GNGTS 2017 - 36° Convegno Nazionale

644 GNGTS 2017 S essione 3.2 shows high sensitivity towards S-wave velocity so usually the unknowns of the inversion are VS and thickness while the value of the VP, or Poisson’s ratio (ν), and density are assumed a priori. The poor sensitivity of SW to the Poisson’s ratio has been addressed by several authors. For instance Nazarian (1984), showed that the variation of the phase velocity due to a variation of Poisson’s ratio is small. However, Foti and Strobbia (2002) showed that a wrong a priori assumption on the value of can significantly affect the inversion results; it has also been shown that the investigation depth of surface waves depends on (see for example Pelekis and Athanasopoulos, 2011). Socco and Comina (2017b) demonstrated that the relationship between the depth of investigation and the wavelength of propagation of SW is sensitive to and this sensitivity increases with depth. The mechanical properties of loose soils, and hence their seismic velocities, depend on the overburden load according to a power-law relationship (Gassmann, 1951). When dry granular materials are concerned, this results in a depth dependency in the form: V P = γ P ( ρ gz ) a p V S = γ S ( ρ gz ) a s (1) where g is the gravity acceleration, z is the depth, ρ is the bulk density, γ p and γ s are depth- independent coefficients mainly related to the elastic properties of the grains for P- and S-wave respectively, and α p and α s are the power-law exponents for P- and S-wave respectively. The dispersion of SW propagation in loose granular media is also characterized by a power law that can be formulated as: c = bλ α s (2) where λ is the wavelength, c is the phase velocity and b is a proportionality coefficient (see for example Gusev et al. , 2006). Bergamo and Socco (2013, 2016) exploited this behavior for a robust inversion of SW. They retrieved the 1D VS profile within the sand formation and, assuming that for shallow investigation depths the propagating wavelength is equal to the depth, they obtained an estimation of the sand bottom depth. They also concluded that if higher modes are available, they can be included in the inversion process and allow the estimation of the Poisson’s ratio and consequently, the 1D VP profile can also be estimated. Here we aim to improve the accuracy of estimation of the sand bottom depth and to estimate the value of the Poisson’s ratio by including in the inversion a method proposed by Socco and Comina (2017a) that relates the wavelength of propagation of SW with the depth of investigation. Method. We use a synthetic model and its relevant dispersion curve to illustrate the method. In Fig. 1a we show the velocity model that simulates a loose sand formation having thickness equal to 30 m over a stiff bedrock. We consider a VS gradient (Eq. 1) for the loose sand and a constant VS value for the bedrock. The power-law parameters for the VS in the sand are γ s = 18.31 and α s = 0.231 (Zimmer et al. , 2007). Poisson’s ratio ( v = 0.2) and density ( ρ = 1560 kg/m 3 ) are considered constant. The synthetic DC is computed using Haskell and Thomson forward operator (Maraschini, 2008) and it is presented in phase velocity-wavelength domain (Fig. 1a). To isolate the part of the DC that refers to the propagation inside the sand only, we define a threshold wavelength, λ b , below which the power law is not any more valid. According to this, we select the data points that belong to the sand and with a power law fitting we obtain the value of α s equal to 0.229 (estimation error 2.42%). The selected data points are used in a Monte Carlo inversion where the unknown is γ s and its value is estimated as 18.44 (the error is 1.5%). Since also the 1 st higher mode is available, the estimation of v is possible and VP can be computed. The Poisson’s ratio value estimation was 0.2102, approximating the true value with an error of 5.1%. For the estimation of the sand thickness we use the wavelength-depth (W/D) relationship methodology proposed by Socco et al. (2017). Based on our synthetic dispersion curve (fundamental mode) and the inverted S-wave velocity profile, we can compute the time-average velocity VSz: