The density and compressibility profiles of a layered fluid are obtained from the reflection coefficient due to plane waves at two precritical angles of incidence and all the frequencies. The inverse scattering problem for a layered fluid, at oblique incidence, is transformed to an equivalent inverse scattering problem for a layered refractive index profile, at normal incidence. The latter inverse scattering problem is transformed to an inverse scattering problem in quantum mechanics whose solution is obtained by the Gelfand-Levitan theory.

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