| 12 Oct 2026
The Structural Topology Model: A Topology–Ontology Framework for Assigning Geological Legends in 3D and 2D Geomodelling
Abstract. Three-dimensional geological modelling of orogenic belts and other highly deformed complexes remains challenging, especially in metamorphic complexes, where the obliteration of stratigraphy complicates the definition of units, boundaries, and their relations. In such contexts, approaches inherited from modelling in sedimentary basins often lead to ambiguous definition of the legend (and the units represented therein) and topologically inconsistent 3D models. Here, we present the Structural Topology Model (STM), a conceptual framework designed to formalise the construction of consistent geological legends by making explicit the relations between units, bounding surfaces, and their structural roles, according to the concept of oriented topology (based on the properties of continuity and conformability). Central to STM is the concept of the Structural Level, which integrates absolute ages, relative ages, and structural relations into a scalar field used to define an ordered sequence of geological units and events, even where chronological constraints are incomplete or ambiguous. STM was conceived for 3D modelling, but it could be applied also in 2D to geological maps and cross-section providing useful constraints and tools to validate topological relationships and conceptual models. The method is illustrated with two case studies in the Helvetic units of the Aar Massif (Helvetics, Central Swiss Alps) and in Penninic units of the Gressoney Valley (Western Italian Alps). In both examples, STM enables the construction of topologically consistent volumetric models that preserve internal structures, foliation patterns, and cross-cutting relationships, while providing an unambiguous framework for labelling units and boundaries. STM, already implemented in the open-source PZero 3D modelling platform, is independent of specific software implementations or interpolation techniques and could be potentially applied in a wide range of geological settings and software. In this way, limitations of implicit 3D modelling in complex polydeformed areas are reduced substantially.
This is an interesting addition to the body of work that transforms geological information into topological relationships and then applies these relationships as constraints to 3D geological modelling. Unfortunately, the paper ignores a large part of the previous work on geological topology, starting with the 50-year old seminal paper of Kerry Burns. I list below a series of publications, from Burns’ first papers to modern implementations and extensions that overlap considerably with the ideas presented in this paper. It also ignores the recent work on geological ontologies. The value of the work is significantly reduced by its lack of reference to and comparison with the existing literature.
Before this paper can be considered for publication the previous work needs to be clearly laid out in the introductory sections, and the genuinely novel parts of this work need to be highlighted as they are introduced, whereas those parts that reproduce or modify existing concepts need to acknowledge those earlier works. The discussion needs to explain why and how the STM is a more complete formulation than or where it could benefit from these earlier works on topology and ontology.
Section 2.1 is essentially describing the potential field method as applied in Geomodeller, SKUA, Leapfrog, LoopStructural… it is not clear why this is a subsection of the Structural Topology Model when it is an established approach?
Section 2.2 covers much of the same ground as Burns 1975, Allen 1981 and Thiele et al. 2016., with an interesting discussion of scale dependence of the system. Both sections 2.1 and 2.2 are probably better framed as Previous Work with the scaling discussion moved to the Discussion section?
Section 2 is titled The Structural Topology Model, however Section 2.3 is also titled STM which shouldn’t really be a subtitle of the same titled section?
Since PZero inherits LoopStructural, much of the approach described in Section 2.3 is inherited from that package, this should be acknowledged here.
One of the applications of the STM is in model validation, so a comparison with the work of Parquer et al 2025 is needed. Parquer et al describe a method for validating 3D geological models which depends heavily on a topological analysis, so the current work needs to explain in the discussion section what it adds to and how it differs from that work on model validation.
The paper title includes the term ontology, however no formal ontology is presented, and no discussion is made as to how the current work differs from or could improve on existing the geological ontologies of Garcia et al., 2020 and Broderic and Richard, 2021.
Key references
1. Primary explorations of geological and temporal topology in 2D & 3D
Burns, K., 1975. Analysis of geological events. J. Int. Assoc. Math. Geol. 7, 295e321. [First description of geological topology as a graph]
Burns, K., Remfry, J., 1976. A computer method of constructing geological histories from field surveys and maps. Comput. Geosci. 2, 141e162. [First attempt to automate topology extraction]
Burns, K., Shepherd, J., Marshall, B., 1978. Analysis of Relational Data from Metamorphic Tectonites; Derivation of Deformation Sequences from Overprinting Relations. Recent Advances in Geomathematics, Pergamon New York, NY, pp. 171e199. [Case study using earlier concepts]
Burns, K.L., 1981. Retrieval of tectonic process models from geologic maps and diagrams. In: Proc. GIS. Geoscience Information Society, pp. 105e111. [First description of geological topology as a graph]
Burns, K.L., 1988. Lithologic topology and structural vector fields applied to subsurface predicting in geology. In: Proc.. of GIS/LIS. [First description of geological subsurface topology as a graph]
Allen, J. F.: Maintaining knowledge about temporal intervals, Commun. ACM, 26, 832–843, 1983. [First description of temporal topology]
Jessell, M.W. 1981. NODDY: An interactive map creation package. University of London. Unpublished MSc thesis, 52 pages. Published as Jessell, M.W. & Valenta, R.K. 1996. Structural Geophysics: Integrated structural and geophysical mapping. In: Structural Geology and Personal Computers (Ed. DePaor, D.G.), 303-324. Elsevier Science, Oxford. [First use of topology in 3D model construction]
Perrin, M., Zhu, B., Rainaud, J.-F., Schneider, S., 2005. Knowledge-driven applications for geological modeling. J. Pet. Sci. Eng. 47, 89e104. [Use of topology in explicit 3D model construction]
Michalak, J., 2005. Topological conceptual model of geological relative time scale for geoinformation systems. Comput. Geosci. 31, 865e876. [Development of temporal aspects]
2. Modern implemetations of topological approaches applied to Geomodelling
Thiele, S.T., Jessell, M.W., Lindsay, M., Wellmann, F. & Pakyuz-Charrier, E. 2016. The Topology of Geology 1: Topological Analysis. Journal of Structural Geology, 91, 27-38. [Application of topology to 3D modelling]
Thiele, S.T., Jessell, M.W., Lindsay, M., Wellmann, F. & Pakyuz-Charrier, E. 2016. The Topology of Geology 2: Topological Uncertainty. Journal of Structural Geology, 91, 74-87. [Application of topology to 3D uncertainty]
Jessell, M., Ogarko, V., Lindsay, M., Joshi, R., Piechocka, A., Grose, L., de la Varga, M., Ailleres, L. & Pirot, G. 2021. Automated geological map deconstruction for 3D model construction using map2loop 1.0 and map2model 1.0 Geoscientific Model Development https://gmd.copernicus.org/articles/14/5063/2021/ [Code to extract temporal and spatial topology from maps and its application to 3D modelling]
Parquer et al. 2025. https://doi.org/10.5194/gmd-18-71-2025 [Application of topology to 3D model validation]
Fang et al., 2026 https://doi.org/10.5194/gmd-19-8407-2026 [Application of topology to 3D model construction]
3. Geological Ontologies
Garcia et al. 2020. The GeoCore ontology: A core ontology for general use in Geology https://doi.org/10.1016/j.cageo.2019.104387
Brodaric, B., & Richard, S. 2021. GeoScience Ontology: Release 1.0.1 (Version 1.0.1) [Computer software]. Zenodo. https://doi.org/10.5281/zenodo.4743221
Lauchi et al. 2026. https://doi.org/10.5194/gmd-19-6517-2026 [Application of ontology to 3D model]