Hierarchical Geostatistical Analysis of an Experimental Stratigraphy

A hierarchical geostatistical analysis is conducted on a high-resolution, multiscale hydraulic conductivity (lnK) map, created by scaling up an experimental stratigraphy. Unlike a previous study which evaluates lnK variograms within individual depositional environments, this study analyzes deposits (or samples) that incorporate multiple depositional environments. Based on conductivity cutoffs selected from a global lnK histogram, an indicator map is created to divide the deposits into 4 categories: sand, silty sand, clayey silt, and clay (Hierarchy-I). Based on facies and facies assemblage types selected using geological criteria, two more indicator maps are created at a higher hierarchy (Hierarchy-II) to divide the deposits into 14 units and 2 units, respectively. For each sample, its experimental lnK variogram is decomposed into 4 autoand cross-transition component variograms. The decomposition characteristics are then evaluated against the underlying heterogeneity and specific division rule. The analysis reveals that: (1) lnK cutoffs (sand contents of the physical stratigraphy) can be used to distinguish the shifts in dominant deposition mode; (2) sample univariate modes depend on the choice of hierarchical division; (3) sample variograms exhibit smooth-varying correlation structures (exponential-like variograms are observed in samples with a large variance in mean facies length); (4) the decomposition characteristics are sensitive to the division based on conductivity cutoffs, but not sensitive to the division based on depositional environment (For all samples, with appropriate division, the sample variogram is closely approximated by the sum of the cross-transition component variograms.); and (5) at the Hierarchy-II level, the 2-unit division gives similar decomposition characteristics as the 14-unit division. For the select samples, parsimony in hierarchical division is achieved at the facies assemblage scale. Y. Zhang ( ) Department of Geology and Geophysics, University of Wyoming, Dept. 3006, 1000 University Ave., Laramie, WY 82071, USA e-mail: [email protected]