Stochastic Inversion of a Tomographic Pumping Test: Identifying Conductivity Horizontal Correlation and Longitudinal Macrodispersivity

Two important properties for modeling flow and transport in heterogeneous aquifers are the horizontal integral scale (I_h) of hydraulic logconductivity (Y = ln K) and the longitudinal macrodispersivity (α_L). Estimating the former generally requires K measurements in many wells, which are typically not available. In this work, we present a method for estimating I_h and α_L from hydraulic tomography (HT) pumping tests. The approach is based on stochastic inversion, assuming head and K are stationary random space functions. Head variance and mean head gradient are calculated from measured head data at large distances from the pumping well and for large times from the start of pumping. These are then used in a theoretical formula for head variance in uniform mean flow to obtain I_h and subsequently α_L, requiring only previous knowledge of the vertical integral scale (I_v) and the logconductivity variance (Formula presented.). The method is applied to data from an HT pumping test at the Boise Hydrogeophysical Research site and results for I_h and α_L are in the range previously reported in the literature. Particularly promising results are found for α_L, which is seen to be robust, with relatively little variation for different values of I_v and (Formula presented.).