Geostatistical Modeling of Heterogeneity in Glaciofluvial, Buried-Valley Aquifers

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In the buried-valley aquifers of the western and central glaciated plains of North America, assemblages of permeable outwash facies may form large and productive regional aquifer systems. In glacially derived aquifers it is common to have low-permeability facies (e.g., till or lacustrine clay) juxtaposed with high-permeability facies (e.g., sand and gravel outwash). The heterogeneity in the Miami buried-valley aquifer system in southwestern Ohio was examined as an example. Practical approaches for evaluating the lithological uncertainty were explored in the areas lacking data. The facies types were represented by an indicator random function, which exhibited an isotropic, exponential covariance structure. A comparative, quantitative analysis of the facies boundaries was accomplished using three different indicator geostatistical methodologies: (1) hydrostratigraphic analysis with indicator point kriging and probability cutoff, (2) hydrostratigraphic analysis with conditional indicator simulation, and (3) leakance zonation with indicator block kriging and grid-cell averaging. With the first method, it was shown in a theoretical analysis that the 0.5 probability level computed by indicator point kriging may or may not correspond to the boundary between high- and low-permeability facies, depending upon the level of data support. With the data support for the Miami aquifer system, the 0.65 probability contour gave an areal distribution of low-permeability facies that honored both the original data and the declustered global mean of the original indicator data. The first and third methods gave rise to a single model, in which the facies distribution was best in some local accuracy sense. The second method gave rise to many alternative models, in which the global texture of the facies distribution took precedence over local estimation of the expected value. The first two methods involved evaluating the geometry of the boundaries between the facies types in advance of creating the grid of the numerical ground-water model, so that grid cell boundaries could be made to correspond to facies boundaries. The third method was useful when updating an existing ground-water model that has grid cell boundaries not necessarily corresponding to facies boundaries.