The importance of the Vp/Vs ratio in determining the error propagation, the stability and the resolution of linear AVA inversion: a theoretical demonstration

The linear Amplitude-Versus-Angle (AVA) inversion has become a standard tool in deep-sediments hydrocarbon exploration since its introduction in the oil and gas industry. However, in the last decades, with the increase of offshore construction activity, applications of this method have been also extended to predict overpressured zones and/or to evaluate the geotechnical properties of shallow sea bottom layers. Among the input parameters requested by linear AVA inversion there is the background Vp/Vs ratio across the reflecting interface and a Vp/Vs ratio of two is frequently assumed. This value is usually very close to the true ratio in case of deep, compacted sediments but it can be a gross underestimation of the true value in case of shallow or overpressured sediments. Despite that, the importance of the background Vp/Vs ratio in AVA inversion is frequently underrated and thus I consider two frequently used approximations of the Zoeppritz equations to study their impact on the outcomes of linear AVA inversion: the three-term Aki and Richards equation and the two-term Ursenbach and Stewart formula. These equations are then analysed, varying the Vp/Vs value, using tools frequently applied in sensitivity analysis. It turns out that the background Vp/Vs ratio controls the error propagation from data to model space and determines the cross-talk between the inverted parameters. Moreover, an increasing Vp/Vs ratio causes a decrease of stability of the AVA inversion and worsens the estimate of the Vs contrast at the reflecting interface.