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Abstract
This paper deals with the transient inverse scattering problem for determining a compactly-supported velocity inhomogeneity embedded in a uniform acoustic waveguide. It is assumed that the sound velocity within the inhomogeneity is a small perturbation of the background velocity, so that a linerized formulation based on the modal expansion of the pressure field applies. If the inhomogeneity is both depth-independent and axisymmetric, we reduce the reconstructionproblem to a uniquely solvable Volterra integral equation of the second kind. However, if the inhomogeneity is not axisymmetric we are able only to derive an infinite set of moment equations for the unknown refraction index.