RELATING SPATIAL CORRELATION OF PERMEABILITY TO SEDIMENTARY ARCHITECTURE IN OUTCROP-ANALOG STUDIES

Outcrop analogs for aquifers allow measurement of permeability with relatively high resolution, the mapping of sedimentary units, and studies that relate univariate and spatial bivariate statistics of permeability to aquifer architecture. Spatial bivariate statistics may be spurious even when univariate statistics are well defined. Sedimentary deposits typically can be organized into a hierarchy of unit types, and associated permeability modes, across scales. In many examples, an appreciable fraction of the global variance arises from differences in mean permeability across units defined at smaller scales. The global bivariate statistics for permeability (covariance or semivariogram) in such deposits will not be representative unless data locations allow proper definition of the transition probabilities of the units. This is can be seen by writing the common global bivariate statistics in a hierarchical, multimodal identity. Focusing on the semivariogram, the global semivariogram is a linear summation of the auto- and cross-semivariograms of units defined at smaller scales, weighted by the proportions and transition probabilities for unit types. The global semivariogram shape in a particular direction of sampling is controlled by the shape of the cross-transition probabilities of strata types having greatest contrast in permeability. Following from these insights, quantification of the stratal architecture can be used to better interpret the shape of equivocal sample semivarigorams. We illustrate these relationships with field data from sites in Ohio and New Mexico.