GNGTS 2014 - Atti del 33° Convegno Nazionale

GNGTS 2014 S essione 3.1 31 sediment exploration, the inverse problem becomes stable as we pass from the three- to the two- term approximation. Conversely, when the Vp / Vs ratio is very high (or Vs / Vp approaches 0), as it occurs for shallow or seabed sediments, the inverse problem is ill-conditioned even if a two-term approximation is considered. Therefore, in the case of linear AVA inversion with very high Vp / Vs ratios, the application of a regularization method (i.e the T-SVD method) is needed to stabilize the inversion process. Now we move to describe the orientation of the eigenvectors in model space for the three- and two-term inversions. We first analyze the Aki and Richards equation and assuming a Vp / Vs ratio of two (Fig. 2a, left column). For low angles, the R p and R d components are equal and R s is zero. Therefore, the vector points in the direction of P-impedance perturbations. This result is obvious: it is known that the zero-offset reflection coefficient depends only on the acoustic impedance contrast at the reflecting interface. The R s component becomes significant for Fig. 2 – a) Eigenvectors in model space versus the maximum observation angle for three-term inversion. The Vp/Vs =2 and Vp/Vs >>2 are represented on the left and on the right, respectively. For each case, the first, second and third eigenvectors are shown from top to bottom, respectively. b) Eigenvectors in model space versus the maximum observation angle for the two-term inversion. The left column represents the Vp/Vs =2 case, whereas the right column displays the Vp/Vs >>2 case. For each case, the first and second eigenvectors are shown at the top and bottom, respectively.