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When estimating hydraulic transmissivity the question of parameterization 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.(More)
A new method for formulating and solving parameter estimation problems based on Fenchel duality is presented. The partial diierential equation is considered as a contraint in a least squares type formulation and is realized as a penalty term involving the primal and dual energy functionals associated with the diierential equation. Splitting algorithms and(More)
We show in this paper how the application of convex duality leads to various reformulations of the classical non optimizable least squares approach to waveform prestack inversion. These reformulations search all for i) a background velocity model and ii) a re-ectivity model deened in the time domain, and linked to the usual depth reeectivity model by(More)
We consider the problem of determining the diffusion coefficient a(x) in a 2D elliptic equation from a distributed measurement z in H1 of the solution u of the equation. For a problem with a simple geometry, we give conditions under which the first derivative of the b = 1=a 7 ! u mapping is coercive. Then we show that its non linearity in a direction d(More)