Variograms with zonal anisotropies and noninvertible kriging systems

Zonal anisotropies are usually simply defined as those that are not geometric (i.e., that cannot be removed by an affine transformation). Such anisotropies have often been associated with zonations and models have been proposed to reflect that association. It is shown by example that such models can lead to noninvertible coefficient matrices in kriging systems, because the models are only (conditionally) semidefinite instead of positive definite. The relationship to the construction used in turning bands algorithm and also to spatial-temporal models is discussed.