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Refinement and coarsening indicators for adaptive parametrization: application to the estimation of hydraulic transmissivities

When estimating hydraulic transmissivity the question of parametrization is of great importance. The transmissivity is assumed to be a piecewise constant space-dependent function and the unknowns are both the transmissivity values and the zonation, the partition of the domain whose parts correspond to the zones where the transmissivity is constant. Refinement and coarsening indicators, which are easy to compute from the gradient of the least squares misfit function, are introduced to construct iteratively the zonation and to prevent overparametrization.