Spatiotemporal stochastic models for earth science and engineering applications

Spatiotemporal processes occur in many areas of earth sciences and engineering. However, most of the available theoretical tools and techniques of space-time daft processing have been designed to operate exclusively in time or in space, and the importance of spatiotemporal variability was not fully appreciated until recently. To address this problem, a systematic framework of spatiotemporal random field (S/TRF) models for geoscience/engineering applications is presented and developed in this thesis.The space-tune continuity characterization is one of the most important aspects in S/TRF modelling, where the space-time continuity is displayed with experimental spatiotemporal variograms, summarized in terms of space-time continuity hypotheses, and modelled using spatiotemporal variogram functions. Permissible spatiotemporal covariance/variogram models are addressed through permissibility criteria appropriate to spatiotemporal processes.The estimation of spatiotemporal processes is developed in terms of spatiotemporal kriging techniques. Particular emphasis is given to the singularity analysis of spatiotemporal kriging systems. The impacts of covariance, functions, trend forms, and data configurations on the singularity of spatiotemporal kriging systems are discussed. In addition, the tensorial invariance of universal spatiotemporal kriging systems is investigated in terms of the space-time trend.The conditional simulation of spatiotemporal processes is proposed with the development of the sequential group Gaussian simulation techniques (SGGS), which is actually a series of sequential simulation algorithms associated with different group sizes. The simulation error is analyzed with different covariance models and simulation grids. The simulated annealing technique honoring experimental variograms, is also proposed, providing a way of conditional simulation without the covariance model fitting which is prerequisite for most simulation algorithms.The proposed techniques were first applied for modelling of the pressure system in a carbonate reservoir, and then applied for modelling of springwater contents in the Dyle watershed. The results of these case studies as well as the theory suggest that these techniques are realistic and feasible