GNGTS 2019 - Atti del 38° Convegno Nazionale

GNGTS 2019 S essione 3.2 707 the reference model and contaminated with Gaussian random noise with a standard deviation of 5. We start by considering the schematic 2-layer model. In this case our aim is to compare the uncertainties affecting the final solution when the dispersion curves lie in different frequency bands. In the first test the dispersion curve extends over [3-30 Hz], whereas in the second case the dispersion curve lies in the interval [6-30 Hz]. Both examples consider a correct number of layers equal to 2. In Fig. 1 top 5 images we represent the results for the 3-30 Hz example. The marginal PPDs of Vs and interface location show that the inversion perfectly recovers the true model and that the estimated layer depth position is perfectly located at 8 meters. Differently the Vp / Vs ratio is not recovered, and the posterior distribution is still very similar to the prior with a depth-independent MAP value equal to 4. Note the fast convergence rate of the chain that need about 30 iterations to reach the stationary regime. The comparison between the observed dispersion curve and the dispersion curves computed on the starting model and on the model sampled at the last iteration, demonstrates that the algorithm perfectly predicts the observed data. Figure 1, bottom 5 images, shows the results for the 6-30 Hz example. We observe that the Vs of the first layer has been recovered with the same accuracy of the previous example. Differently, the position of the interface and particularly the velocity of the deepest layer are now estimated with higher uncertainties. This is mainly related to the fact that the low frequencies are crucial to constraint the Vs of the deepest layer. Indeed, this model parameter influences the Fig 2 - a) Synthetic and noise-contaminated shot gather. b) Close-up of a). c) Fourier amplitude spectra of a). d) Phase velocity spectra derived on a): blue and red colors are low and high amplitude values, respectively.