GNGTS 2015 - Atti del 34° Convegno Nazionale

GNGTS 2015 S essione 3.1 15 is that they directly provide equations (relating the petrophysical to the elastic properties) with an easily interpretable rock-physical meaning. Conversely, the NN result is a sort of “ black box ”. In this work, the SR approach returns the following equations: (3 a ) (3 b ) (3 c ) whereas with GA we obtain: (4 a ) (4 b ) (4 c ) where: the depth ( z ) is expressed in meters and Sw , φ and Sh in percentage. We note that the intercepts and the coefficients in Eqs. 3 and 4 are very similar. In addition, the exponents in Eq. 4 are very close to one. These characteristics enable us to conclude that, in the specific case under examination, the relations linking the petrophysical to the elastic properties are close to be linear. This is confirmed by the very similar predictions returned by GA and SR (as previously evidenced in commenting Fig. 1). The possibility of describing the RPM by means of the linear equations will simplifies the uncertainty propagation in the probabilistic petrophysical-seismic inversion discussed in the aforementioned companion paper. From Eqs. 3 and 4 we note that, as expected, Vp , Vs and density increase as the depth increases (the z parameter has always a positive coefficient), and decreases as the porosity increases (the φ parameter has always a negative coefficient). Hydrocarbons are usually characterized by low bulk modulus and density and this fact explains the Vp and density increases as the water saturation increases (in Eqs. 3a, 3c and 4a, 4c, the Sw parameter has a positive coefficient). Conversely, the shear modulus is not affected by the saturating fluid and this fact, together with the density decrease produced by the increase of hydrocarbon saturation, explains the Vs increase as the water saturation decreases (in Eqs. 3b and 4b, the Sw parameter has a negative coefficient). The negative coefficients associated to the shale content can be related to the specific depth interval considered in this work (2400-3000 m), characterized by a mechanical compaction regime. As discussed in Avseth et al. (2005) in this depth interval the P-wave and S-wave velocities and the density of shales are usually lower than those of sands. Focusing our attention on the coefficients associated to the petrophysical variables we conclude that the porosity plays the major role in determining the elastic properties, followed by the shale content and the water saturation. Therefore, in the following seismic-petrophysical inversion, we expect that the porosity and, secondarily, the shale content will be the best determined parameters, whereas water saturation will be poorly resolvable (see the companion paper). In Fig. 2 we have represented the so called rock-physics template (RPT) (Avseth et al., 2005). The RPT is a cross-plot that shows the influence of each petrophysical property on the elastic attributes (in this work we consider the P-impedance ( Ip ) and S-impedance ( Is )). Fig. 2a shows the RPT derived from the actual well-log data and the associated petrophysical properties. The well-known hydrocarbon trend is also represented. As expected, we observe a decrease of Ip and an increase of Is as the water saturation decreases and a decrease of both Ip and Is with the increasing of porosity and with the increasing of shale content. These general trends are well matched by the RPTs derived from the empirical (Figs. 2b, 2c and 2e) and the theoretical (Fig. 2c) RPMs. As previously discussed, the RPTs estimated by GA and SR are very similar, and even in this case the NN method yields a better match with the actual RPT