GNGTS 2023 - Atti del 41° Convegno Nazionale

Session 3.3 ______ ___ GNGTS 2023 where represents the frequency dependent average phase slowness between the receiver pair ( and ), and is the computed ray path between the receiver pair. The frequency dependent ray path between each receiver pair (i.e., the fastest path) is computed by solving the eikonal equation using a finite-difference method (Noble et al., 2014). In case of straight-ray SWT, all ray paths between the receiver couple are assumed to be straight lines. We use the inversion algorithm that was proposed by Boiero (2009). We minimize the misfit function in the least squares sense in a deterministic approach. The misfit function ( ) is defined as: (2) where is the model parameters, represents the observed data, is the vector of forward response of the model, shows the uncertainties of the observed data, represents the spatial regularization matrix and is the covariance of the spatial regularization. The defined misfit function in Eq. (2) is minimised iteratively. At the n th iteration, the current model is updated as: (3), where represents the sensitivity matrix of the data and is the damping factor. Numerical Example We generated synthetic data using a 3D- finite difference code (Bohlen, 2002). The 3D model includes a sequence of layers with vertically increasing velocity values that have surrounded two velocity anomalies (Figure 1). The Poisson’s ratio and the density values are constant in the whole model and are equal to 0.33 and 2000 kg/m3, respectively. Receivers are located with a 1 m spacing in an area of 20 m 20 m (Figure 1a). The dispersion curves were retrieved using an automatic two-station code (Papadopoulou, 2021). We start the inversion from an initial model that consists of five layers with the thickness 2 m for each layer. Each inversion block extends 2m on the side and has an initial constant VS value of 200 m/s. The Poisson ratio and density values are assumed to be equal to their true values. Both straight- and curved-ray methods start from the same initial model. The obtained VS models at the end of the inversion are displayed in Figure 2.