Abstract The spatial covariance of ln(k) can be modeled with a hierarchy of covariance structures corresponding to the organization of bedding within and among the lithofacies of a sedimentary sequence. Such a model accounts for the spatial correlation of ln(k) within and across bedding units defined at any one level ( Ritzi et al., 2004 ). This is related to correlation of ln(k) at a higher level (larger scale) through the spatial correlation of indicator variables representing the proportions, geometry, and juxtaposition patterns of the units at the lower level. In this paper the fitting of the components of the hierarchical model, written as nested functions, is considered in developing a hierarchical covariance model for use in estimation, simulation, or analytical derivation of macrodispersivity models. The least-squares criterion, along with parameter prior information and other weighted constraints, is used as the objective function of the inverse problem, which is solved by the Gauss-Newton-Levenberg-Marquardt method. The method is tested on synthetic data and illustrated with real data from a site with glaciofluvial sand and gravel deposits.

Abstract Predicting flow and contaminant transport in sedimentary aquifers requires three-dimensional, quantitative characterizations of facies distributions, including the proportions, mean lengths and spatial correlation of the facies. Sedimentary facies analysis focuses on these same characteristics and, when coupled with geostatistical methodologies, can provide the necessary quantification of facies distributions as well as ideas about the origin and typical geometry of facies, what we call quantitative facies models. Because they incorporate an understanding of depositional processes, quantitative facies models must be based upon facies distributions that are genetically related. In aquifer systems composed of facies having sharp permeability contrasts, and in which indicator geostatistics can be utilized, genetically related facies assemblages are the appropriate statistical populations. We illustrate these points by considering a portion of the Miami Valley aquifer system in southwestern Ohio, where three facies assemblages can be defined. These assemblages, which differ in mean facies proportions, mean facies thicknesses and lateral facies dimensions are attributed to different combinations of depositional processes associated with Pleistocene glaciation.