Bai, H., Montési, L. G. J., and Behn, M. D.: MeltMigrator: A MATLAB-based software for modeling three-dimensional melt migration and crustal thickness variations at mid-ocean ridges following a rules-based approach, Geochem. Geophy. Geosy., 18, 445–456, https://doi.org/10.1002/2016GC006686, 2017.
Bertoncello, A., Sun, T., Li, H. Mariethoz, G., and Caers, J.: Conditioning Surface-Based Geological Models to Well and Thickness Data, Math. Geosci., 45, 873–893, https://doi.org/10.1007/s11004-013-9455-4, 2013.
Bezhanishvili, N., Ciancia, V., Gabelaia, D., Grilletti, G., Latella, D., and Massink, M.: Geometric Model Checking of Continuous Space, Log. Meth. Comput. Sci., 18, 7:1–7:38, https://doi.org/10.46298/lmcs-18(4:7)2022, 2022.
Bond, C. E.: Uncertainty in structural interpretation: Lessons to be learnt, J. Struct. Geol., 74, 185–200, https://doi.org/10.1016/j.jsg.2015.03.003, 2015.
Botella, A., Lévy, B., and Caumon, G.: Indirect unstructured hex-dominant mesh generation using tetrahedra recombination, Comput. Geosci., 20, 437–451, https://doi.org/10.1007/s10596-015-9484-9, 2016.
Braid, I. C.: The Synthesis of Solids Bounded by Many Faces, Comm. ACM, 18, 209–216, 1975.
Brodaric, B.: Characterizing and representing inference histories in geologic mapping, Int. J. Geogr. Inf. Sci., 26, 265–281, https://doi.org/10.1080/13658816.2011.585992, 2012.
Brodaric, B. and Gahegan, M.: Representing Geoscientific Knowledge in Cyberinfrastructure: challenges, approaches and implementations, in: Geoinformatics, Data to Knowledge, edited by: Sinha, A. K., Geol. Soc. Am. Spec. Pap., 397, 1–20, https://doi.org/10.1130/2006.2397(01), 2006.
Brodaric, B. and Richard, S. M.: The GeoScience Ontology reference. Geological Survey of Canada, Open File, 8796, 34, https://doi.org/10.4095/328296, 2021.
Brodaric, B., Gahegan, M., and Harrap, R.: The art and science of mapping: Computing geological categories from field data, Comput. Geosci., 30, 719–740, https://doi.org/10.1016/j.cageo.2004.05.001, 2004.
Burns, K. L.: Analysis of geological events, Math. Geol., 7, 295–321, 1975.
Burch, T. K.: Data, Models, Theory and Reality: The Structure of Demographic Knowledge, in: Agent-Based Computational Demography, Contributions to Economics, edited by: Billari, F. C. and Prskawetz, A., Physica, Heidelberg, https://doi.org/10.1007/978-3-7908-2715-6_2, 2003.
Burns, K. L.: Lithologic topology and structural vector fields applied to subsurface prediction in geology, Proceedings of International GIS/LIS'88 accessing the World, Third Annual International Conference, San Antonio, Texas, USA, 26–34, ISBN-13 978-0944426210, 1988.
Burns, K. L. and Remfry, J. G.: A Computer Method of Constructing Geological Histories from Field Surveys and Maps, Comput. Geosci., 2, 141–162, 1976.
Burns, K. L., Shepherd, J., and Marshall, B.: Analysis of Relational Data from Metamorphic Tectonites: Derivation of Deformation Sequences from Overprinting Relations, Proceedings of the International Association for Mathematical Geology (IAMG) 25th International Congress in Sydney, Australia, August 1976, in: Recent Advances in Geomathematics, An International Symposium, edited by: Merriam, D. F., Syracuse University, Computers and Geology Volume 2, 171–199, 1978.
Claramunt, C. and Jiang, B.: An integrated representation of spatial and temporal relationships between evolving regions, J. Geogr. Syst., 3, 411–428, 2001.
