GNGTS 2019 - Atti del 38° Convegno Nazionale

708 GNGTS 2019 S essione 3.2 slope of the fundamental mode at low frequencies (Socco and Strobbia, 2004). The Vp / Vs ratio is not recovered with a posterior distribution similar to the prior. The computed χ 2 probability ( p (χ 2 )) and the BIC values obtained for a correct 2-layer parametrization are p (χ 2 )=0.0408 and BIC=34.61, we also performed an inversion with an erroneous 3-layer parameterization (not shown here for brevity) that provides a p (χ 2 ) and BIC values of 0.0105 and 44.54, respectively. The higher p (χ 2 ) and lower BIC values clearly indicate that the 2-layer is the most appropriate parameterization, thus proving that these statistical tools could constitute a valid help to select the optimal model parameterization. We now describe the results provided for the experimental inversion tests. In this case the observed dispersion curves have been picked on the frequency-phase velocity spectra derived from synthetic shot gathers computed making use of the reflectivity method. We employ a 15 [Hz] Ricker wavelet as the source signature with a sampling interval of 2 [ms]. We simulate an off-end acquisition geometry with a minimum offset of 10 m and 48 receivers equally spaced of 5 m, resulting in a maximum offset of 245 m. Fig. 2 shows a synthetic shot gather, the Fourier amplitude spectra of the signal and its phase velocity spectra. Note that the Vs of the second layer is lower than that of the first layer: this velocity inversion complicates the picking of the fundamental mode because higher modes become more energetic than the fundamental mode at high frequencies. In cases of velocity inversions the consideration of only the fundamental model severely increases the ill-conditioning of the inversion procedure, and for this reason in these situations higher modes are often of crucial importance to better constraint the final estimates. Fig. 3 displays the inversion results. The Vs of the shallowest layer is perfectly resolved and also the Vs of the second layer is well predicted, although the MAP solution slightly Fig. 3 - a) True Vs model and marginal Vs PPD (colour scale). b) True Vp/Vs model and marginal Vp/Vs PPD (colour scale). c) Marginal PPD for interface location. d) Evolution of the L2 norm misfit. e) Comparison between the picked dispersion curve, data generated on the starting model and the data generated on the last sampled model.