Formal representation of 3D structural geological models

The development and widespread application of geological modeling methods has increased demands for the integration and sharing services of three dimensional (3D) geological data. However, theoretical research in the field of geological information sciences is limited despite the widespread use of Geographic Information Systems (GIS) in geology. In particular, fundamental research on the formal representations and standardized spatial descriptions of 3D structural models is required. This is necessary for accurate understanding and further applications of geological data in 3D space. In this paper, we propose a formal representation method for 3D structural models using the theory of point set topology, which produces a mathematical definition for the major types of geological objects. The spatial relationships between geologic boundaries, structures, and units are explained in detail using the 9-intersection model. Reasonable conditions for describing the topological space of 3D structural models are also provided. The results from this study can be used as potential support for the standardized representation and spatial quality evaluation of 3D structural models, as well as for specific needs related to model-based management, query, and analysis.