Born-type schemes for the acoustic probing of 1-D fluid media from time-harmonic planar reflection coefficients at two incidences

Abstract

The probing of a 1-D (depth-) inhomogeneous fluid half-space is carried out from a limited knowledge of plane-wave reflection coefficients with respect to frequency at two precritical incidences. Born-type inversion algorithms are investigated. First, index profiles as a function of a density-dependent pseudodepth are retrieved at two incidences; then density and speed-of-sound profiles versus depth are extracted. A Born-iterative scheme builds up the solution as the limit of a sequence of solutions of approximate, constrained linear problems. A Born-extended scheme directly yields a linearized solution. Two variants of the Born-iterative scheme are developed, the first one when data are known in both amplitude and phase, the second one with amplitude-only data. Possible—but not limiting—applications are in underwater acoustics, once the planar reflection coefficient of a seabed has been found, e.g., from the depth-dependent Green’s function in the spectral domain. Numerical simulations illustrate the schemes. Good index profiles are obtained with reasonable behavior versus noise or other causes of limitations. As is expected, separate probing of speed and density profiles remains difficult. The computationally costly exact scheme is not better than the cheaper approximate one when good data are available, but handles more complicated situations.