On the inversion of sound channel data

Research Report MRR99-038

On the inversion of sound channel data

M.R.Osborne

Abstract: If the velocity-depth profile in a deep ocean has a well defined minimum at finite depth then acoustic signals of high enough frequency are trapped in an associated sound channel and propagate with relatively little attenuation over large distances. The problem considered is the inverse one of determining the velocity-depth profile given sound channel observations. This is an inverse eigenvalue problem in which the eigenvalue data (typically group velocity) depends on the frequency as an auxilliary parameter, and the inversion is rescued from the characteristic extreme illconditioning of the inverse eigenvalue problem by sampling in the frequency domain. However, the inversion appears to have the unusual characteristic that if a p parameter model is to be determined then observations are required on at least p propagating modes.

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