GNGTS 2024 - Atti del 42° Convegno Nazionale

Session 3.3 GNGTS 2024 A comparison between the obtained results at the horizontal positon of 10m and the available borehole data revealed an accurate reproducton of all the main velocity variatons (Figure 1d). In partcular, the two high velocity layers are clearly identfed at depths 10-15m and 19-25 m with a Vs value around 430 m/s. In between, there is a very thin layer (around 3m of thickness) characterized by a lower Vs velocity, around 370 m/s. We are also able to observe the velocity inversion around 25m of depth, at the botom edge of the model. As expected, this velocity layer is also characterized by the highest standard deviaton values (Figure 1b), considering that it is below the high velocity layer and at the edge of the model. We need to consider that the standard deviaton map suggests small uncertaintes for all the velocity models (less than 40 m/s). In Figure 2a we can see the evoluton of the negatve log-likelihood for all the chains, and we can notce that, afer the end of the burn-in period, all the chains oscillate around the same values, meaning that we have reached the statonary regime. Figure 2b shows the acceptance rato for the fve chains, calculated as the rato between the number of accepted models and the number of iteratons. We can see that all the values are very high, compared to the ones usually achieved with standard gradient-free MCMC methods (around 20%), highlightng the superior efciency of the proposed method. A comparison between the lefmost shot of the observed data (afer pre- processing) and the data computed on the startng model of Figure 1a revealed signifcant cycle- skipping, indicatng that any local approach would fail in locatng the global minimum of the error functon (Figure 3a). Diferently, our approach fnally provides a mean posterior model that is capable of successfully reproducing the observed seismic data (Figure 3b). This capability was emphasized by the close-ups of Figures 3c and 3d, in which we can appreciate the signifcant diferences between the observed and inital data and how the cycle skips vanish when the data computed on the posterior mean model is considered. This means that the implemented approach could be also used to defne an optmal startng model suitable for a subsequent step of local FWI. Fig. 2 (a) Evoluton of the negatve log-likelihood, which measures the misft between observed and predicted data, for all the fve chains and the end of the burn-in period (dashed black); (b) Acceptance rato for all the fve chains.