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| We study the inverse problem for the reduced wave equation using the Dirichlet to Neumann map at selected frequencies. We establish Lipschitz stability estimates for wavespeeds in the form of finite linear combinations of known functions defined on a Lipschitz partition $\mathcal{D}_N=\cup_{j=1}^{N}D_j$ of the underlying domain $\Omega$.
A crucial role for the effective reconstruction is played by the Lipschitz constant appearing in the estimates, in particular its dependence on the mesh size of the partition $\mathcal{D}_N$.
We establish an explicit optimal bound of the Lipschitz constant with respect to the mesh size and this is used to derive a multifrequency convergent iterative method for the reconstruction of the wavespeed. |
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