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
    • Department of Civil and Environmental EngineeringStanford University
  • Peter K. Kitanidis
    • Department of Civil and Environmental EngineeringStanford University
  • David Watson
    • Environmental Sciences DivisionOak Ridge National Laboratory
  • Philip Jardine
    • Environmental Sciences DivisionOak Ridge National Laboratory

DOI: 10.1023/

Cite this article as:
Fienen, M.N., Kitanidis, P.K., Watson, D. et al. Mathematical Geology (2004) 36: 101. doi:10.1023/


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.

flowmeterheterogeneityfractured aquifer

Copyright information

© International Association for Mathematical Geology 2004