Mathematical Geology

, Volume 36, Issue 1, pp 101–126

An Application of Bayesian Inverse Methods to Vertical Deconvolution of Hydraulic Conductivity in a Heterogeneous Aquifer at Oak Ridge National Laboratory

  • Michael N. Fienen
  • Peter K. Kitanidis
  • David Watson
  • Philip Jardine
Article

Abstract

A Bayesian inverse method is applied to two electromagnetic flowmeter tests conducted in fractured weathered shale at Oak Ridge National Laboratory. Traditional deconvolution of flowmeter tests is also performed using a deterministic first-difference approach; furthermore, ordinary kriging was applied on the first-difference results to provide an additional method yielding the best estimate and confidence intervals. Depth-averaged bulk hydraulic conductivity information was available from previous testing. The three methods deconvolute the vertical profile of lateral hydraulic conductivity. A linear generalized covariance function combined with a zoning approach was used to describe structure. Nonnegativity was enforced by using a power transformation. Data screening prior to calculations was critical to obtaining reasonable results, and the quantified uncertainty estimates obtained by the inverse method led to the discovery of questionable data at the end of the process. The best estimates obtained using the inverse method and kriging compared favorably with first-difference confirmatory calculations, and all three methods were consistent with the geology at the site.

flowmeter heterogeneity fractured aquifer 

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references

  1. Bailey, Z. C., 1988, Preliminary evaluation of ground-water flow in Bear Creek Valley, The Oak Ridge Reservation, Nashville, TN: U.S. Geological Survey Report: WRI 88-4010, 12 p.Google Scholar
  2. Box, G. E. P., and Cox, D. R., 1964, An analysis of transformations: J. R. Stat. Soc. B (Methodol.) v.26, 2, p. 211-252.Google Scholar
  3. Christakos, G., 1990, A Bayesian/maximum-entropy view to the spatial estimation problem: Math. Geol., v.22, 7, p. 763-777.Google Scholar
  4. Deutsch, C. V., and Journel, A. G., 1992, GSLIB: Geostatistical software library and user's guide: Oxford University Press, New York, 369p.Google Scholar
  5. Dorsch, J., Katsube, T. J., Sanford, W. E., Dugan, B. E., and Tourkow, L. M., 1996, Effective porosity and pore throat sizes of Conasauga Group Mudrock: Application, test and evaluation of petrophysical techniques: U.S. Department of Energy, Report ORNL/GWPO-021, Oak Ridge National Laboratory, Oak Ridge, TN.Google Scholar
  6. Erickson, T. A., 1999, Contributions to best linear unbiased estimation: Unpublished Thesis, Stanford University, Department of Civil and Environmental Engineering,78 p.Google Scholar
  7. Jacobs EM Team, 1997, Feasibility study for Bear Creek Valley at the Oak Ridge Y-12 Plant, Oak Ridge, TN: Volume II: Appendixes [sic]: U.S. Department of Energy, Office of Environmental Management, Oak Ridge, p. F-1-F-109.Google Scholar
  8. Jardine, P. M., Wilson, G. V., Luxmoore, R. J., and Gwo, J. P., 2001, Conceptual model of vadose-zone transport in fractured weathered shales. Conceptual models of flow and transport in the fractured vadose zone: National Academy Press, Washington, p. 87-114.Google Scholar
  9. Kitanidis, P. K., 1995, Quasi-linear geostatistical theory for inversing: Water Resour. Res. v.31, 10, p. 2411-2419.Google Scholar
  10. Kitanidis, P. K., 1997, Introduction to geostatistics: Applications in hydrogeology: Cambridge University Press New York, 249 p.Google Scholar
  11. Kitanidis, P. K., 1999, Generalized covariance functions associated with the Laplace equation and their use in interpolation and inverse problems: Water Resour. Res. v.35, 5, p. 1361-1367.Google Scholar
  12. Kitanidis, P. K., and Shen, K. F., 1996, Geostatistical interpolation of chemical concentration: Adv. Water Resour. v.19, 6, p. 369-378.Google Scholar
  13. Kitanidis, P. K., and Vomvoris, E. G., 1983, A geostatistical approach to the inverse problem in groundwater modeling (steady state) and one-dimensional simulations: Water Resour. Res. v.19, 3, p. 677-690.Google Scholar
  14. Lozier, W. B., Spiers, C. A., and Pearson, R., 1987, Aquifer pump test with tracers: Golder Associates, Atlanta, GA, 98p.Google Scholar
  15. Michalak, A. M., and Kitanidis, P. K., 2003, A method for the enforcing parameter nonnegativity in Bayesian inverse problems with an application to contaminant source identification: Water Resour. Res. v.39, 2, p. 1033-1047.Google Scholar
  16. Molz, F. J., Boman, G. K., Young, S. C., and Waldrop, W. R., 1994, Borehole flowmeters; field application and data analysis: J. Hydrol. v.163,no. (34), p. 347-371.Google Scholar
  17. Snodgrass, M. F., and Kitanidis, P. K., 1997, A geostatistical approach to contaminant source identification: Water Resour. Res. v.33, 4, p. 537-546.Google Scholar
  18. Solomon, D. K., Moore, G. K., Toran, L. E., Dreier, R. B., and McMaster, W. M., 1992, A hydrologic framework for the Oak Ridge Reservation, Oak Ridge, TN: U.S. Department of Energy, Oak Ridge National Laboratory, Environmental Sciences Division, 70 p.Google Scholar
  19. Waldrop, W. R., and Pearson, H. S., 2001, Results of field test with the electromagnetic borehole flowmeter at the Oak Ridge National Laboratory, Oak Ridge, TN: Quantum Engineering Corporation, Loudon, TN, 17 p.Google Scholar
  20. Woodbury, A. D., and Ulrych, T. J., 1998, Minimum relative entropy and probabilistic inversion in groundwater hydrology: Stochastic Hydrol. Hydraulics v.12, 5, p. 317-358.Google Scholar
  21. Young, S. C., Julian, H. E., Pearson, H. S., Molz, F. J., and Boman, G. K., 1998, Application of the electromagnetic borehole flowmeter: United States Environmental Protection Agency, Cincinnati, OH, 71 p.Google Scholar

Copyright information

© International Association for Mathematical Geology 2004

Authors and Affiliations

  • Michael N. Fienen
    • 1
  • Peter K. Kitanidis
    • 1
  • David Watson
    • 2
  • Philip Jardine
    • 2
  1. 1.Department of Civil and Environmental EngineeringStanford UniversityStanford
  2. 2.Environmental Sciences DivisionOak Ridge National LaboratoryOak Ridge

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