Parametric sonars are instruments capable of transmitting acoustic signals in the water with a very narrow beam and almost no sidelobes. These features are exploited in this paper to define a methodology for quantitative estimation of the geo-acoustic and morphological properties of the uppermost seafloor sediment layer. The three major components of the approach are the parametric instrument itself; the modelling of the forward-propagation problem, with the use of the Kirchhoff approximation for surface scattering and of the small-perturbation theory for the volume scattering; and the definition of a criterion for comparison between data and model predictions, which is accomplished by a generalized time-frequency analysis. In this way the estimation becomes one of a model-based identification, or a model-based inverse problem. Results from a field trial in a shallow water area of the Mediterranean are shown, and compared with independently gathered ground truth.