When is MCMC feasible for AVO inversion?

I show that one is able to use a McMC method for solving the AVO problem. A linear forward model is used for inversion of synthetic datasets, each with different signal-to-noise ratios. The (mean of the) obtained posterior distribution is compared to the closed-form expression (MAP-solution), to conclude that this approach samples the right distribution. An autocorrelation analysis is applied to obtain the autocorrelation time τ for each posterior distribution. One finding is that for each S/N ratio, τ stagnates. Furthermore, an exponential relation is found between S/N and τ.