GNGTS 2019 - Atti del 38° Convegno Nazionale

GNGTS 2019 S essione 3.3 727 model. A kriging interpolation is employed to preserve the a-priori vertical correlation in all the sampled models. Results The prior model and the vertical transition matrix are derived from actual well-log data pertaining to 5 wells investigating a gas-saturated clastic reservoir located in a shale-sand sequence. One of the two remaining wells is used as a blind test in the following inversion examples. Fig. 1 shows the a-priori non-parametric (Fig. 1a) and the Gaussian-mixture (Fig. 1b) marginal distributions for each elastic property derived for the reservoir interval. The non- parametric prior model is used by the MCMC algorithm, while the Gaussian-mixture is used by the analytical inversion approach. We note some important differences between the non- parametric and Gaussian-mixture distributions. In particular, the distributions are very similar for shale, but significatively different for brine sand and gas sand where the non-parametric distribution shows skewness or even multimodalities. Obviously, the Gaussian-mixture model does not capture these characteristics and for this reason it constitutes an oversimplified statistical model in this context. For this reason, we expect that the MCMC inversion outperforms the analytical approach. These considerations are confirmed by the normal probability plots of Fig. 1c where we observe significative deviations from the Gaussian model for Vp and Vs in the Fig. 1 - a) The a-priori non-parametric model derived through the kernel density estimation algorithm. b) The Gaussian-mixture prior model. c) Normal probability plot derived from the actual well log data. b) Normal probability plot derived on the normal score transformed actual well log data. In c) and d) the dotted lines represent the theoretical Gaussian distribution, whereas the circles represent the actual well log data.