One of the most difficult tasks of modeling spatial and spatiotemporal random fields is that of deriving an accurate representation of the dependence structure. In practice, the researcher is faced with selecting the best empirical representation of the data, the proper family of parametric models, and the most efficient method of parameter estimation once the model is selected. Each of these decisions has direct consequence on the prediction accuracy of the modeled random field. In order to facilitate the process of spatial dependence modeling, a general class of covariogram estimators is introduced. They are derived by direct application of Bochner's theorem on the Fourier-Bessel series representation of the covariogram. Extensions are derived for one, two and three dimensions and spatiotemporal extensions for one, two and three spatial dimensions as well. A spatial application is demonstrated for prediction of the distribution of sediment contaminants in Galveston Bay estuary, Texas. Also included is a spatiotemporal application to generate predictions for sea surface temperatures adjusted for periodic climatic effects from a long-term study region off southern California.