Application of the pilot point method to the identification of aquifer transmissivities

Abstract

A method is presented to estimate smoothly varying (as opposed to zoned) hydraulic parameters, transmissivity in particular, appearing in a time-dependent flow equation. A finite difference model based on a nested grid discretization reduces the computational effort while allowing local refinement. Structuring of the unknown parameter field, use of a priori information, and parameterization of the inverse problem are geostatistically based. Calibration is carried out by minimizing a quadratic objective function depending on head data. A primal-adjoint discrete-gradient method is used, where the unknowns are parameter values at a number of user-defined points, the “pilot points”. The key feature of this method consists of kriging together the pilot point values and the measured values, if any, in order to generate the parameter field needed at each iteration to solve the primal and adjoint systems. Minimization is performed by a BFGS algorithm. Two numerical examples are considered, where transmissivity is the unknown. The first one is adapted from Carrera and Neuman's [1] synthetic problem. The purpose is to compare kriged and zoned results obtained from different types of observation data sets e.g., stationary vs. transient head or drawdown. The second example is a case study of the Dijon (France) aquifer. Pilot point-based identification is applied to the same model (domain, equations, grid), which was manually calibrated in 1985. Only the measured data were made available. The results from manual calibration were kept unknown until the end of the inversion trials. Sensible use of pilot points and of a priori information appears to play a key role in yielding plausible results.