| Citation: | Yabo Zhao, Weihua Hua, Guoxiong Chen, Dong Liang, Zhipeng Liu, Xiuguo Liu. Stochastic Modeling of Folded Structures in Scarce Data Scenarios Using Transiogram with Locally Varying Anisotropy. Journal of Earth Science, 2026, 37(4): 1608-1619. doi: 10.1007/s12583-022-1646-9
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Sampling is usually scarce in geological modeling, and hence, complex and continuous geological phenomena are difficult to simulate when anisotropy changes locally. The current study aimed to present a method for modeling folded structures using transiogram with locally varying anisotropy in scarce data scenarios. Based on the direction fields of locally varying anisotropy, a pathline-based algorithm was proposed to simulate the folds that are flattened and calculate the relative position of any two random points thereafter. Compared to the traditional two-point spatial continuity measures (such as the variogram), the locally varying anisotropy transiogram could not only describe the high order Markovian of the spatial distribution of geological bodies, but also do so with explicable physical implication. The report revealed that the locally varying anisotropy transiogram of horizontal strata can be directly obtained if the stratigraphic sequence and stratum thickness are known. In the case study, only one geological map was used in a real complex-fold area to successfully simulate the 3-D stratigraphic model.
| Allmendinger, R. W., Cardozo, N., Fisher, D. M., 2011. Structural Geology Algorithms. Cambridge University Press, Cambridge. 1–22 |
| Bartier, P. M., Keller, C. P., 1996. Multivariate Interpolation to Incorporate Thematic Surface Data Using Inverse Distance Weighting (IDW). Computers & Geosciences, 22(7): 795–799. https://doi.org/10.1016/0098-3004(96)00021-0 |
| Benediktsson, J. A., Swain, P. H., 1992. Consensus Theoretic Classification Methods. IEEE Transactions on Systems, Man, and Cybernetics, 22(4): 688–704. https://doi.org/10.1109/21.156582 |
| Bianchi, M., Turner, A. K., Lark, M., et al., 2021. Uncertainty in 3-D Geological Models. In: Turner, A. K., Kessler, H., van der Meulen, M. J., eds., Applied Multidimensional Geological Modeling: Informing Sustainable Human Interactions with the Shallow Subsurface. John Wiley & Sons, Hoboken. 357–382 |
| Boisvert, J. B., Manchuk, J. G., Deutsch, C. V., 2009. Kriging in the Presence of Locally Varying Anisotropy Using Non-Euclidean Distances. Mathematical Geosciences, 41(5): 585–601. https://doi.org/10.1007/s11004-009-9229-1 |
| Boisvert, J. B., Deutsch, C. V., 2011. Programs for Kriging and Sequential Gaussian Simulation with Locally Varying Anisotropy Using Non-Euclidean Distances. Computers & Geosciences, 37(4): 495–510. https://doi.org/10.1016/j.cageo.2010.03.021 |
| Borghi, A., Renard, P., Fournier, L., et al., 2015. Stochastic Fracture Generation Accounting for the Stratification Orientation in a Folded Environment Based on an Implicit Geological Model. Engineering Geology, 187: 135–142. https://doi.org/10.1016/j.enggeo.2014.12.019 |
| Calcagno, P., Chilès, J. P., Courrioux, G., et al., 2008. Geological Modelling from Field Data and Geological Knowledge Part Ⅰ. Modelling Method Coupling 3D Potential-Field Interpolation and Geological Rules. Physics of the Earth and Planetary Interiors, 171(1/2/3/4): 147–157. https://doi.org/10.1016/j.pepi.2008.06.013 |
| Cao, G. F., Kyriakidis, P. C., Goodchild, M. F., 2011. Combining Spatial Transition Probabilities for Stochastic Simulation of Categorical Fields. International Journal of Geographical Information Science, 25(11): 1773–1791. https://doi.org/10.1080/13658816.2010.528421 |
| Carle, S. F., Fogg, G. E., 1996. Transition Probability-Based Indicator Geostatistics. Mathematical Geology, 28(4): 453–476. https://doi.org/10.1007/BF02083656 |
|
Carle, S. F., Labolle, E. M., Weissmann, G. S., et al., 1998. Conditional Simulation of Hydrofacies Architecture: A Transition Probability/Markov Approach. In: Fraser, G. S., Matthew Davis, J., eds., Hydrogeologic Models of Sedimentary Aquifers. SEPM Society for Sedimentary Geology, Tuksa, Oklahoma. 1: 147–170. |
| Chiles, J., Aug, C., Guillen, A., et al., 2004. Modelling the Geometry of Geological Units and Its Uncertainty in 3D from Structural Data: The Potential-Field Method, Proceedings of International Symposium on Orebody Modelling and Strategic Mine Planning, Perth, Australia. 313–320 |
| Chiles, J., Delfiner, P., 1999. Geostatistics: Modeling Spatial Uncertainty. John Wiley & Sons, Hoboken. 30–96 |
| Curriero, F. C., 2006. On the Use of Non-Euclidean Distance Measures in Geostatistics. Mathematical Geology, 38(8): 907–926. https://doi.org/10.1007/s11004-006-9055-7 |
