Comparing statistical models of physical heterogeneity in buried-valley aquifers

The hypothesis that physical heterogeneity has similarities in separate aquifers created by similar depositional environments is tested by comparing statistical characteristics of facies assemblages. The comparisons are made for a number of data‐rich sites in two buried‐valley aquifers in the North American midcontinent: the White River aquifer in Indiana and the Miami Valley aquifer in Ohio. These were proglacial valleys that directed drainage away from Quaternary ice margins and were filled with glaciofluvial sediments: predominantly sand and gravel (s) lithofacies, with interbedded mud and diamicton (m) lithofacies. At scales encompassing assemblages of both lithofacies m and s, permeability is strongly bimodal. We find that it is useful to compare statistics that characterize the proportions, geometry, and spatial distribution of each facies. The results give rise to a general model for heterogeneity in valley‐fill sediments along the proglacial sluiceway in both aquifers. The proportion of facies m is ∼15%. The mean thickness of facies m is 3.5 m and of the order of 10 m for facies s. The coefficient of variation in thickness for either facies is of the order of 1, with thickness ranging over orders of magnitude. Correspondingly, the vertical autotransition probabilities are exponential, and they are relatively symmetric with effective range of the order of 10 m. The lateral facies lengths are indicated to vary over orders of magnitude and to be multimodally distributed, with mean lengths of the order of 102 m, effective range in correlation structure of the order of 103 m, and lateral anisotropy ratio