GNGTS 2014 - Atti del 33° Convegno Nazionale

34 GNGTS 2014 S essione 3.1 in any case the T-SVD method reduces the order of magnitude of the error associated with each parameter estimation. Conclusions. The sensitivity analysis highlights the strong influence of the Vp / Vs ratio on both the stability of the linear AVA inversion and on the physical meaning expressed by the G matrix. Specifically, we have analyzed how the Vp/Vs value influences the condition number, the orientation of eigenvectors in model space, the resolution for each inverted parameter and the error propagation from data to model space. From the analysis of the condition number we note that if Vp / Vs is equal to 2 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 (as occurs for shallow 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. Moreover, the orientation of the eigenvectors in model space shows that for high Vp/Vs ratios the eigenvectors associated with the Vs -related parameter ( R s and R J ) span the null-space of the inversion kernel. This fact, combined with the observation of the resolution matrices, highlights that the determination of the Vs contrast (or the S-impedance contrast) for shallow sediments or at sea bottom becomes a hopelessly non-unique problem in the case of high Vp/Vs values. Finally, we observe that for increasing the Vp/Vs values the error propagation from data to model space becomes more and more severe. The same happens to the cross-talk between R p and R d making it impossible their independent estimation. References Aki K. and Richards P. G.; 1980: Quantitative seismology: Theory and methods. WH Freeman and Co. Aster R. C., Borchers B. and Thurber C. H.; 2005: Parameter estimation and inverse problems. Elsevier Academic Press. Castagna J. P., Swan H. W. and Foster, D. J.; 1998: Framework for AVO gradient and intercept interpretation . Geophysics, 63(3), 948-956. De Nicolao A., Drufuca G. and Rocca F.; 1993: Eigenvalues and eigenvectors of linearized elastic inversion . Geophysics, 58(5), 670-679. Drufuca G., and Mazzotti A.; 1995: Ambiguities in AVO inversion of reflections from a gas-sand. Geophysics, 60(1), 134-141. Mazzotti A.; 1990: Prestack amplitude analysis methodology and application to seismic bright spots in the Po Valley, Italy . Geophysics, 55, 157-166. Mazzotti A.; 1991: Amplitude, Phase and Frequency versus Offset Applications. Geophysical Prospecting. 39, 863- 886. Ostrander W.; 1984: Plane-wave reflection coefficients for gas sands at non-normal angles of incidence . Geophysics, 49(10), 1637-1648. Riedel M. and Theilen, F.; 2001: AVO investigations of shallow marine sediments . Geophysical Prospecting, 49(2), 198-212. Rutherford S. R. and Williams R. H.; 1989: Amplitude-versus-offset variations in gas sands . Geophysics, 54(6), 680- 688. Tarantola A.; 2005: Inverse problem theory and methods for model parameter estimation . Siam. Ursenbach C. P. and Stewart R. R.; 2008: Two-term AVO inversion: Equivalences and new methods . Geophysics, 73(6), 31-38. Wang Y.; 1999: Approximations to the Zoeppritz equations and their use in AVO analysis . Geophysics, 64(6), 1920- 1927.