[1] Cross-stratified deposits can give rise to a hierarchy of permeability modes, across scales, corresponding to a hierarchy of sedimentary unit types. The shape of the sample semivariogram for permeability can be largely controlled by the shape of the crosstransition probabilities of unit types having the greatest contrast in permeability. The shape of those cross-transition probabilities can be, in turn, largely determined by the variance of the lengths of those unit types. A sufficient condition for an exponential-like semivariogram is the repeated occurrence of unit types having both a contrast in permeability and a large length variance. These relationships are shown through writing the identities for spatial correlation of permeability in a hierarchical and multimodal form and as a function of the transition probabilities for the sedimentary unit types. These relationships are also illustrated through analyzing data representing cross-stratified sediments within a point bar deposit.
Abstract. When using indicator geostatistics to represent the distribution of hydrofacies or lithofacies, the range and curvature of the autotransition probabilities or the autovariogram are related to the variation in facies lengths. As the coefficients of variation for the length of each facies increase toward unity, the effective range increases while the indicator-correlation structure evolves from a periodic linear structure to a somewhat periodic spherical structure to an aperiodic exponential structure. Multimodal distributions of facies lengths can give rise to autotransition probabilities or autovariograms that appear to have nested structures. With the understanding of these relationships it is possible to choose a model form and model parameters for the autotransition probability or autovariogram based upon the facies proportions and the modality, mean, and variance in length of the facies. This is illustrated with data from a case study.
Porosity in sediments that contain a mix of coarser- and finer-grained components varies as a function of the porosity and volume fraction of each component. We considered sediment mixtures representing poorly sorted sands and gravely sands. We expanded an existing fractional-packing model for porosity to represent mixtures in which finer grains approach the size of the pores that would exist among the coarser grains alone. The model well represents the porosity measured in laboratory experiments in which grain sizes and volume fractions were systematically changed within sediment mixtures. Permeability values were determined for these sediment mixtures using a model based on grain-size statistics and the expanded fractional-packing porosity model. The permeability model well represents permeability measured in laboratory experiments using air- and water-based permeametry on the model sediment mixtures.
[1] As analogs for aquifers, outcrops of sedimentary deposits allow sedimentary units to be mapped, permeability to be measured with high resolution, and sedimentary architecture to be related to the univariate and spatial bivariate statistics of permeability. Sedimentary deposits typically can be organized into hierarchies of unit types and associated permeability modes. The types of units and the number of hierarchical levels defined on an outcrop might vary depending upon the focus of the study. Regardless of how the outcrop sediments are subdivided, a composite bivariate statistic like the permeability semivariogram is a linear summation of the autosemivariograms and cross semivariograms for the unit types defined, weighted by the proportions and transition probabilities associated with the unit types. The composite sample semivariogram will not be representative unless data locations adequately define these transition probabilities. Data reflecting the stratal architecture can often be much more numerous than permeability measurements. These lithologic data can be used to better define transition probabilities and thus improve the estimates of the composite permeability semivariogram. In doing so, bias created from the incomplete exposure of units can be reduced by a Bayesian approach for estimating unit proportions and mean lengths. We illustrate this methodology with field data from an outcrop in the Española Basin, New Mexico.Citation: Dai, Z., R. W. Ritzi Jr., and D. F. Dominic (2005), Improving permeability semivariograms with transition probability models of hierarchical sedimentary architecture derived from outcrop analog studies, Water Resour. Res., 41, W07032,
[1] Highly resolved data from the Borden research site provide a unique opportunity to study the horizontal spatial bivariate correlation of hydraulic and reactive attributes affecting subsurface transport. The data also allow quantitatively relating this correlation to the hierarchical sedimentary architecture of the aquifer. The data include collocated samples of log permeability, Y, the log of the perchloroethene sorption distribution coefficient, Ä, and lithologic unit type. The horizontal Y and Ä autosemivariograms and the Ä-Y cross-semivariogram have the same underlying correlation structure (shape and range in the rise to a sill). The common structure is not due to Ä-Y point correlation or in-unit spatial correlation. The common structure is defined by how the proportion of lag transitions crossing different unit types (i.e., the cross-transition probability structure) increases with increasing lag distance. The common underlying cross-transition structure contains two substructures with different correlation ranges corresponding to two scales of unit types within the sedimentary architecture. For each substructure, a large standard deviation in the length of units relative to the mean length gives rise to an exponential-like shape and the proportions and mean length of units define the ranges. The horizontal Ä-Y spatial cross correlation is primarily defined by the larger-scale substructure and the differences in mean Ä and Y between larger-scale unit types.
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