GNGTS 2018 - 37° Convegno Nazionale

560 GNGTS 2018 S essione 3.1 a field dataset, Gaussian random noise is added to the synthetic stack traces by imposing a signal-to-noise ratio equal to 10. Fig. 3a represents the results obtained for the blind well when the non-parametric p ( m , d  | f ) distribution is employed. We observe that the predicted seismic trace perfectly matches the observed trace and that the predicted 1D Ip profile reliably reproduces the vertical variability of the actual impedance values but, more importantly, the 95% confidence interval always encloses the logged Ip . Note that the filtering effect introduced by the convolutional forward operator produces Ip predictions with lower vertical resolution with respect to the logged Ip values. As expected, the filtering effect now translates into less accurate MAP porosity predictions with respect to the well log examples. In particular, the additional uncertainties arising from the seismic inversion yield wider posterior distributions, that is we are now less confident on the final porosity predictions with respect to the previous tests at the well log scale. However, notwithstanding the resolution issue, the inversion still recovers the significant porosity increase occurring at the sand layers. The estimated facies profile still shows satisfactory predictions, although the filtering effect results in final predictions with lower vertical resolution with respect to the previous examples on well logs. Fig. 3b represents the results achieved by the Gaussian-mixture model. By comparing Figs. 3a and 3b we observe that the non-parametric distribution again provides superior porosity estimations and facies profile than the analytical p ( m , d  | f ). In particular, only the main gas-saturated layer located at 940 ms is correctly identified by the Gaussian-mixture model, while the other sand layers are erroneously misclassified as shaly intervals. The 90% coverage probability values confirm these qualitative descriptions being equal to 0.7687 and 0.6331 for the non-parametric and Gaussian-mixture models, respectively. As expected the Gaussian model (Fig. 3c) achieves less accurate porosity estimations, higher uncertainties, and less reliable prediction intervals resulting in a coverage probability equal to 0.6026; a value lower than those yielded by the Gaussian-mixture and the non-parametric p ( m , d  | f ) distributions. Conclusions. This work demonstrated that the correct modelling of the facies dependency of porosity and Ip values could be crucial to achieve accurate estimations and reliable prediction intervals. Both the Gaussian-mixture and the non-parametric distributions provide satisfactory results, although the non-parametric statistical model usually achieves superior porosity estimations and litho-fluid facies classifications. Differently, the Gaussian assumption demonstrated to be a too oversimplified model that, totally neglecting the facies-dependency of the porosity and Ip values, provides less accurate prediction intervals, poorer match with actual porosity profiles, and higher uncertainties with respect to the other two statistical models. In the seismic experiments, as expected, the filtering effect introduced by the convolutional operator and the additional uncertainties arising from the post-stack seismic inversion, provided less accurate porosity estimations characterized by wider posterior uncertainties and predicted porosity and facies profiles affected by lower vertical resolution with respect to the examples at the well log scale. The choice of the underlying statistical model is usually complicated because it is not only case-dependent but should constitute a reasonable compromise between the accuracy of the final predictions, the stability of the inversion procedure, the total computational effort, and the actual fitting between the underlying and the considered petrophysical models. References Grana, D. (2018). Joint facies and reservoir properties inversion. Geophysics, 83(3), M15-M24.