FULL-BAYESIAN INVERSION OF THE EDWARDS AQUIFER, TEXAS

The Bayesian inverse approach proposed by Woodbury and Ulrych (2000) is extended to estimate the transmissivity fields of highly heterogeneous aquifers for steady state ground water flow. Boundary conditions are Dirichlet and Neumann type, and sink and source terms are included. A first-order approximation of Taylor’s series for the exponential terms introduced by sinks and sources or Neumann condition in the governing equation is adopted. Such a treatment leads to a linear finite element formulation between hydraulic head and the logarithm of the transmissivity [denoted as ln (T)] perturbations. An updating procedure similar to that of Woodbury and Ulrych (2000) can then be performed.

This new algorithm is examined against a generic example. It is found that the linearized solution approximates the true solution with a R2 coefficient=0.96 for an ln (T) variance of 9 for the test case. The addition of hydraulic head data is shown to improve the ln (T) estimates, in comparison to simply interpolating the sparse ln (T) data alone.

The new Bayesian code is also employed to calibrate a high-resolution finite difference (MODFLOW) model of the Edwards Aquifer in southwest Texas. The goal of the study was to provide calibrated transmissivity values at approximately 88,000 locations corresponding to the grid locations of a MODFLOW model that is being constructed by the US Geological Survey. The posterior ln (T) field from this application yields better head fit when compared to the prior ln (T) field determined from upscaling and co-kriging. We believe that traditional MODFLOW grids could be imported into the new Bayes code fairly seamlessly and thereby enhance existing calibration of many aquifers.