| Abstract: |
| An acoustic medium occupying a compact domain with non-constant sound speed is probed by an impulsive plane wave, and the far-field response is measured in all directions for all frequencies. A longstanding open problem, called the fixed angle scattering inverse problem, is the recovery of the sound speed from this far-field response. In some situations, the acoustic properties of the medium are modeled by a Lorentzian metric and then the goal is the recovery of this metric from the far field measurements corresponding to a finite number of incoming plane waves. We consider a time domain, near field version of this problem and show that natural fixed angle measurements distinguish between a constant velocity (the Minkowski metric) medium and a non-constant velocity (a general Lorentzian metric) medium. |
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