Application of the Sagar method for the solution of the inverse problem in ground water hydrology

Abstract

The flow of ground water through porous media can be described by partial differential equations involving potentiometric head as a function of space and time together with aquifer parameters. The direct problem is to calculate heads, given these parameters and initial and boundary conditions. The alternating direction implicit procedure with finite-difference approximations is a numerical technique used for the solution. The inverse problem is to determine aquifer parameters from measured heads. The Sagar method treats parameters as unknowns and the partial derivatives in head as knowns, using spline-function interpolation and a least-squares optimization technique. The Sagar method has been tested by employing heads generated in a finite-difference model to try to recover the transmissivity (T) distribution used in the model. Storage coefficient and pumping were assumed known. For the cases presented, T was recoverable from model output, particularly for homogeneous T. For T heterogeneous and isotropic, many estimates had relative errors within ±30% error using three measured-head distributions, and the errors were significantly improved by adding a fourth head distribution to the procedure. But the distributions used must be the result of different areal pumpage in order to produce better estimates of transmissivity.