GNGTS 2019 - Atti del 38° Convegno Nazionale

GNGTS 2019 S essione 3.2 681 IMPROVED SURFACE WAVE TOMOGRAPHY: IMPOSING WAVELENGTH-BASED WEIGHTS. F. Khosro Anjom, L.V. Socco DIATI, Politecnico di Torino, Turin, Italy Introduction. Surface wave tomography (SWT) is a well-stablished method in local and global scale, to reconstruct the shear wave velocity (VS) model of the near-surface (Papadopoulou et al. , 2019; Socco et al. , 2014; Picozzi et al. , 2009) and crust/upper mantle (Wespestad et al. , 2019; Bao et al. , 2015; Boiero, 2009; Yao et al. , 2006). Conventionally, SWT methods are integrated with a two-station processing method, by which the surface- wave average dispersion curves (DCs) are acquired along different paths. In the two-station data processing scheme, commonly, the DCs are estimated uniformly in frequency. However, uniform sampling of the phase velocities in frequency, prompts a non-uniform sampling in wavelength. Consequently, the DCs will contain lower population of data points for the large wavelengths compared to shorter wavelength portion. Since the investigation depth of the surface waves is directly related to the wavelength (Yao et al. , 2006; Socco et al. , 2010), having larger distribution of data points for short wavelengths will drive the inversion to the shallowest portion of the model. In other words, high frequency/short-wavelength data points will rule the inversion and they will limit the investigation depth. To overcome this problem and improve the investigation depth, we propose imposing weights to the data points of the DCs, according to the wavelength distribution. Here, we explain the method to impose wavelength-based weights to the data points for the inversion. Then, we show an application of surface wave tomographic inversion to a synthetic data set, where the wavelength-based weights are assigned to the dispersion data points, and we compare it to the result of the inversion without imposing any weight. Method. Considering the average DCs of multiple paths, first, we transform the average DCs to wavelength-phase velocity domain by dividing phase velocity and frequency elements. Then, for each point of the average DC, we compute the corresponding weight as the distance to the closest data point in terms of wavelength. We define the misfit function Q in scheme of 1 weighted least square of the average slowness (–––––––––––––), as:                    Phase Velocity (1) where S true and S M are the true and synthetic average slowness of the paths, respectively, and W is the diagonal matrix of wavelength-based weights corresponding to the data points. We use a damped least square Levenberg-Marquandt method (Boiero, 2009) to minimize the misfit function Q iteratively and update the model parameters at each iteration as: (2) where M n and M n +1 are the current and the new model parameters, respectively. λ is the damping factor which attempts to trade off the accuracy and feasibility of the solution, and G is the Jacobian representing the sensitivity matrix. Synthetic Example. The initial model of the synthetic example is consisting of 60 1D layered models evenly spaced along a 2 km line. Each model includes 8 layers over the half- space, where the density and Poisson’s ratio of all layers are constant and equal to 2800 kg/m 3 and 0.3, respectively. The initial model was strongly perturbed (20%) by altering the 1D VS models negatively and positively to form a checkerboard 2D model (true model). In Figs 1a and 1b, we show the initial VS model and the scheme of the perturbation, respectively. In Fig. 1c, we show the perturbed (true) VS model after applying the perturbation (Fig. 1b) to the initial model (Fig. 1b). To achieve a large and uniform data coverage, we defined 240 paths, uniformly distributed