Geologic Uncertainty Using Coupled Markov Chain.” Engineering Geology 207: 129–140. doi:10.1016/j.enggeo.2016.04.017.
   Web of Science ®Google Scholar
• Robertson, P. K. 2016. “Cone Penetration Test (CPT)-based Soil Behaviour Type (SBT) Classification System - an Update.” Canadian Geotechnical Journal 53 (12): 1910–1927. doi:10.1139/cgj-2016-0044.
   Web of Science ®Google Scholar
• Robertson, P. K., and C. E. Wride. 1998. “Evaluating Cyclic Liquefaction Potential Using the Cone Penetration Test.” Canadian Geotechnical Journal 35: 442–459. doi:10.1139/t98-017.
   Web of Science ®Google Scholar
• Sauvin, G., M. Vanneste, M. E. Vardy, R. T. Klinkvort, and F. C. Fredrik. 2019. “Machine Learning and Quantitative Ground Models for Improving Offshore Wind Site Characterization.” Proceedings, Offshore Technology Conference, Houston, TX, OTC-29351-MS.
   Google Scholar
• Shi, C., and Y. Wang. 2021. “Development of Subsurface Geological Cross-Section from Limited Site-Specific Boreholes and Prior Geological Knowledge Using Iterative Convolution XGBoost.” Journal of Geotechnical and Geoenvironmental Engineering 147 (9): 04021082. doi:10.1061/(ASCE)GT.1943-5606.0002583.
   Web of Science ®Google Scholar
• Shi, C., and Y. Wang. 2021. “Nonparametric and Data-Driven Interpolation of Subsurface Soil Stratigraphy from Limited Data Using Multiple Point Statistics.” Canadian Geotechnical Journal 58 (2): 261–280. doi:10.1139/cgj-2019-0843.
   Web of Science ®Google Scholar
• Shiono, K., and K. Wadatsumi. 1991. “Binary Relations and Symbolic Expression of Geological Knowledge for Artificial Intelligence: The Principle of Superposition.” Geoinformatics 2 (2): 225–233. doi:10.6010/geoinformatics1990.2.2_225.
   Google Scholar
• Shuku, T., and K. K. Phoon. 2023. “Comparison of Data-Driven Site Characterization Methods Through Benchmarking: Methodological and Application Aspects.” ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering 9 (2): 04023006. doi:10.1061/AJRUA6.RUENG-977.
   Google Scholar
• Skilling, J. 2006. “Nested Sampling for General Bayesian Computation.” Bayesian Analysis 1 (4): 833–859. doi:10.1214/06-BA127.
   Web of Science ®Google Scholar
• Stuedlein, A. W., B. Cami, D. D. Curzio, S. Javankhoshdel, S. Nishimura, W. Pula, G. Vessia, Y. Wang, and J. Ching. 2021. “Summary of Random Field Model Parameters of Geotechnical Properties.” TC304 State-of-the-art Review of Inherent Variability and Uncertainty in Geotechnical Properties and Models, 95–129.
   Google Scholar
• Swendsen, R. H., and J. S. Wang. 1987. “Nonuniversal Critical Dynamics in Monte Carlo Simulations.” Physical Review Letters 58 (2): 86–88. doi:10.1103/PhysRevLett.58.86.
   PubMed Web of Science ®Google Scholar
• Vanmarcke, E. H. 1977. “Probabilistic Modeling of Soil Profiles.” Journal of Geotechnical Engineering (ASCE 103 (GT11): 1227–1246. doi:10.1061/AJGEB6.0000517.
   Google Scholar
• Wang, X., Z. Li, H. Wang, Q. Rong, and R. Y. Liang. 2016. “Probabilistic Analysis of Shield-Driven Tunnel in Multiple Strata Considering Stratigraphic Uncertainty.” Structural Safety 62: 88–100. doi:10.1016/j.strusafe.2016.06.007.
   Web of Science ®Google Scholar
• Wang, H., J. F. Wellmann, Zhao Li, X. Wang, and R. Y. Liang. 2017. “A Segmentation Approach for Stochastic Geological Modeling Using Hidden Markov Random Fields.” Mathematical Geology 49: 145–177. doi: 10.1007/s11004-016-9663-9.
   Google Scholar
• Wellmann, J. F., F. G. Horowitz, E. Schill, and K. Regenauer-Lieb. 2010. “Towards Incorporating Uncertainty of Structural Data in 3D Geological Inversion.” Tectonophysics 490: 141–151. doi:10.1016/j.tecto.2010.04.022.
   Web of Science ®Google Scholar
• Wellmann, J. F., and K. Regenauer-Lieb. 2012. “Uncertainties Have a Meaning: Information Entropy as a Quality Measure for 3-D Geological Models.” Tectonophysics 526-529: 207–216. doi:10.1016/j.tecto.2011.05.001.
   Web of Science ®Google Scholar
• Zhan, J. Z., Z. Q. Liu, D. M. Zhan, H. W. Huang, K. K. Phoon, and Y. D. Xue. 2022. “Improved Coupled Markov Chain Method for Simulating Geological Uncertainty.” Engineering Geology 298: 106539. doi:10.1016/j.enggeo.2022.106539.
   Web of Science ®Google Scholar