  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. We aim
at estimating the statistical properties of the random fluctuations of the
index of refraction in the water column and the characteristics of the sea
bottom. We first explain from first principles how acoustic wave propagation
can be expressed as Markovian dynamics for the complex mode amplitudes of the
sound pressure, which makes it possible to express the cross moments of the
sound pressure in terms of the parameters to be estimated. We then show how the
estimation problem can be formulated as a nonlinear inverse problem using this
formulation, that can be solved by minimization of a misfit function. We apply
this method to experimental data collected by the ALMA system (Acoustic
Laboratory for Marine Applications).
