Design and experiment of a topological structure adapted to tetrahedral modeling

Topological relationships between geological objects are of great interest in the process of mining and petroleum exploration. Indeed, adjacency, inclusion and intersection are common relationships between geological objects such as faults, geological units, fractures, reservoirs... However, in the context of 3D modeling, actual geometric data structures used to store objects of interest are not designed to manage explicit topological relationships. For example, with Gocad© software, topological analyses are possible but they require a series of successive manipulations and are time consuming. This paper presents the development of a 3D topological query prototype, TQuery, compatible with Gocad© modeling platform. It allows the user to export Gocad© objects to a data storage structure that regularizes the spatial topological relationships between objects. The development of TQuery was oriented toward the use of volumetric objects that are composed of tetrahedrons. Exported data are then retrieved and used for 3D metric and topological spatial queries. Query results are subsequently imported back into Gocad© as objects that the user can manipulate. One of the advantages of TQuery is that different types of objects can be queried at the same time without restricting the operations to voxel regions. TQuery allows the user to analyze data more quickly and efficiently and does not require a 3D modeling specialist to use it which is particularly attractive in the context of a decision-making system. The prototype was tested on a 3D model of a continental red-bed copper deposit in the Silurian Robitaille Formation (the Transfiguration property, Québec, Canada).