ABSTRACT
This chapter considers parametric covariance structures for geostatistical data, which are specified by a parametric model for either the spatial covariance function, semivariogram, or generalized covariance function. Two necessary properties of a covariance function are evenness and positive definiteness. Methods of constructing such functions are reviewed. A table listing more than 25 valid isotropic covariance functions is provided, followed by plots of most of them, including the commonly used exponential, spherical, Gaussian, and Matern models. Realizations of processes with several different covariance functions are displayed. Parameters controlling various aspects of the spatial dependence are described, such as the process variance, nugget effect, range or practical range, and smoothness parameter. Extensions of the covariance models to accommodate anisotropy and nonstationarity are presented; the latter include models for the semivariogram and generalized covariance function.
