The determination of scattering strengths in shallow water is difficult due to multipath effects. A method is described that is based on global inversion of reverberation data, which allows both the bottom scattering strength and geoacoustic parameters (bottom loss) to be determined simultaneously. Ellis [J. Acoust. Soc. Am. 97, 2804 (1995)] has described a computationally efficient reverberation model based on normal modes and ray-mode analogies. This is combined with the global inversion method of Gerstoft [J. Acoust. Soc. Am. 95, 770 (1994)]. Using broadband reverberation data from a shallow-water site north of Elba in the Mediterranean Sea, bottom scattering strengths and bottom sound speeds have been extracted. The reliability of estimating other environmental parameters is also investigated. By using the data from all frequencies simultaneously in the inversion, the stability of the estimates is significantly improved.