GNGTS 2019 - Atti del 38° Convegno Nazionale

706 GNGTS 2019 S essione 3.2 starting point in the following iteration; 4. Return to step 1. In this work the potential energy is defined as: (5) where G is the non-linear forward modelling operator that computes the dispersion curves for the considered model, C d is the data covariance matrix, d is the observed dispersion curve, q prior is the prior model with prior covariance matrix given by C q . In this work, the mass matrix is computed as a local approximation (around the considered model) of the posterior covariance matrix (see Fictner et al. 2019): (6) where J is the Jacobian matrix that expresses the partial derivative of the data with respect to model parameters. We assume Gaussian distributed and uncorrelated a-priori model parameters. We employ very simple Gaussian prior models: the prior for Vs has a mean value of 160 m/s with a standard deviation of 30 m/s, whereas the prior for layer thickness has a mean value of 5 with a standard deviation of 2. Obviously, different prior models can be easily included into the inversion framework. For example, we can consider a depth-dependent prior model for Vs or even non-Gaussian priors. The starting point for the HMC sampling is randomly generated from the prior. Synthetic and experimental inversion tests. We start by considering a very simple and schematic synthetic model constituted by two layers separated by an interface located at 8 m depth. In this example our aim is to compare the uncertainties affecting the estimated model when the dispersion curves lie in different frequency bands. In the first case the dispersion curve extends over [4-30 Hz], whereas in the second case the dispersion curve lies in the interval [6-30 Hz]. In the performed inversions the dispersion curves have been analytically computed from Fig. 1 - Synthetic inversion results for a 2-layer model. From a) to e): inverted bandwidth between 4 and 30 Hz. From f) to l): inverted bandwidth between 6 and 30 Hz. In both panels we represent from left to right: True model (green line) and marginal Vs PPD (colour scale); True Vp/Vs model (green line) and marginal Vp/Vs PPD (colour scale); Marginal PPD for interface location; Evolution of the L2 norm misfit; comparison between the observed noisy data (black line), the data generated on the starting model (red line) and the data generated on the last sampled model (green line).