Acoustic and geoacoustic inverse problems in randomly perturbed shallow-water environments

The main goal of this paper is to estimate the regional acoustic and geoacoustic shallow-water environment from data collected by a vertical hydrophone array and transmitted by distant time-harmonic point sources. The aim is to estimate the statistical properties of the random fluctuations of the index of refraction in the water column and the characteristics of the sea bottom. It is explained from first principles how acoustic wave propagation can be expressed as Markovian dynamics for the complex mode amplitudes of the sound pressure. This makes it possible to express the cross moments of the sound pressure in terms of the parameters to be estimated. Then it is shown how the estimation problem can be formulated as a nonlinear inverse problem using this formulation, which can be solved by minimization of a misfit function. The method is applied to experimental data collected by the Acoustic Laboratory for Marine Applications system. A Bayesian analysis quantifies the uncertainty of the estimation.