In Geostatistical modelling of the spatial distribution of rock attributes, the multivariate distribution of a Random Function defines the range of possible values and the spatial relationships among them. Under a decision of stationarity, the Random Function distribution and its statistics are inferred from data within a spatial domain deemed statistically homogenous. Assuming stationary multiGaussianity allows spatial prediction techniques to take advantage of this simple parametric distribution model. These techniques compute the local distributions with surrounding data and global spatially invariant statistics. They often fail to reproduce local changes in the mean, variability and, particularly, the spatial continuity, that are required for geologically realistic modelling of rock attributes. The proposed alternative is to build local Random Function models that are deemed stationary only in relation to the locations where they are defined. The corresponding location-dependent distributions and statistics are inferred by weighting the samples inversely proportional to their distance to anchor locations. These distributions are locally Gaussian transformed. The transformation models carry information on the local histogram. The distance weighted experimental measures of spatial correlation are able to adapt to local changes in the spatial continuity and are semi-automatically fitted by locally defined variogram models. The fields of local variogram and transformation parameters are used in locally stationary spatial prediction algorithms. The resulting attribute models are rich in non-stationary spatial features. This process implies a higher computational demand than the traditional techniques, but, if data is abundant enough to allow a reliable inference of the local statistics, the proposed locally stationary techniques outperform their stationary counterparts in terms of accuracy and precision. These improved models have the potential of providing better decision support for engineering design. / Mining Engineering
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:AEU.10048/1275 |
| Date | 11 1900 |
| Creators | Machuca-Mory, David Francisco |
| Contributors | Deutsch, Clayton V. (Civil and Environmental Engineering), Askari-Hasab, Hooman (Civil and Environmental Engineering), Leung, Juliana (Civil and Environmental Engineering), Sanchez-Azofeifa, Arturo (Earth and Atmospheric Sciences), Chils, Jean-Paul (Centre de Gosciences, MINES, ParisTech) |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 6192420 bytes, application/pdf |
| Relation | Machuca-Mory, D.F.and Deutsch, C.V (2008). Location-dependent variograms. Proceedings paper and presentation at the Eighth International Geostatistics Congress, GEOSTATS 2008, Santiago, Chile. |
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