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arXiv · 1801.03144

Reconstruction of piecewise smooth wave speeds using multiple scattering

Peter Caday·Maarten V. de Hoop·Vitaly Katsnelson·Gunther Uhlmann
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Abstract

Let $c$ be a piecewise smooth wave speed on $\mathbb R^n$, unknown inside a domain $\Omega$. We are given the solution operator for the scalar wave equation $(\partial_t^2-c^2\Delta)u=0$, but only outside $\Omega$ and only for initial data supported outside $\Omega$. Using our recently developed scattering control method, we prove that piecewise smooth wave speeds are uniquely determined by this map, and provide a reconstruction formula. In other words, the wave imaging problem is solvable in the piecewise smooth setting under mild conditions. We also illustrate a separate method, likewise constructive, for recovering the locations of interfaces in broken geodesic normal coordinates using scattering control.

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Peter Caday, Maarten V. de Hoop, Vitaly Katsnelson, Gunther Uhlmann. 2018-01-09. Reconstruction of piecewise smooth wave speeds using multiple scattering. https://arxiv.org/abs/1801.03144

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