Abstract of the conference proceedings paper ``Inversion with variational constraints''

Fermat's principle shows that a definite convex set of feasible slowness models - depending only on the seismic traveltime data and locations of the sources and receivers - exists for the fully nonlinear traveltime inversion problem. Similarly, Dirichlet's principle shows that a definite convex set of feasible conductivity models exists for the nonlinear electrical impedance tomography problem (in which electrical boundary measurements are used to determine interior distributions of conductivity). New stable iterative reconstruction methods have been developed using these physically based feasibility constraints. The minimum number of feasibility violations is used as a figure of merit to determine the optimum size of the model correction at each step. In the presence of noise, the new algorithms produce good reconstructions even for very high contrast materials where standard methods tend to diverge.

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