GNGTS 2015 - Atti del 34° Convegno Nazionale

GNGTS 2015 S essione 3.1 25 to density. However, we note that, although with a different resolution, the predicted elastic properties close match the true ones. Now we move to describe the results of the petrophysical inversion obtained by applying both the linear, empirical, rock-physics model and the non-linear, theoretical, rock-physics model. The final, multimodal, Gaussian mixture distributions p(R|d obs ), derived for both the petrophysical inversions are represented in Figs. 2b and 2c. Fig. 2b shows the outcomes of the petrophysical inversion in which the theoretical, non-linear, rock-physics model (TPRM in the companion paper) has been considered, whereas Fig. 2c shows the results obtained when the empirical, linear, model (SR in the companion paper) has been used. In both cases we note that, as expected, the water saturation is poorly resolvable in the range 0-95% due to its minor influence in the Ip and Is values (although the main gas sand interval at 2.46 s has been correctly predicted), whereas the shaliness and, particularly, the porosity are well resolved. Comparing the predicted petrophysical properties with the true ones (shown by the dotted white lines), we note that, within the resolution of the seismic data, both the theoretical and the empirical rock-physics models are able to correctly predict the porosity and the shaliness values. In particular, both petrophysical inversions have been able to predict the many porosity and shaliness variations that occur between 2.45 and 2.50 s, where a finely layered sand-shale sequence occurs. As expected, a lower match between each predicted and true value and a higher uncertainty characterize the water saturation estimates. For the water saturation, we also note that the theoretical rock-physics model seems to produce a better fit with the true water saturation values with respect to the empirical rock-physics model. This fact can be ascribed to the difficulty of a linear rock-physics model to takes into account the non-linearity that characterizes the influence of the water saturation on the P and S impedances. In conclusion, both the outcomes of the empirical, linear, and the theoretical, non-linear, rock-physics models show a fair match with the actual well-log measurements. This confirms the reliability and the applicability of the two rock-physics models in the petrophysical inversion. However, with respect to the analytical rock-physics model the theoretical model is more computer demanding as it requires a Monte Carlo simulation to compute the joint probability distribution p(m,R). This peculiarity must be taken into account when the petrophysical inversion is performed on multiple CMP gathers. The discussion about the field data inversion is limited to a single CMP location where a well-control is available. This CMP is the nearest to the well that has already been considered in the synthetic inversion. The seismic data have been processed paying particular attention at preserving the true amplitude of the reflections. However, due to the strong attenuation of high frequencies produced by several gas clouds occurring in the shallow layers, these seismic data are very poor in high frequencies. Consequently, the dominant frequency, at the depth of the target level, is around 15-18 Hz. Fig. 3a illustrates the results of the Bayesian AVA inversion for the considered CMP gather. In the observed seismic data, despite the very low resolution, a clear class III AVA anomaly is visible at the target level (around 2.46 s). In blue are illustrated the true elastic properties resampled at the seismic sampling interval, the green lines show the true properties up-scaled to the seismic frequency band, the red curves represent the MAP solutions, while the gray lines are Monte Carlo realizations derived from the posterior distribution. As observed in the previous synthetic example the uncertainties increase passing from the impedances to the density estimates. However, the true up-scaled elastic properties (green lines) show a fair match with the estimated ones (red lines) and, more importantly, they lie inside the range defined by the Monte Carlo realizations. Figs. 3b and 3c show the conditional probability distributions of the petrophysical properties predicted by using the theoretical, non-linear, and the empirical, linear, rock-physics models, respectively. At the low resolution of the seismic data, the differences in the results obtained with the two rock-physics models are negligible. Differently, from the previous synthetic test,