Conditional statistical inverse modeling in groundwater flow by multigrid methods

Due to the notorious lack of data, stochastic simulation and conditioning of 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 conditioning approach is presented which treats the distributed parameters directly without projection onto lower dimensional spaces and preserves certain desired statistical properties by explicitly stating them as constraints for the conditioning optimization problem. Typically, the conditioning task must be performed very often and the conditioning optimization problems are highly dimensional. Therefore, a second main focus of the paper is on the presentation of efficient multigrid methods for the solution of the conditioning problems. Numerical results are given for a practical application problem.