On the inversion of sound channel data

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. An inverse problem of determining the velocity-depth profile given sound channel observations is considered here. This is an inverse eigenvalue problem in which the eigenvalue data (typically recorded as group velocity data) depends on the frequency as an auxiliary parameter, and the inversion has the possibility of being rescued from the characteristic extreme ill-conditioning 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 it is desirable to have sequences of observations on each of at least p propagating modes.