Conditional statistical inverse modeling in groundwater flow by multigrid methods

Due to the notorious lack of data, stochastic simulation and conditioning o f distributed parameter fields is generally acknowledged as a major task in order to produce realistic prognoses for groundwater flow phenomena, thus honouring the maximum of information available. In this paper, a new condit ioning approach is presented which treats the distributed parameters direct ly without projection onto lower dimensional spaces and preserves certain d esired statistical properties by explicitly stating them as constraints for the conditioning optimization problem. Typically, the conditioning task mu st be performed very often and the conditioning optimization problems are h ighly dimensional. Therefore, a second main focus of the paper is on the pr esentation of efficient multigrid methods for the solution of the condition ing problems. Numerical results are given for a practical application probl em.