We cast the genetic algorithm-full waveform inversion (GA-FWI) in a probabilistic framework that through a multi-step procedure, allows us to estimate the posterior probability distribution (PPD) in model space. Since GA is not a Markov chain Monte Carlo method, it is necessary to refine the PPD estimated by GA (GA PPD) via a resampling of the model space with a Gibbs sampler (GS), thus obtaining the GA+GS PPDs. We apply this procedure to two acoustic 2D models, an inclusion model and the Marmousi model, and we find a good agreement between the derived PPDs and the varying resolution due to changes in the seismic illumination. Finally, we randomly extract several models from the so derived PPDs to start many local full-waveform inversions (LFWIs), which produce final high-resolution models. This set of models is then used to numerically estimate the final uncertainty (GA+GS+LFWI PPD). The multimodal and wide PPDs derived from the GA optimization, become unimodal and narrower after LFWI and, in the well illuminated parts of the subsurface, the final GA+GS+LFWI PPDs contain the true model parameters. This confirms the ability of the GA optimization in finding a velocity model suitable as input to LFWI
