Comparing Statistical Models of Physical Heterogeneity in Buried-Valley Aquifers

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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 103m, and lateral anisotropy ratio <2. There is some variation in how the facies m are vertically embedded within the facies s. The White River aquifer and areas in the Miami aquifer have facies proportions relatively stationary with elevation. In other areas of the Miami, there are near-horizontal zones having relatively higher or lower proportions. However, such variations on the general model give rise to similar statistics for mass transport within the context of a relevant remediation problem and thus would lead to a similar conclusion or decision. Thus one general model is applicable to both aquifers in this context. In a broader sense, we have illustrated a method by which other examples developed from data-rich sites can be compared.