Identification of spatially discontinuous parameters in second-order parabolic systems by piecewise regularisation

A novel piecewise regularisation approach has been developed for the identification of spatially discontinuous parameters in second-order parabolic systems. First, previous results on the regularisation identification approach are reviewed; regularisation is interpreted as enforced compactness of the parameter space. Then, a piecewise regularisation identification approach is rigorously formulated in a functional analytic framework. The theoretical results are applied to the history matching of one-dimensional fractured reservoirs. The performance of the proposed algorithm is evaluated by numerical experiments.