Uniqueness and stability of the determination of aquifer properties with inverse problems

The identification of the physical parameters of groundwater flow and transport models is often performed with an inverse problem (IP). In the continuous case, if the IP is properly posed and if enough information is available, the IP admits a unique solution, which however is not stable. In the discrete case the IP often requires the minimization of an objective function, whose convexity is difficult to evaluate and which might have several local minima and be flat over a wide range of values for the model parameters so that the IP is ill conditioned.