Interpolation in stationary spatial and spatial-temporal datasets

Abstract

In the early 1950s the study on how to determine true ore-grade distributions in the mining sector, sparked the development of a series of statistical tools that specifically allows for spatial and subsequently spatial-temporal dependence. These statistics are commonly referred to as geostatistics, and has since been incorporated in several fields of study characterized by this dependence. Basic descriptive statistics and mapping tools for geostatistics are defined and illustrated by means of a simulated dataset. The moments are modelled according to predefined conditions and model structures to describe the spatial and spatial-temporal variance in the data. These variograms and covariance structures are subsequently utilized in the least square procedure, namely kriging. At present, kriging is most commonly used in geostatistics for the interpolation and simulation of spatial or spatial-temporal data. The univariate and multivariate spatial and spatial-temporal kriging techniques are tested on the simulated dataset, to demonstrate how interpolation weights are determined according to the lag distances and underlying variance structure. The strength, weaknesses and inherent complexities of the methodologies are highlighted.