Multivariate Geostatistical Simulation using Principal Component Analysis
Ortiz, Julian M.
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Multivariate geostatistical simulation is aimed at reproducing the statistical relationships between variables and their spatial distribution. We present a methodology whereby grades and a filler variable are transformed to log-ratios, to impose the sum to 100%. Then, these log-ratios are linearly transformed to Principal Components (PCs). Sequential Gaussian Simulation is performed and the simulated factors are then back-transformed to simulated log-ratios, and these are backtransformed to grades. An application to a Nickel laterite deposit is presented. Spatial dependences are checked by use of cross-variograms. This confirms that PCA tends to spatially decorrelate the factors, allowing for the independent simulation of each PCs, instead of requiring a co-simulation. The results of SGS showed that the simulated grades resulting from the proposed approach reproduce reasonably well the spatial and statistical relationships between the grades. Co-simulation of the log-ratios considering the spatial cross relationships between the variables using a linear model of coregionalization was performed and the results were compared with the backtransformed grades after Principal Component Analysis.