Crossley, M. D.: Essential topology, Springer-Verlag, London, 226 pp., ISBN 1-85233-782-6, 226, 2005.
de Kemp, E. A.: Truth Tables for consistency-checking 3D geological models, Zenodo [data set], https://doi.org/10.5281/zenodo.13948382, 2024.
de Kemp, E. A., Sprague, K., and Wong, W.: Interpretive Geology with Structural Constraints: An introduction to the SPARSE © plug-in, Americas GOCAD User Meeting, Houston Texas, 1–16, Zenodo https://doi.org/10.5281/zenodo.4646210, 2004.
de Kemp, E. A., Schetselaar, E. M., Hillier, M. J., Lydon, J. W., and Ransom, P. W.: Assessing the Workflow for Regional Scale 3D Geological Modelling: An Example from the Sullivan Time Horizon, Purcell Anticlinorium East Kootenay Region, Southeastern British Columbia, Interpretation, Special section: Building complex and realistic geologic models from sparse data, 4, SM33–SM50, https://doi.org/10.1190/INT-2015-0191.1, 2016.
de Kemp, E. A., Jessell, M. W., Aillères, L., Schetselaar, E. M., Hillier, M., Lindsay, M. D., and Brodaric, B.: Earth model construction in challenging geologic terrain: Designing workflows and algorithms that makes sense, in: Proceedings of Exploration'17: Sixth DMEC – Decennial International Conference on Mineral Exploration, edited by: Tschirhart, V. and Thomas, M. D., Integrating the Geosciences: The Challenge of Discovery, Toronto, Canada, 21–25 October 2017, 419–439,
https://www.dmec.ca/decennial-conference-proceedings (last access: 7 January 2025), 2017.
de la Varga, M. and Wellmann, J. F.: Structural geologic modeling as an inference problem: A Bayesian perspective, Interpretation, 4, SM1-SM16, https://doi.org/10.1190/INT-2015-0188.1, 2016.
de la Varga, M., Schaaf, A., and Wellmann, F.: GemPy 1.0: open-source stochastic geological modeling and inversion, Geosci. Model Dev., 12, 1–32, https://doi.org/10.5194/gmd-12-1-2019, 2019.
Deutsch, C. V.: All Realizations All the Time, in: Handbook of Mathematical Geosciences, edited by: Daya Sagar, B., Cheng, Q., and Agterberg, F., Springer, Cham, https://doi.org/10.1007/978-3-319-78999-6_7, 2018.
Dutranois, A., Wan-Chiu, L., Dulac, J.-C., Lecomte, J.-F., Callot, J.-P., and Rudkiewicz, J.-L.: Breakthrough in basin modeling using time/space frame, Offshore, 70,
https://www.offshore-mag.com/geosciences/article/16763653/breakthrough-in-basin-modeling-using-time-space-frame (last access: 7 January 2025), 2010.
Egenhofer, M., Sharma J., and Mark D.: A critical comparison of the 4-intersection and 9- intersection models for spatial relations: formal analysis, in: Autocarto 11, edited by: McMaster, R. and Armstrong, M., Minneapolis, MN, 1–11, 1993.
Egenhofer, M. J.: A formal definition of binary topological relationships, in: Foundations of Data Organization and Algorithms, FODO 1989, Lecture Notes in Computer Science, edited by: Litwin, W. and Schek, H. J., Springer, Berlin, Heidelberg, 367, https://doi.org/10.1007/3-540-51295-0_148, 1989.
Fattah, M.: Physical Geology, On line course, UDEMY,
https://www.udemy.com/course/geology-fundamentalz/, last access: 6 April 2024), 2018.
Finkl, C. W. (Ed.): Field Geology, in: Applied Geology, Encyclopedia of Earth Sciences Series, vol 3. Springer, Boston, MA, https://doi.org/10.1007/0-387-30842-3_21, 1984.
Fossen, H.: Structural Geology, Cambridge University Press, New York, 524 pp., ISBN-13 978-1107057647, 2016.
