We study integral represenations, approximation by solutions of the Helmholtz equation, stability in the problem of the continuation of solutions and report on several numerical algorithms ( in 3D) of processing the data from outside acoustical measurements to determine vibrations of elastic surface generating the acoustical field. We study increasing stability with growing frequency and with better regularity constraints on the field. We suggest a (space) localized version of reconstruction algoritm. We propose a more complete model incorporating equations for vibrating elastic surfaces and a-priori information about sources of the acoustical field.
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