Using third-order cumulants to investigate spatial variation: a case study on the porosity of the Bunter Sandstone

The multivariate cumulants characterize aspects of the spatial variability of a regionalized variable. A centred multivariate Gaussian random variable, for example, has zero third-order cumulants. In this paper it is shown how the third-order cumulants can be used to test the plausibility of the assumption of multivariate normality for the porosity of an important formation, the Bunter Sandstone in the North Sea. The results suggest that the spatial variability of this variable deviates from multivariate normality, and that this assumption may lead to misleading inferences about, for example, the uncertainty attached to kriging predictions.