Reconstruction of piecewise smooth wave speeds using multiple scattering

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Let c be a piecewise smooth wave speed on Rⁿ, unknown inside a domain Ω. We are given the solution operator for the scalar wave equation (∂ₜ²-c²Δ)u=0, but only outside Ω and only for initial data supported outside Ω. 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.