The importance of the Vp/Vs ratio in determining the error propagation and the resolution in linear AVA inversion

The Amplitude-Versus-Angle (AVA) method exploits the variation in seismic reflection amplitude with increasing incidence angle to infer the contrast in seismic velocities and densities at the reflecting interfaces (Castagna, 1998). For this characteristic the AVA technique has been extensively used worldwide for lithology and fluid prediction in deep hydrocarbon exploration (e.g., Ostrander, 1984; Rutherford and Williams, 1989; Mazzotti, 1990; Mazzotti, 1991). The AVA method is based on the Zoeppritz equations (Zoeppritz, 1919) which describe the variation in seismic amplitude with increasing angle of incidence for a plane wave incident on an idealized interface separating two semi-infinite half spaces. The system of equation formulated by Zoeppritz is so algebraically complex that many different approximated formulas have been derived to simplify and linearise the inversion process. These simplified equations, valid under certain assumptions, are those frequently used in AVA inversion and interpretation (Ursenbach and Stewart, 2008; Wang, 1999). Performing linear AVA inversion a Vp/Vs ratio equal to two is usually assumed (Castagna, 1998). This ratio is a good approximation of the true value in case of classical deep sediments exploration (hydrocarbon exploration), but generally it is an underestimation of the true ratio in case of shallow or seabed sediments. This may constitute a problem because, in addition to the classical deep exploration, the AVA inversion can also be useful for characterizing shallow layers (Riedel and Theilen, 2001) and, thus can be of help for shallow hazard assessment and well site analysis. While performing linear AVA inversion the importance of the Vp/Vs ratio is usually underrated and its value is set without worrying too much. Therefore, in this work we want to point out that the assumed Vp/Vs ratio plays a crucial role in determining the expected resolution and the uncertainties associated with each inverted parameter. To this end we have considered the well known three terms Aki and Richards (Aki and Richards, 1980) equation and the two terms Ursenbach and Stewart formula (Ursenbach and Stewart, 2008), which are analyzed making use of the sensitivity analysis tools applied to the inversion kernel. We have first studied how the Vp/Vs value influences the condition number, the amplitude of the eigenvalues (not shown here for the lack of space) and the orientation of associated eigenvectors in model space. Moreover, also applying the classical truncated SVD method and studying the resolution and the covariance matrices, we have analyzed how the Vp/Vs ratio determines both the expected resolution of each inverted parameter and the error propagation from data space to model space.