Active sonar reverberation returns offer the possibility to invert for geo-acoustic bottom parameters to characterise the underwater environment. We present the results of synthetic inversions of reverberation returs generated with a ray-based reverberation model in which bottom scattering is modelled according to a modified Lambert's rule. The inverted parameters are sediment sound speed, attenuation and the scattering strength, parametrised by Lambert's constant and a low grazing angle threshold. The sediment density is calculated during the inversions through an empirical relationship to sediment sound speed. Results of inversions of synthetic data using a genetic algorithm are presented both for a soft muddy bottom and a harder and rougher bottom consisting of coarse sand. We also investigate the effect of an error in water depth.