A formal framework for the representation of stack-based terrains

This paper presents a formal framework for the representation of three-dimensional geospatial data and the definition of common geographic information system (GIS) spatial operations. We use the compact stack-based representation of terrains (SBRT) in order to model geological volumetric data, both at the surface and subsurface levels, thus preventing the large storage requirements of regular voxel models. The main contribution of this paper is fitting the SBRT into the geo-atom theory in a seamless way, providing it with a sound formal geographic foundation. In addition we have defined a set of common spatial operations on this representation using the tools provided by map algebra. More complex geoprocessing operations or geophysical simulations using the SBRT as representation can be implemented as a composition of these fundamental operations. Finally a data model and an implementation extending the coverage concept provided by the Geography Markup Language standard are suggested. Geoscientists and GIS professionals can take advantage of this model to exchange and reuse geoinformation within a well-specified framework.