Dakota Home Introduction Subsurface Hydrology Geologic Framework Petrophysics Water Quality
Dakota Aquifer Program--Geologic Framework--Stochastic Modeling


The purpose of this project is to derive a means for producing a high-resolution model for aquifer heterogeneity in the Terra Cotta Clay Member of the central Kansas Dakota Formation. The internal heterogeneity of the Terra Cotta aquifer in central Kansas is complex, and exact discrimination of aquitard and aquifer units from direct observation is cost prohibitive (Macfarlane, et al., 1994). High resolution models of aquifer heterogeneity are thus needed to help economically exploit water resources from these strata. In order to improve upon the resolution of modeling techniques currently available, we have developed an innovative approach to geometric modeling methods.

Modelers using geometric methods first define the geometric building blocks which constitute a target aquifer, then simulate this aquifer by using stochastic computer models to generate potential stacking patterns for the defined building blocks (e.g. Poeter, 1994). Potential stacking patterns are usually limited by parameters developed from estimates of block spatial distribution (typically derived through geostatistics) and quantitative descriptions of block dimensions.

Most geometric models define discrete grain-size based lithofacies as the geometric building blocks of an aquifer (e.g. Anderson, 1989). Such lithofacies are easily defined and measured for model input. Unfortunately, similar lithology may reflect very different origins. Similarly, the same process may generate a range of different lithologies. This limits the modelers› ability to attach a unique and predictable process to each lithology, and thus limits their ability to use sedimentary process information to further constrain the likely stacking patterns of these lithofacies-based geometries.

Our modeling approach utilizes the basic techniques of geometric modeling; however, we have modified the typical approach by modifying the criteria used for defining geometric building blocks. Instead of using lithofacies alone to define building blocks, we rely on discrete geometric units with sharp bounding surfaces that represent deposition from a unique and predictable depositional process. The task of the sedimentologist in such modeling is to define these sharp-bounded geometric building blocks, and to assess process-based behavioral parameters for each geometry type that will help the modeler predict the most likely dimensions and stacking patterns of these building blocks.

Sequence stratigraphy (e.g.; Van Wagoner, et al., 1990) facilitates distinction of such discrete boundary-defined genetic units. Sequence stratigraphy defines systems tracts which are bounded by well-defined sharp surfaces, are depositionally related internally, and are predictable in their distinction. For instance, a highstand systems tract is bounded by a maximum flooding surface below and a sequence boundary above, and all the deposits bounded by these surfaces represent progradation of the shoreline during a sea level highstand event (highstand deposits can be confidently predicted to lie above transgressive systems tracts). Thus, their spatial distribution in the overall stacking pattern of systems tracts is easily constrained in models. Target Dakota strata, however, constitute valley fill deposits of only one, or possibly two, sequences (Hamilton, 1989), and further distinction of systems tracts within these valley-filled strata is highly questionable. Sequence stratigraphy thus provides an excellent starting point for distinction of genetic geometric units, but present sequence-stratigraphic divisions are too coarse to provide the level of model resolution desired in this study. A method which further distinguishes geometric units within definable sequence-stratigraphic packages is needed.

The method used here to further divide existing sequence-stratigraphic units in Dakota strata is architectural-element analysis (Miall, 1985). Architectural-element analysis subdivides fluvial strata into eight geometric building blocks, called architectural elements; each with consistent internal lithofacies, distinct bounding-surface geometrics, and predictable origins (Appendix D). As an example, a channel-filled element is lobate in cross-section, ribbon-like in plain view, is filled with a range of fluvial lithofacies, and represents filling of incised river channels. Architectural elements are typically on the order of 100 to 101 meters in intermediate dimension, and thus provide a means of defining small-scale building blocks for high-resolution geometric modeling. Predictability of the processes which generate specific elements also allows the modeler to constrain closely what constitutes reasonable geometries, dimensions, and stacking patterns for these geometric units.

Our computer model will generate multiple realizations of stacking patterns for the architectural elements identified from Dakota strata in the field. Possible stacking patterns will be constrained according to individual element demential range, probability of occurrence, probable orientation, and likely spatial relationship with other elements, as determined from field observations and assessment of element-generating processes. Possible lithofacies fills will be added to elements based on observation of element fills in outcrop. Field estimates of permeability for element-filling lithofacies can then be substituted for strata in the model, providing a realization of heterogeneity in hydraulic conductivity.

The resulting simulation(s) will provide realizations of Dakota aquifer heterogeneity on a level of resolution of 101 m. Moreover, this method simulates distribution of element boundaries, and thus reveals potential hydraulic boundaries. Such boundaries are simulated in our geometric models, but are not revealed by pure geostatistical models. Once the model is developed, and the elements in Dakota strata of the study area are established, the model can be used in Dakota strata at any site in the central Kansas area. This would involve adjustment of the element frequency in the model to coincide with element frequencies determined at the site from outcrop or subsurface data.

This goal of the first year was to define the elements in basal Terra cotta and Rocktown Channel strata of the Dakota Formation in Russell and Ellsworth counties, Kansas, and to develop the basic computer code for the modeling program. The following report discusses the results of this first year of research.

Previous Page--Abstract || Next Page--Stratigraphic and depositional setting
Dakota Home || Start of the Stochastic Modeling Report

Kansas Geological Survey, Dakota Aquifer Program
Updated July 5, 1996.
Scientific comments to P. Allen Macfarlane
Web comments to webadmin@kgs.ku.edu
The URL for this page is HTTP://www.kgs.ku.edu/Dakota/vol1/geo/stochas2.htm