| Grose, L., Ailleres, L., Laurent, G., et al., 2019. Inversion of Geological Knowledge for Fold Geometry. Journal of Structural Geology, 119: 1–14. https://doi.org/10.1016/j.jsg.2018.11.010 |
| Hillier, M. J., Schetselaar, E. M., de Kemp, E. A., et al., 2014. Three-Dimensional Modelling of Geological Surfaces Using Generalized Interpolation with Radial Basis Functions. Mathematical Geosciences, 46(8): 931–953. https://doi.org/10.1007/s11004-014-9540-3 |
| Jessell, M., Aillères, L., de Kemp, E., et al., 2014. Next Generation Three-Dimensional Geologic Modeling and Inversion. Society of Economic Geologists Special Publication, 18(18): 261–272. https://doi.org/10.5382/sp.18.13 |
| Journel, A. G., 2002. Combining Knowledge from Diverse Sources: An Alternative to Traditional Data Independence Hypotheses. Mathematical Geology, 34(5): 573–596. https://doi.org/10.1023/A:1016047012594 |
| Krishnan, S., 2008. The Tau Model for Data Redundancy and Information Combination in Earth Sciences: Theory and Application. Mathematical Geosciences, 40(6): 705–727. https://doi.org/10.1007/s11004-008-9165-5 |
| Lee, J. C., Angelier, J., 1994. Paleostress Trajectory Maps Based on the Results of Local Determinations: The "Lissage" Program. Computers & Geosciences, 20(2): 161–191. https://doi.org/10.1016/0098-3004(94)90004-3 |
|
Levannier, A., Chabbert, A., Neumaier, M., et al., 2017. Geological Modeling in Structurally Complex Settings Using a Depositional Space and Cut-Cell Unstructured Grids. SPE Middle East Oil & Gas Show and Conference, March 6–9, 2017, Manama, Kingdom of Bahrain. SPE: D031S026R007. |
| Li, W. D., 2007. Transiograms for Characterizing Spatial Variability of Soil Classes. Soil Science Society of America Journal, 71(3): 881–893. https://doi.org/10.2136/sssaj2005.0132 |
| MacDonald, F. A., Mitchell, K., Stewart, A. J., 2005. Amelia Creek: A Proterozoic Impact Structure in the Davenport Ranges, Northern Territory. Australian Journal of Earth Sciences, 52(4/5): 631–640. https://doi.org/10.1080/08120090500170401 |
|
Machuca-Mory, D. F., Rees, H., Leuangthong, O., 2015. Grade Modelling with Local Anisotropy Angles: A Practical Point of View. In: 37th Application of Computers and Operations Research in the Mineral Industry (APCOM 2015), May 23–27, Fairbanks, AK. 1118–1128. |
| Mallet, J. L., 2004. Space-Time Mathematical Framework for Sedimentary Geology. Mathematical Geology, 36(1): 1–32. https://doi.org/10.1023/B:MATG.0000016228.75495.7c |
| Mariethoz, G., Kelly, B. F. J., 2011. Modeling Complex Geological Structures with Elementary Training Images and Transform-Invariant Distances. Water Resources Research, 47(7): W07527. https://doi.org/10.1029/2011WR010412 |
| Nussbaumer, R., Mariethoz, G., Gloaguen, E., et al., 2018. Which Path to Choose in Sequential Gaussian Simulation. Mathematical Geosciences, 50(1): 97–120. https://doi.org/10.1007/s11004-017-9699-5 |
| Ritzi, R. W., Jr, 2000. Behavior of Indicator Variograms and Transition Probabilities in Relation to the Variance in Lengths of Hydrofacies. Water Resources Research, 36(11): 3375–3381. https://doi.org/10.1029/2000WR900139 |
| Sartore, L., Fabbri, P., Gaetan, C., 2016. SpMC: An R-Package for 3D Lithological Reconstructions Based on Spatial Markov Chains. Computers & Geosciences, 94: 40–47. https://doi.org/10.1016/j.cageo.2016.06.001 |
| Stewart, A. J., Blake, D. H., Wyche, S., 1986. Booney Well Sheet SF53-2. 1 : 250 000: Second ed. Geological Series, Australia |
| te Stroet, C. B. M., Snepvangers, J. J. J. C., 2005. Mapping Curvilinear Structures with Local Anisotropy Kriging. Mathematical Geology, 37(6): 635–649. https://doi.org/10.1007/s11004-005-7310-y |
| Tran, T. T., 1994. Improving Variogram Reproduction on Dense Simulation Grids. Computers & Geosciences, 20(7/8): 1161–1168. https://doi.org/10.1016/0098-3004(94)90069-8 |
| Wang, R., Madison, R., 1993. Interactive Visualization and Programming-a 3D Vector Field Visualization System. IEEE Transactions on Magnetics, 29(2): 1997–2000. https://doi.org/10.1109/20.250801 |
| Xu, W. L., 1996. Conditional Curvilinear Stochastic Simulation Using Pixel-Based Algorithms. Mathematical Geology, 28(7): 937–949. https://doi.org/10.1007/BF02066010 |
| Young, D. S., 1987. Random Vectors and Spatial Analysis by Geostatistics for Geotechnical Applications. Mathematical Geology, 19(6): 467–479. https://doi.org/10.1007/BF00896915 |
|
Yu, H. F., Wang, C. L., Ma, K. L., 2007. Parallel Hierarchical Visualization of Large Time-Varying 3D Vector Fields. Proceedings of the 2007 ACM/IEEE Conference on Supercomputing. Reno Nevada. IEEE, 24: 1–12. |
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