We discuss two Bayesian seismic-petrophysical inversion techniques, the two-stage and single-stage approach, which estimate petrophysical properties from prestack seismic data. Both approaches are developed considering linear approximations and are applied for reservoir appraisal studies in the Nile Delta. The two-stage approach first uses an amplitude-variation-with-angle (AVA) inversion to infer P-wave velocity, S-wave velocity, and density. Then, a linear empirical rock-physics model, properly calibrated for the investigated area, is used to transform the estimated elastic parameters into the petrophysical properties of interest under the assumption of Gaussian mixture distributed petrophysical properties. The single-stage approach uses the linear rock-physics model to rewrite the time-continuous P-wave reflectivity equation as a function of the petrophysical contrasts instead of the elastic constants. This reformulation, together with the assumption of a Gaussian prior model, allows us to directly derive (in a single-stage inversion) the petrophysical properties from AVA data. Despite the differences in the forward-model parameterization and in the assumed a priori distribution for the petrophysical properties, the two inversion methods yield comparable predictions that are consistent with borehole data. For the investigated zone, this work demonstrates that, although neglecting the facies-dependent behavior of petrophysical properties, the a priori Gaussian assumption for the petrophysical properties can provide reliable predictions with a very limited computational effort. In addition, the good match between predicted and logged properties proves the suitability of the linear rock-physics model for reservoir characterization in the Nile Delta.

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