Frank, T.: Advanced visualization and modeling of tetrahedral meshes., Thèse de doctorat dirigée par Mallet, Jean-Laurent Géosciences Vandoeuvre-les-Nancy, INPL 2006,
https://hal.univ-lorraine.fr/tel-01752480v1 (last access: 31 December 2024), 2006.
Frodeman, R.: Geological reasoning: geology as an interpretive and historical science, Geol. Soc. Am. Bull., 107, 960–968, 1995.
Galton, A.: Spatial and temporal knowledge representation, Earth Sci. Inform., 2, 169–187, https://doi.org/10.1007/s12145-009-0027-6, 2009.
Garcia, L. F., Abel, M., Perrin, M., and dos Santos Alvarenga, R.: The GeoCore ontology: A core ontology for general use in Geology, Comput. Geosci., 135, 104387, https://doi.org/10.1016/j.cageo.2019.104387, 2020.
Geodes-Solutions:
https://geode-solutions.com/opengeode/, last access: 10 September 2024.
Giraud, J., Lindsay, M., Jessell, M., and Ogarko, V.: Towards plausible lithological classification from geophysical inversion: honouring geological principles in subsurface imaging, Solid Earth, 11, 419–436, https://doi.org/10.5194/se-11-419-2020, 2020.
Giraud, J., Caumon, G., Grose, L., Ogarko, V., and Cupillard, P.: Integration of automatic implicit geological modelling i
n deterministic geophysical inversion, Solid Earth, 15, 63–89, https://doi.org/10.5194/se-15-63-2024, 2024.
Gleeson, T., Wagener, T., Döll, P., Zipper, S. C., West, C., Wada, Y., Taylor, R., Scanlon, B., Rosolem, R., Rahman, S., Oshinlaja, N., Maxwell, R., Lo, M.-H., Kim, H., Hill, M., Hartmann, A., Fogg, G., Famiglietti, J. S., Ducharne, A., de Graaf, I., Cuthbert, M., Condon, L., Bresciani, E., and Bierkens, M. F. P.: GMD perspective: The quest to improve the evaluation of groundwater representation in continental- to global-scale models, Geosci. Model Dev., 14, 7545–7571, https://doi.org/10.5194/gmd-14-7545-2021, 2021.
Gong, P. and Mu, L.: Error detection through consistency checking, Geogr. Inf. Sci., 6, 188–193, 2000.
Grose, L., Ailleres, L., Laurent, G., Armit, R., and Jessell, M.: Inversion of geological knowledge for fold geometry, J. Struct. Geol., 119, 1–14, https://doi.org/10.1016/j.jsg.2018.11.010, 2019.
Groshong Jr., R. H.: 3-D Structural Geology a Practical Guide to Quantitative Surface and Subsurface Map Interpretation, 2nd Edn., Springer-Verlag Berlin Heidelberg, ISBN 13 978-3540310549, 2006.
Harrap, R.: A Legend Language for Geologic Maps, Precambrian Times, Geological Association of Canada, Precambrian Division Newsletter, 1, 3–9, 2001.
Hillier, M., de Kemp, E. A., and Schetselaar, E. M.: Implicitly modelled stratigraphic surfaces using generalized interpolation, in: AIP conference proceedings, 1738, 050004, International Conference of Numerical Analysis and Applied Mathematics, 22–28 September 2015, Rhodes, Greece, https://doi.org/10.1063/1.4951819, 2016.
Hillier, M. J., Schetselaar, E. M., de Kemp, E. A., and Perron, G.: Three-dimensional modelling of geological surfaces using generalized interpolation with radial basis functions, Math. Geosci., 46, 931–953, 2014.
Hillier, M. J., Wellmann, F., Brodaric, B., de Kemp, E. A., and Schetselaar, E.: Three-Dimensional Structural Geological Modeling Using Graph Neural Networks, Math. Geosci., 53, 1725–1749, https://doi.org/10.1007/s11004-021-09945-x, 2021a.
