Non-stationary Geostatistical Modeling Based on Distance Weighted Statistics and Distributions (original) (raw)
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Medium and short term mine planning require models of mineral deposits that account for internal geological structures that permit scheduling of mine production at a weekly and monthly production periods. Modified kriging estimation techniques are used for accounting for such geologic structures. However, in the case of simulation, it is strongly linked to the use of sequential Gaussian simulation which has difficulties in reproducing internal geologic patterns. This thesis presents: (1) a set of tools to verify the impact of mean and variance trends in a domain; (2) a methodology for identifying highly variable sub-regions within domains; and (3) a simulation methodology that accounts for the internal structures in the domain required by medium and short term planning. Specifically, the simulation approach consists of: (1) moving the domain to a high dimensional space where the features of the internal structures in the domain are more stationary, (2) simulating the realizations via sequential Gaussian simulation, and (3) projecting the results to the initial dimensional space. I am grateful to the Centre of Computational Geostatistics (CCG) for providing financial support during my studies and its industrial sponsors that keep supporting the research made in the CCG. Dr. Clayton Deutsch is an inspiration in the CCG, during the group meetings he is a source of motivation and his leadership urges the necessity to keep improving and developing new ideas. My gratitude also goes to my friends, Yupeng Li, Behrang Koushavand, Tong Wang, Abhay Kumar and especially Enrique Gallardo for their support and willingness to discuss academic and non-academic topics.
Traditional geostatistical estimation relies on a stationary variogram within chosen rock types or spatial domains; however, there are often locationdependent variations across the chosen domain. Subdividing the domain is not always practical; the number of data becomes too few for reliable inference. Moreover, changes in the spatial behaviour of the variable can occur smoothly across the domain. Location dependent variograms based on spatial weights are proposed to depict the local spatial variability. The weights applied to the sample pairs are obtained by a Gaussian Kernel function. The location dependent experimental variograms are semi-automatically modelled to yield local variogram parameters. These parameters define the local anisotropy orientation, ranges, nugget effect, and variogram shape. They are smoothly interpolated at the resolution of estimation and subsequently used in a quasistationary kriging approach. The same variogram is considered for all distances within the search radius centered at the location being estimated. This assures the positive definiteness of the kriging equations. The improvement in local estimation is significant. Local features are better reproduced in estimation, while the smoothing effect is mitigated. The kriging variances provide a more complete measure of local accuracy.