A Lipschitz Stable Reconstruction Formula for the Inverse Problem for the Wave Equation

Lauri Oksanen
University College London

Room: REC 103

Sep 11, 2013 3:30 PM EDT

We consider the problem to reconstruct a wave speed $c$ in a domain $M \subset {\mathbb R}^n$ from acoustic boundary measurements modelled by the hyperbolic Dirichlet-to-Neumann map $\Lambda$. We introduce a reconstruction formula for $c$ that is based on the Boundary Control method and incorporates features also from the complex geometric optics solutions approach. Moreover, we show that the reconstruction formula is locally Lipschitz stable for a low frequency component of $c^{-2}$ under the assumption that the Riemannian manifold $(M, c^{-2} dx^2)$ has a strictly convex function with no critical points. The talk is based on a joint work with Shitao Liu, University of Helsinki. For the related preprint, see arXiv:1210.1094.