Hinojosa, J. H. and Mickus, K. L.: Foreland basin-a FORTRAN program to model the formation of foreland basins resulting from the flexural deflection of the lithosphere caused by a time-varying distributed load, Comput. Geosci., 19, 1321–1332, https://doi.org/10.1016/0098-3004(93)90032-Z, 1993.
Hobbs, B., Regenauer-Lieb, K., and Ord, A.: Thermodynamics of Folding in the Middle to Lower Crust, Geology, 35, 175–178, https://doi.org/10.1130/G23188A, 2007.
Jayr, S., Gringarten, E., Tertois, A.-L., Mallet, J.-L., and Dulac, J.-C.: The need for a correct geological modelling support: The advent of the UVT-transform, First Break, 26, 73–79, https://doi.org/10.3997/1365-2397.26.10.28558, 2008.
Jessell, M., Aillères, L., de Kemp, E. A., Lindsay, M., Wellmann, J., Hillier, M., Laurent, G., Carmichael, T., and Martin, R.: Next generation three-dimensional geologic modeling and inversion, Soc. Eco. Geo. Spc. Pub., 18, 261–272, 2014.
Jessell, M., Ogarko, V., de Rose, Y., Lindsay, M., Joshi, R., Piechocka, A., Grose, L., de la Varga, M., Ailleres, L., and Pirot, G.: Automated geological map deconstruction for 3D model construction using
map2loop 1.0 and
map2model 1.0, Geosci. Model Dev., 14, 5063–5092, https://doi.org/10.5194/gmd-14-5063-2021, 2021.
Jessell, M. W.: Noddy: an interactive map creation package, Unpublished MSc Thesis, University of London,
https://tectonique.net/noddy/ (last access: 31 December 2024), 1981.
Kardel, T. and Paul Maquet, P.: Nicolaus Steno: Biography and Original Papers of a 17th Century Scientist, 2013'th (Kindle) Edition, Springer, 2013th Edn., 739, ISBN-13 978-3642250781, 2012.
Lajaunie, C., Courrioux, G., and Manuel, L.: Foliation fields and 3D cartography in geology: principles of a method based on potential interpolation. Math. Geol., 29, 571–584, https://doi.org/10.1007/BF02775087, 1997.
Lajevardi, S. and Deutsch, C. V.: Stochastic regridding of geological models for flow simulation, B. Can. Petrol. Geol., 63, 374–392, https://doi.org/10.2113/gscpgbull.63.4.374, 2015.
Le, H. H., Gabriel, P., Gietzel, J., and Schaeben, H.: An object-relational spatio-temporal geoscience data model, Comput. Geosci., 57, 104–115, https://doi.org/10.1016/j.cageo.2013.04.014, 2013.
Lindsay, M. D., Aillères, L., Jessell, M. W., de Kemp, E. A., and Betts, P. G.: Locating and quantifying geological uncertainty in three-dimensional models: Analysis of the Gippsland Basin, southeastern Australia, Tectonophysics, 546–547, 10–27, https://doi.org/10.1016/j.tecto.2012.04.007, 2012.
Lyell, C.: Principles of Geology: Or, the Modern Changes of the Earth and Its Inhabitants, Considered As Illustrative of Geology, Legare Street Press, ISBN-13 978-1015539976, (reprinted 2022), 496, 1833.
Mallet, J.-L.: Space–Time Mathematical Framework for Sedimentary Geology, Math. Geol., 36, 1–32, https://doi.org/10.1023/B:MATG.0000016228.75495.7c, 2004.
Maxelon, M., Renard, P., Courrioux, G., Brändli, M., and Mancktelow, N.: A workflow to facilitate three-dimensional geometrical modelling of complex poly-deformed geological units, Comput. Geosci., 35, 644–658, https://doi.org/10.1016/j.cageo.2008.06.005, 2009.
