Improving multivariate geostatistical modelling with data transformations


Maria Bolgkoranou, The Robert M. Buchan Department of Mining, Queen's University at Kingston; Julian Ortiz, The Robert M. Buchan Department of Mining, Queen's Universty at Kingston

The main goal of geostatistical modeling is to characterize the spatial distribution of attributes in space and perform estimation and simulation. Availability of high dimensional geological data has become common. Therefore, the complexity of the data sets, requires advanced multivariate geostatistical methods. For multivariate observations, we should model associations at a specific location and between locations, and also among variables. There are many methods for multivariate geostatistical modelling, but they rely on a multiGaussian assumption. Various data transformations can be applied to make the data consistent with this assumption. This allows the use of conventional geostatistical methods.  In this paper, we briefly review the current multivariate modeling techniques and we explain the challenges and restrictions that arise due to the assumptions in which those techniques are based. Finally, we present various mathematical transformations such as Principal Component Analysis (PCA) and Local Linear Embedding (LLE) and show how they can be used to improve multivariate geostatistical modeling.