Résumé: Tel que le notent si bien Oliver et al. (1990), la plupart des méthodes d’interpolation classiques sont basées sur les modèles des méthodes numériques différents des modèles probabilistes de variation spatiale. Les distributions des variables des données spatiales se comportent plus comme des variables aléatoires et la théorie des variables régionalisées comporte un ensemble de méthodes stochastiques pour les analyser. Le krigeage et le cokrigeage, basés sur cette théorie, expriment les variations spatiales de variables en termes de variogrammes et ils minimisent les erreurs de prédiction qui sont elles-mêmes estimées. Appliquées aux données des variables pédologiques des champs de la Station de recherches de Lennoxville, les méthodes ou techniques d’interpolation de la géostatistique: les krigeages et cokrigeages ordinaires, universels et par bloc, ainsi dénommées, sont explorées et comparées en vue d’en identifier la méthode appropriée intégrable dans un système d’information géographique, pour obtenir l’optimum de la modélisation, la présentation et celui de l’analyse spatiale. Les valeurs krigées et cokrigées des techniques choisies sont obtenues à l’aide de l’algorithme Cokri (Marcotte, 1991, 1993) et sont comparées aux valeurs initiales dont elles en sont les estimations. Des tests de similarité appliqués à ces données et résultats attestent la similarité de leurs distributions respectives. En d’autres termes, les types de krigeage et de cokrigeage examinés bénéficient de la même homogénéité des données qui est vérifiée par des outils de comparaison visuels et des traitements géostatistiques. De plus l’utilisation de ces méthodes donne des erreurs minimes proches de la réalité. Ainsi, selon la nature spécifique des données spatiales, en l’occurence les données homogènes sans structure spatiale particulière cachée, un estimateur linéaire simple ou la moyenne arithmétique de ces données, suffit pour représenter les variables étudiées.||Abstract: As Oliver et al. (1990) pointed it out so well, most of iraditional methods of interpolation are based on numerical method models as distinct from stochastic models of spatial variation. Spatially distributed data behave more like random variables, however, and regionalized variable theory provides a set of stochastic methods for analyzing them. Kriging and cokriging, based on that theory, depend on expressing spatial variation of the property in terms of variograms, and they minimize the prediction erros which are themselves estimated. Used on pedological parameters data, oridinary, universai and block krigings and cokrigings, geostatistical interpolation methods or techniques, are expiored and compared in order to identify the appropriate method which can be integrated into a Geographic Information System to provide optimum modelting, presentation and spatial analysis. Kriged and cokriged values are obtained by Cokri algorithm (Marcotte, 1991, 1993), and are compared to estimated initial data. Similarity tests applied to these data and values show that their respective distributions are similar. In othe words, the examined kriging and cokriging types perfom equally well. They ail take advantage of the data homogeneity, verified by visual comparison and geostatiatical tools or techniques, for providing doser minimum error terms. Thus, according to the special nature of spatial data, namely the homogeneous ones without a hiden particular spatial structure, a simple linear estimator, such as the data arithmetical mean, is sufficient for representing die variables under consideration.

The urban environment is complex, heterogeneous and temporally changeable. Man is the main actor in the transformation of urban areas where he interacts with intensity. Spatial differentiation is a result of human occupation in the urban environment. This occupation may vary according to land use, population density, social and economic characteristics and environment. This leads us to say that the socio-economic and environmental indicators change according to the various locations in the urban area and through time. Our goal is to measure the socio-economic and environmental changes in the urban area of the city of Sherbrooke using remote sensing data synchronized with the censuses and that we will then integrate into the geographic information system (GIS). We have used data from the 1981 and 2006 censuses, 1983 aerial photos, 2007 orthophotos and 1983 MSS and 2006 Ikons satellite images to measure the socio-economic and environmental changes in the city of Sherbrooke. We have used spatial analysis tools to integrate image data with census data.The methods uses such as global indices, principal component analysis combined with the variation between the two dates have yielded interesting results.The first factor in principal component analysis with orthogonal rotation (Varimax) justified a substantial percentage of the variance in global indices.The use of dissemination areas resulted in detailed information on the change in the city. From the perspective of spatial distribution, we noted a major difference between the central areas and the peripheral areas in 1981 and 2006. From the perspective of evolution between 1981 and 2006, we observed that are positive and negative changes at various levels took place. We also observed the evolution of ethnicity in the Sherbrooke city and Lennoxville municipality.The study showed that the French population is prevalent in the old city of Sherbrooke as the English population is prevalent in Lennoxville.The European population is spread over the two cities.The aboriginal population is well distributed over the city of Sherbrooke.The population from Asian and Oceanic backgrounds are [i.e. is] concentrated (sometimes on an exclusive basis) in the north and west-centre area of Jardins-Fleuris, in the eastern area of l'Assomption, the northeastern area of Sainte-Famille and the center area of Marie-Reine. We also find concentrations of immigrant populations from all backgrounds in areas such as in the southern part of the Immaculée-Conception and Saint-Joseph and in the south-eastern part of Sainte-Jeanne-d'Arc. This indicates that ethnic neighborhoods are taking roots in the city of Sherbrooke.