McKay, G. and Harris, J. R.: Comparison of the Data-Driven Random Forests Model and a Knowledge-Driven Method for Mineral Prospectivity Mapping: A Case Study for Gold Deposits Around the Huritz Group and Nueltin Suite, Nunavut, Canada. Nat. Resour. Res., 25, 125–143, https://doi.org/10.1007/s11053-015-9274-z, 2016.
McMechan, M. E., Root, K. G., Simony, P. S., and Pattison, D. R. M.: Nailed to the craton: Stratigraphic continuity across the southeastern Canadian Cordillera with tectonic implications for ribbon continent models, Geology, 49, 101–105, https://doi.org/10.1130/G23188A, 2021.
Melnikova, Y., Cordua, K. S., and Mosegaard, K.: History Matching: Towards Geologically Reasonable Models. Abstract fro
m EAGE Integrated Reservoir Modelling: Are we doing it right?, Dubai, United Arab Emirates, https://doi.org/10.3997/2214-4609.20142866, 2012.
Michalak, J.: Topological conceptual model of geological relative time scale for geoinformation systems, Comput. Geosci., 31-7, 865–876, https://doi.org/10.1016/j.cageo.2005.03.001, 2005.
Morley, C. K.: Out-of-sequence thrusts, Tectonics, 7, 539–561, 1988.
Nikoohemat, S., Diakité, A. A., Lehtola, V., Zlatanova, S., and Vosselman, G.: Consistency grammar for 3D indoor model checking, Trans. GIS, 25, 189–212, https://doi.org/10.1111/tgis.12686, 2021.
Pellerin, J., Caumon, G., Julio, C., Mejia-Herrera, P., and Botella, A.: Elements for measuring the complexity of 3D structural models: Connectivity and geometry, Comput. Geosci., 76, 130–140, https://doi.org/10.1016/j.cageo.2015.01.002, 2015.
Pellerin, J., Botella, A., Bonneau, F., Mazuyer, A., Chauvin, B., Lévy, B., and Caumon, G.: RINGMesh: A programming library for developing mesh-based geomodeling applications, Comput. Geosci., 104, 93–100, https://doi.org/10.1016/j.cageo.2017.03.005, 2017.
Perrin, M., Morel, O., Mastella, L., and Alexandre, L.: Geological Time Formalization: an improved formal model for describing time successions and their correlation, Earth Sci. Inform., 4, 81–96, https://doi.org/10.1007/s12145-011-0080-9, 2011.
Perrin, M., Poudret, M., Guiard, N., and Schneider, S.: Chapter 6: Geological Surface Assemblage, in: Shared Earth Modeling, Knowledge driven solutions for building and managing subsurface 3D geological models, Energies Nouvelles Publications 0- TECHNIP, Paris, France, 115–139,
https://www.researchgate.net/publication/236901352_Geological_Surface_Assemblage (last access: 7 January 2025), 2013.
Pizzella, L., Alais, R., Lopez, S., Freulon X., and Rivoirard, J.: Taking Better Advantage of Fold Axis Data to Characterize Anisotropy of Complex Folded Structures in the Implicit Modeling Framework, Math. Geosci., 54, 95–130, https://doi.org/10.1007/s11004-021-09950-0, 2022.
Pyrcz, M. J., Sech, R. P., Covault, J. A., Willis, B. J., Sylvester, Z., Sun, T., and Garner, D.: Stratigraphic rule-based reservoir modeling, B. Can. Petrol. Geol., 63, 287–303, 2015.
Qu, Y., Perrin, M., Torabi, A., Abel, M., and Giese, M.: GeoFault: A well-founded fault ontology for interoperability in geological modeling, Comput. Geosci., 182, 105478, https://doi.org/10.1016/j.cageo.2023.105478, 2024.
Ranalli, G.: A stochastic model for strike-slip faulting, Math. Geol., 12, 399–412, https://doi.org/10.1007/BF01029423, 1980.
Rauch, A., Sartori, M., Rossi, E., Baland, P., and Castelltort, S.: Trace Information Extraction (TIE): A new approach to extract structural information from traces in geological maps, J. Struct. Geol., 126, 286–300, https://doi.org/10.1016/j.jsg.2019.06.007, 2019.
