Bayesian and maximum entropy inversion of highly heterogeneous aquifers

The Bayesian inverse approach proposed by Woodbury and Ulrych (2000) is extended to estimate the transmissivity fields of highly heterogeneous aquifers for steady state groundwater flow. A first-order approximation of Taylor’s series for the exponential terms introduced by sinks and sources or Neumann conditions in the governing equation is adopted. Such a treatment leads to a linear finite element formulation between hydraulic head and logarithm transmissivity [denoted as ln (T)] perturbations. The new inversion algorithm is examined against generic examples. It is found that the linearized partial difference equations yield acceptable head approximations for ln (T) variance up to 9 for the test case. The addition of the hydraulic head data is shown to improve the ln (T) estimates, in comparison to simply interpolating the sparse ln (T) data alone.