The accuracy of AVA approximations in isotropic media assessed via synthetic numerical experiments: Implications for the determination of porosity

Analyses of seismic amplitude vs. angle are widely used to estimate hydrocarbon reservoir properties. This paper investigates the accuracy of existing approximations based on the Zoeppritz equation, using synthetic numerical experiments that correlate P-wave reflectivity in isotropic media with reservoir porosity. An effective medium non-interacting approach (NIA) in rock physics modelling was used to compute the properties of fluid-saturated (water + gas) reservoir, which were then used in seismic modelling. In parallel, a Bayesian approach was used to estimate reservoir porosities from angle-dependent reflection coefficients and seismic amplitudes. A Maximum a posteriori solution of the Bayesian approach was also utilised to obtain an inverted porosity distribution in the reservoir model. The results of our forward models are important as they suggest that most of the approximations deviate from the exact Zoeppritz solutions with increasing angles of incidence of seismic waves. The results from the Bayesian inversion show that the Rüger and Bortfeld approximations agree with the exact Zoeppritz solutions to accurately estimate reservoir porosity. All the other approximations, except for Smith's, underestimate reservoir porosity and should be used in pre-stack inversion with caution. Smith's and Fatti's approximations failed to estimate reservoir porosity because of associated uncertainties.