Two Dimensional Velocity Inversion for Acoustic Waves with Incomplete Information
We consider a two-dimensional inverse problem. The index of refraction or propagation speed of a medium is known, in some localized region up to small perturbations. Our objective is to construct these small perturbations from observation of the scattered field generated by a known incident field. It follows that in the ideal case the observations have to be collected along a closed curve surrounding the finite support of the perturbations. We shall present a method to solve the incomplete problem, where the data collection took place along a part of the closed curve.
KeywordsHelmholtz Equation Scattered Field Fredholm Integral Equation Incident Field Finite Support
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