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Redatuming is a data processing technique to transform measurements recordedin one acquisition geometry to an analogous data set corresponding to anotheracquisition geometry, for which there are no recorded measurements. We considera redatuming problem for a wave equation on a bounded domain, or on a manifoldwith boundary, and model data acquisition by a restriction of the associatedNeumann-to-Dirichlet map. This map models measurements with sources andreceivers on an open subset $\Gamma$ contained in the boundary of the manifold.We model the wavespeed by a Riemannian metric, and suppose that the metric isknown in some coordinates in a neighborhood of $\Gamma$. Our goal is to movesources and receivers into this known near boundary region. We formulateredatuming as a collection of unique continuation problems, and provide a twostep procedure to solve the redatuming problem. We investigate the stability ofthe first step in this procedure, showing that it enjoys conditional H\"{o}lderstability under suitable geometric hypotheses. In addition, we providecomputational experiments that demonstrate our redatuming procedure.

An Exact Redatuming Procedure for the Inverse Boundary Value Problem for the Wave Equation