This paper introduces a single-receiver geoacoustic-inversion method based on dispersion analysis and adapted to low-frequency impulsive sources in shallow-water environments. In this context, most existing methods take advantage of the modal dispersion curves in the time-frequency domain. Inversion is usually performed by matching estimated dispersion curves with simulated replicas. The method proposed here is different. It considers the received modes in the frequency domain. The modes are transformed using an operator called modal reversal, which is parameterized using environmental parameters. When modal reversal is applied using parameters that match the real environment, dispersion is compensated for in all of the modes. In this case, the reversed modes are in phase and add up constructively, which is not the case when modal reversal is ill-parameterized. To use this phenomenon, a criterion that adds up the reversed modes has been defined. The geoacoustic inversion is finally performed by maximizing this criterion. The proposed method is benchmarked against simulated data, and it is applied to experimental data recorded during the Shallow Water 2006 experiment.