In this work, the exact and quadratic approach expression of Knott-Zöeprtiz are presented, as well as its coefficients, amplitudes, Rpp and Rsp, respectively, all of them as a function of the relative contrast, as well as the inversion of quadratic parameters of AVO data. In this inversion of the quadratic parameters, we have used the non-linear Levenberg-Marquadt algorithm, considering only converted and reflected events, either in the non-combined form. In the study of the physical parameters impedance contrast, shear modulus and P wave velocity, we have werified which of those parameters can be effectively inverted. The results have shown that the impedance contrast (δz) is very well solved when it is related with the P wave velocity contrast (δα) or with the shear contrast (δμ), considering reflected events in the case of high, moderate and low model contrasts. On the other hand, when the impedance constrast is fixed and the two other parameters in consideration are related, the results show that these parameters are bad solved, e.g., the ambiguity region becomes large and the parameters become ambiguous and unstable. In the case of a converted event and in the combination of converted and reflected events, considering low and moderate contrast models (δz) is well solved, which is not the case when we consider a high contrast model.
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