AbstractsMathematics

The development of spatio–temporal geoscience information systems (TGSIS) as the next generation of geographic information systems (GIS) and geoscience information systems (GSIS) was investigated with respect to the following four aspects: concepts, data models, software, and applications. These systems are capable of capturing, storing, managing, and querying data of geo–objects subject to dynamic processes, thereby causing the evolution of their geometry, topology and geoscience properties. In this study, five data models were proposed. The first data model represents static geo–objects whose geometries are in the 3–dimensional space. The second and third data models represent geological surfaces evolving in a discrete and continuous manner, respectively. The fourth data model is a general model that represents geo–objects whose geometries are n–dimensional embedding in the m–dimensional space R^m, m >= 3. The topology and the properties of these geo–objects are also represented in the data model. In this model, time is represented as one dimension (valid time). Moreover, the valid time is an independent variable, whereas geometry, topology, and the properties are dependent (on time) variables. The fifth data model represents multiple indexed geoscience data in which time and other non–spatial dimensions are interpreted as larger spatial dimensions. To capture data in space and time, morphological interpolation methods were reviewed, and a new morphological interpolation method was proposed to model geological surfaces evolving continuously in a time interval. This algorithm is based on parameterisation techniques to locate the cross–reference and then compute the trajectories complying with geometrical constraints. In addition, the long transaction feature was studied, and the data schema, functions, triggers, and views were proposed to implement the long transaction feature and the database versioning in PostgreSQL. To implement database versioning tailored to geoscience applications, an algorithm comparing two triangulated meshes was also proposed. Therefore, TGSIS enable geologists to manage different versions of geoscience data for different geological paradigms, data, and authors. Finally, a prototype software system was built. This system uses the client/server architecture in which the server side uses the PostgreSQL database management system and the client side uses the gOcad geomodeling system. The system was also applied to certain sample applications.