Rothery, D.: Geology: A Complete Introduction, Quercus, 1st Edn., 16 Feb. 2016, ISBN 13 978-1473601550, 2016.
Schaaf, A., de la Varga, M., Wellmann, F., and Bond, C. E.: Constraining stochastic 3-D structural geological models with topology information using approximate Bayesian computation in GemPy 2.1, Geosci. Model Dev., 14, 3899–3913, https://doi.org/10.5194/gmd-14-3899-2021, 2021.
Schetselaar, E. M. and de Kemp, E. A.: Topological encoding of spatial relationships to support geological modelling in a 3-D GIS environment, Int. Assoc. for Mathematical Geology XIth International Congress, Université de Liège – Belgium,
https://iamgmembers.org/catalog/index.php?main_page=product_info&cPath=65&products_id=192 (last access: 7 January 2025), 2006.
Shokouhi, P., Kumar, V., Prathipati, S., Hosseini, S. A., Giles, C. L., and Kifer, D.: Physics-informed deep learning for prediction of CO
2 storage site response, J. Contam. Hydrol., 241, 103835, https://doi.org/10.1016/j.jconhyd.2021.103835, 2021.
Thapa, P. and McMechan, M. E.: Methodology for portraying 3D structure using ArcGIS: a test case from the southern Canadian Rocky Mountains, British Columbia and Alberta, Geological Survey of Canada, Open File 8576, https://doi.org/10.4095/314941, 2019.
Thiele, S. T., Jessel, M. W., Lindsay, M., Ogarko, V., Wellmann, J. F., and Pakyuz-Charrier, E.: The topology of geology 1: Topological analysis, J. Struct. Geol., 91, 27–38, https://doi.org/10.1016/j.jsg.2016.08.009, 2016a.
Thiele, S. T., Jessel, M. W., Lindsay, M., Wellmann, J. F., and Pakyuz-Charrier, E.: The topology of geology 2: Topological uncertainty, J. Struct. Geol., 91, 74–87, https://doi.org/10.1016/j.jsg.2016.08.010, 2016b.
van Giffen, B. Herhausen, D., and Fahse, T.: Overcoming the pitfalls and perils of algorithms: A classification of machine learning biases and mitigation methods, J. Bus. Res., 144, 93–106, https://doi.org/10.1016/j.jbusres.2022.01.076, 2022.
Van Oosterom, P.: Maintaining consistent topology including historical data in a large spatial database, Auto-Carto XIII, Proceedings of the Annual Convention and Exposition Technical Papers 7–10 April 1997, Seattle, Washington, 13, 327–336,
https://cartogis.org/docs/proceedings/archive/auto-carto-13/pdf/maintaining-consistent-topology-including-historical-data-in-a-large.pdf (last access: 31 December 2024), 1997.
von Harten, J., de la Varga, M., Hillier, M., and Wellmann, F.: Informed Local Smoothing in 3D Implicit Geological Modeling, Minerals, 11, 1281, https://doi.org/10.3390/min11111281, 2021.
Wellmann, F. and Caumon, G.: 3-D Structural geological models: Concepts, methods, and uncertainties, Adv. Geophys., 59, 1–121, https://doi.org/10.1016/bs.agph.2018.09.001, 2018.
Zhan, X., Liang, J., Lu, C., and Hu, G.: Semantic Description and Complete Computer Characterization of Structural Geological Models, Geosci. Model Dev. Discuss. [preprint], https://doi.org/10.5194/gmd-2018-305, 2019.
Zhan, X., Lu, C., and Hu, G.: A Formal Representation of the Semantics of Structural Geological Models, Sci. Program., 5553774, 18 pp., https://doi.org/10.1155/2022/5553774, 2022.
Ziggelaar, A.: The age of Earth in Niels Stensen's geology, Geol. Soc. Am. Mem., 203, 135–142, 2009.
