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Seismic full-waveform inversion aims to reconstruct subsurface medium parameters from recorded seismic data. It is solved as a constrained optimization problem in the deterministic approach. Many different objective functions have been proposed to tackle the nonconvexity that originated from the cycle-skipping issues. The analogy between objective functions in the deterministic inversion and likelihood functions in Bayesian inversion motivates us to analyze the noise model each objective function accounts for under the Bayesian inference setting. We also show the existence and wellposedness of their corresponding posterior measures. In particular, the theorem shows that theWasserstein-type likelihood offers better stability with respect to the noise in the recorded data. Together with an application of the level-set prior, we demonstrate by numerical examples the successful reconstruction from Bayesian full-waveform inversion under the proper choices of the likelihood function and the prior distribution.