GNGTS 2014 - Atti del 33° Convegno Nazionale

GNGTS 2014 S essione 3.1 33 highest resolution. Also in this case, the resolution of the Vs -related parameter R J decreases with the increasing Vp / Vs ratio. Now we describe the unit covariance matrix, which is obtained after applying the T-SVD method (Fig. 3c) to eliminate the smallest singular value of the G matrix and to stabilize the inversion. We start with the three-term inversion. For high Vp / Vs ratios, the error is mapped onto the R p and R d parameters because the third eigenvalue, pointing toward the R s parameters, has been eliminated by the truncation. We also observe a strong negative covariance (expressed by the off-diagonal terms and indicating a correlation) between R p and R d , which confirms the strong cross-talk between these two unknowns and the difficulties of achieving an independent estimation. As expected, both the correlation between R p and R d and the error magnitude decrease if we consider a Vp / Vs ratio equal to two. In this case, the error is more homogeneously distributed among the three parameters. Also by observing the unit covariance matrix for the two-term inversion, we see that the error magnitude decreases from the Vp / Vs >>2 case to the Vp / Vs =2 case. Moreover, the truncation of the second singular values (in the case of Vp / Vs >>2) results in the error being mapped entirely onto the R I parameters, whereas in the case of Vp / Vs =2, the error also affects the R J values. Finally, by comparing Fig. 3a and 3c, we can see that Fig. 3 – a) Unit covariance matrices in the case of a least-squares inversion. b) Model resolution matrices after applying the T-SVD method. c) Unit covariance matrices after applying the T-SVD method. In all cases both the Vp/Vs =2 and Vp/Vs >>2 (left and right columns, respectively) and the three- and two-term inversions (top and bottom rows, respectively) are considered.