An inverse method for reconstructing the density and sound speed profiles of a layered ocean bottom

A standard inverse problem in underwater acoustics is the reconstruction of the ocean subbottom structure (e.g., the density and sound speed profiles) from an aperture- and bandlimited knowledge of the reflection coefficient. In this paper we describe an inverse solution method due to Candel et al. [12] which is based on the scattering of acoustic plane waves by a one-dimensional inhomogeneous medium. As a consequence of applying the forward scattering approximation to a local wave representation of the acoustic field, they obtain an expression for the reflection coefficient in the form of a nonlinear Fourier transform of the logarithmic derivative of the local admittance. Inversion of this integral transform enables the recovery of the admittance profile via the numerical integration of two first-order differential equations which require as reflection data a single impulse response of the medium. Separate recovery of both the density and sound speed profiles requires two impulse responses for two different grazing angles. In this case, four differential equations need to be integrated instead of two. To illustrate the capability of the method, we present numerical reconstructions which are based on synthetic reflection data for a geoacoustic model that represents the acoustic properties of the surficial sediments for a site in the Hatteras Abyssal Plain.