GNGTS 2016 - Atti del 35° Convegno Nazionale

GNGTS 2016 S essione 3.1 515 right, second row: from top to bottom). Note that, moving from the center to the lateral edges of the model, the PPDs become broader and multimodal. Analogously, moving from the top to the bottom of the model, the PPDs suffer multimodality and widening. These characteristics are in agreement with the expected loss of information due to the poorer illumination in the lateral and deep parts of the model. Next, we extract 200 models from the PPD derived by the BGA inversion and the Gibbs sampling and we employ them as starting models for LFWI. We use the time-domain steepest- descent method, with 5 iterations at 4, 5, 6, 8, and 10 Hz. The mean value of all the resulting final models is displayed in Fig. 2a and it can be directly compared with the true model of Fig. 1a, finding a satisfactory match. Fig. 2b shows the approximate 99% confidence interval of the set of final models. Note that the highest uncertainties are mainly localized where seismic illumination is poorer. Fig. 2c shows the 1D marginal PPDs, at the same positions indicated in Fig. 1d. Again, note the loss of resolution from the centre to the lateral edges, and from the shallow to the deeper parts of the model. Comparing Fig. 1d with Fig. 2c, we observe that the multimodal behaviour disappears and that the distributions are narrower. We also show three velocity profiles (Fig. 3a) from the far left to the centre of the model (at offsets 0 m, 2000 m, and 4500 m); the set of starting models is displayed by the grey beam, the set of final models is displayed by the cyan beam, and the true model by the black line. The velocity profiles (Fig. 3) and the comparison between the distributions (Figs. 1d and 2c) highlight several points: 1) the set of models (grey beam) resulting from GA FWI reconstructs well the low frequency trend of the true velocity model; 2) the loss of resolution with depth and near the edges of both the GA and LFWI solutions, 3) the narrowing of the distributions after local FWI, and (4) the improvement in the estimation of the true model after local FWI, especially for the central part of the model where the seismic illumination is higher. Finally, note that the marginal PPDs (Fig. 2c) do not display multimodal shapes, thus demonstrating that the whole set of starting models converge toward the same model-space region, and that, where the model is sufficiently illuminated by the wave-fronts, the true Vp values lay within the final PPDs. Conclusions. Standard approaches for determining a starting model for FWI, such as reflection tomography, provide a single velocity macro-model. The method that we investigate Fig. 2 – a) The mean model of the set of final models (after GA+GS+LFWI); b) the 99% confidence interval of the set of final models; c) the uncertainties associated with some model parameters (first row: at surface from left to right; second row, central line from top to bottom).