Empirical orthogonal functions analysis applied to the inverse problem in hydrogeology: Evaluation of uncertainty and simulation of new solutions

To fulfil the need to generate more realistic solutions, stochastic inverse simulations in hydrogeology are now constrained on both piezometric head a nd hydraulic conductivity data. These inverse techniques, often based on ge ostatistics. allow modifications of an initial solution conditioned only on hydraulic conductivity data to arrive at a final solution that also matche s observed heads. By repeating the process as many times as necessary with different initial solutions, one generates an ensemble of final solutions t hereby addressing the uncertainty of the inverse problem. This requires a m ethod able to handle the whole ensemble and to work on its relevant charact eristics. From this standpoint, the analysis by Empirical Orthogonal Functi ons (EOF) appears promising. The method builds an orthogonal decomposition of the covariance matrix, calculated over the whole set of solutions, and t he areas in space where the first functions have a greater influence corres ponding to locations of maximum uncertainty, in the solutions. These locati ons depend both on the hydraulic characteristics of the flow problem and on the spatial distribution of available data. The EOF analysis is used on a synthetic problem that mimics a possible behavior of the Culebra aquifer of the Waste Isolation Pilot Plant (WIPP, New Mexico). The method also allows new solutions to be generated at lower computational cost by a random comp osition of the functions obtained by the EOF analysis. These new solutions keep the main characteristics of the initial ensemble and because they can be conditioned, they return very good results when they are used to solve t he direct problem.