A variational method for determining uncertain parameters and geometry in hydrogeology

Hydraulic potential, solution of the groundwater flow equation, is submitted to several types of uncertainties. These uncertainties are found not only in the parameters of the flow equation and in the boundary conditions, but also in the structure of the geological medium. This ‘structure uncertainty’ comes from the necessary interpolation between borehole information or seismic information at different locations of the geological site. case of parameter uncertainties, sensitivity coefficients are usually evaluated in order to solve an inverse problem based on the knowledge of measures of hydraulic potential at locations sparsely distributed in the flow region. pose, in this paper, to apply the same principle to structure uncertainty, that is, to calculate explicitly (under some hypotheses) the sensitivity coefficients of hydraulic potential for displacements of interfaces delimiting successive geological layers. Therefore, we have derived a first order variational formula which is used for the solution of the inverse problem in an iterative algorithm. Some iterations are used to reduce the effects of approximations made in the variational formula. The algorithm is described and numerical results are discussed for test problems.