Solving an inverse problem for the wave equation by using a minimization algorithm and time-reversed measurements

Lauri Oksanen

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arXiv · 1101.4836

Solving an inverse problem for the wave equation by using a minimization algorithm and time-reversed measurements

Lauri Oksanen

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Abstract

We consider the inverse problem for the wave equation on a compact Riemannian manifold or on a bounded domain of $\R^n$, and generalize the concept of {\em domain of influence}. We present an efficient minimization algorithm to compute the volume of a domain of influence using boundary measurements and time-reversed boundary measurements. Moreover, we show that if the manifold is simple, then the volumes of the domains of influence determine the manifold. For a continuous real valued function $τ$ on the boundary of the manifold, the domain of influence is the set of those points on the manifold from which the travel time to some boundary point $y$ is less than $τ(y)$.

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Lauri Oksanen. 2011-01-25. Solving an inverse problem for the wave equation by using a minimization algorithm and time-reversed measurements. https://arxiv.org/abs/1101.4836

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