Multivariate geostatistical simulation of compositional data using Principal Component Analysis

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Bolgkoranou, Maria
Geostatistics , Multivariate Geostatistical Modeling , Principal Component Analysis
In the mining industry, there is interest in the use of spatial processes to model spatially collected data. For the multivariate observations, we should model associations at a specific location and between locations, but also among variables. Common methods for multivariate modeling rely on the Linear Model of Coregionalization (LCM), which is limited in higher dimensions and generates models that do not properly reproduce the features of the original multivariate samples. In this thesis we present a simple methodology for multivariate geostatistical modeling of compositional data using Principal Component Analysis (PCA). According to the methodology, grades are, first, transformed to log-ratios. Then, these log-ratios are linearly transformed to Principal Components (PCs). PCA tends to spatially decorrelate the factors, allowing for the independent simulation of each PCs, instead of requiring a co-simulation. Sequential Gaussian Simulation is performed independently on each Principal Component and the simulated factors are then back-transformed to simulated log-ratios, and these are finally back-transformed to grades. Using a 6-dimensional data set from a Nickel-Laterite deposit, we demonstrate the difference between the proposed methodology and classical co-simulation. The statistics and the further validation of the back-transformed grades after PCA and Sequential Gaussian Simulation showed that the proposed methodology tends to respect the relationships between the variables whereas co-simulation of the grades tends to respect the statistics but the reproduced relationships are not representative.
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