Numerical Schemes for the Estimation of Functional Parameters in Distributed Models for Mixing Mechanisms in Lake and Sea Sediment Cores

摘要

We consider distributed parameter models for vertical mixing in lake and sea sediment cores. Finite dimensional approximation schemes are developed for the solution of associated inverse problems. The schemes permit one to estimate temporally and spatially varying functional parameters which appear in the parabolic partial differential equations and boundary conditions constituting the models. Theoretical convergence results are established. Numerical findings are presented which demonstrate the potential of the methods. An example involving the identification of a depth dependent mixing parameter based upon volcanic ash data from the North Atlantic is included.