Parameter estimation for a huge multi-aquifer system is a challenge. It is important to use a fast computer code on a fast machine to achieve good calibration results. In this paper two indirect methods to solve the inverse problem are used. One is Gauss-Newton plus Line Search (GNLS). The other one is Adjoint State Conjugated Gradient (ASCG). The behaviour of both methods is analyzed for a small ... [Show full abstract] test case as well as for the calibration of the "Venloer Scholle" multi-aquifer system.