Pilot points method incorporating prior information for solving the groundwater flow inverse problem

The pilot points method is often used in nonlinear geostatistical calibration. The method consists of estimating the values of the hydraulic properties at a set of arbitrary (pilot) points so as to best fit the aquifer response as measured by available indirect observations (i.e., heads or drawdowns). Though this method remains general and appealing, no prior information of the hydraulic properties is usually included in the optimization process, which constrains the number of pilot points to ensure stability. In this paper, we present a modification of the pilot points method, including prior information in the optimization process by adding a plausibility term to the objective function to be minimized. This results from formulating the inverse problem in a maximum likelihood framework. The performance of the method is tested on a synthetic example. Results show that including the plausibility term improves the identification of heterogeneity. Furthermore, this term makes the inverse problem more stable and allows the use of larger number of pilot points, thus improving the identification of the heterogeneity as well. Therefore, the use of the plausibility term is recommended.