Analogies and correspondences between variograms and covariance functions

Variograms and covariance functions are key tools in geostatistics. However , various properties, characterizations, and decomposition theorems have be en established for covariance functions only. We present analogous results for variograms and explore the connections with covariance functions. Our f indings include criteria for covariance functions on intervals, and we appl y them to exponential models, fractional Brownian motion, and locally polyn omial covariances. In particular, we characterize isotropic locally polynom ial covariance functions of degree 3.