GNGTS 2019 - Atti del 38° Convegno Nazionale

748 GNGTS 2019 S essione 3.3 Results on cross-hole traveltime tomography. In all the analytical tests we performed (only two of these tests have been presented in the previous section) AM and AM_sd, from one side, and DEMC and DREAM, from the other side, show very similar performances. For this reason, for the sake of brevity only RWM, AM and DEMC are compared in this synthetic seismic example. We use a very schematic Vp model with 784 cells, illuminated by 26 sources and 26 receivers evenly located at the opposite edges of the models. The traveltimes are computed using a numerical approximation of the eikonal equation. Random noise is added to the observed data to better simulate a field dataset. The likelihood is computed from a L2 norm misfit value between predicted and observed data. For the prior we assume a Gaussian model with a constant mean value of 2900 m/s. To reduce the ill-conditioning, we include lateral constrains to the prior in the form of a Gaussian variogram model. All the methods use 10 chains running for 30000 iterations each, with a burn-in period of 5000 samples. Fig. 3a shows the final predicted mean models. All the methods successfully locate the two velocity anomalies, whereas the smoothness of the results is related to the lateral constraints that are although essential to reduce the null-space of solutions. The negative velocity anomaly is better resolved than the positive one because located in a more illuminated portion of the model. The similar a-posteriori standard deviations provided by all the methods (Fig. 3b) confirm their successful convergence toward the stationary regime. We also observe that the posterior uncertainty is congruent with the seismic illumination and increases moving from Fig. 2 - Results for the 2D analytical distribution: a) Comparison of sampled and target pdfs . B) Evolution of the PSRF value after the burn-in period.