Probabilistic estimation of reservoir properties by means of wide-angle AVA inversion and a petrophysical reformulation of the Zoeppritz equations

We apply a target-oriented amplitude versus angle (AVA) inversion to estimate the petrophysical properties of a gas-saturated reservoir in offshore Nile Delta. A linear empirical rock-physics model derived from well log data provides the link between the petrophysical properties (porosity, shaliness and saturation) and the P-wave, S-wave velocities and density. This rock-physics model, properly calibrated for the investigated reservoir, is used to re-parameterize the exact Zoeppritz equations. The so derived equations are the forward model engine of a linearized Bayesian AVA-petrophysical inversion that, for each data gather, inverts the AVA of the target reflections to estimate the petrophysical properties of the reservoir layer, keeping fixed the cap-rock properties. We make use of the iterative Gauss-Newton method to solve the inversion problem. For each petrophysical property of interest, we discuss the benefits introduced by wide-angle reflections in constraining the inversion and we compare the posterior probability distributions (PPDs) analytically obtained via a local linearization of the inversion with the PPDs numerically computed with a Markov Chain Monte Carlo (MCMC) method. It results that the porosity is the best resolved parameter and that wide-angle reflections effectively constrain the shaliness estimates but do not guarantee reliable saturation estimates. It also results that the local linearization returns accurate PPDs in good agreement with the MCMC estimates.