GNGTS 2015 - Atti del 34° Convegno Nazionale

GNGTS 2015 S essione 3.1 27 the low resolution of the seismic data makes a detailed characterization of the petrophysical properties in the subsurface impossible. However, despite the low-resolution issue, the petrophysical inversion has been able to predict the increase of porosity and the decrease of shaliness that occur between 2.45 and 2.50 s where the alternating shale-sand sequence occurs, but, differently from the synthetic inversion, this finely layered shale-sand sequence is resolved as a unique layer. Conclusions. We presented a two-step probabilistic petrophysical inversion applied to reservoir characterization in offshore Nile delta. The first step of this procedure is a Bayesian linearized AVA inversion that returns the posterior probability distributions of the elastic properties ( Ip , Is and density) in the subsurface. The second step is a probabilistic petrophysical inversion that makes use of the results of the previous AVA inversion, of the prior distribution of the petrophysical variables, and of a suitable rock-physics model to determine the posterior distribution of the petrophysical properties in the subsurface. This method propagates the uncertainties from seismic to petrophysical properties, including the effect of seismic noise error, the degree of approximation of the rock-physics model and the uncertainties that affect the estimated elastic properties. The Gaussian mixture model approach allows us to take into account the multimodality and the correlation that usually characterize the distribution of the petrophysical properties in the subsurface. The petrophysical inversion was performed making use of two different rock-physics models: a linear model (named SR in the companion paper) derived empirically by means of a stepwise regression from the available log data, and a non- linear model based on theoretical equations (named TRPM in the companion paper). Both rock-physics models returned very similar results, thus confirming their reliability and their applicability in the specific case under examination. The unique difference lies in the fact that the theoretical rock-physics 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 applying the petrophysical inversion on multiple CMP locations. The inversion of synthetic and field data confirmed the applicability of the proposed methodology. Shaliness and, particularly, porosity are the best resolved parameters. Conversely, water saturation in the range 0%-95% is poorly resolvable due to its minor influence on the Ip and Is values. The field data inversion was performed on a single CMP location where well- control was available to validate the results. The main limit of the seismic data is the very narrow frequency bandwidth that makes them unsuitable for detailed reservoir characterization studies. The results of the Bayesian linearized AVA inversion have been also used to perform a probabilistic litho-fluid facies classification that makes use of Markov-chain models. For the lack of space, the outcomes of this classification procedure have not been discussed here. Acknowledgments. The authors wish to thank EDISON for making the seismic and the well log data available and for the permission to publish this work. References Aki, K. and Richards, P.G.; 1980: Quantitative Seismology: Theory and Methods . WH Freeman & Co. Avseth, P., Mukerji, T. and Mavko, G.; 2005: Quantitative seismic interpretation: Applying rock physics tools to reduce interpretation risk . Cambridge university press. Buland, A. and Omre, H.; 2003: Bayesian linearized AVO inversion . Geophysics, 68(1), 185-198. Castagna, J.P. and Swan, H.W.; 1997: Principles of AVO crossplotting . The leading edge, 16(4), 337-344. Chiappa, F. and Mazzotti, A.; 2009: Estimation of petrophysical parameters by linearized inversion of angle domain pre-stack data. Geophysical Prospecting, 57(3), 413-426. Grana, D. and Della Rossa, E.; 2010: Probabilistic petrophysical-properties estimation integrating statistical rock physics with seismic inversion . Geophysics, 75(3), O21-O37. Hastie, T., Tibshirani, R., Friedman, J. and Franklin, J.; 2005: The elements of statistical learning: data mining, inference and prediction . The Mathematical Intelligencer, 27(2), 83-85. Papoulis, A.; 1984: Probability, random variables and stochastic processes . McGraw-Hill. Stolt, R. H. and Weglein, A. B.; 1985: Migration and inversion of seismic data . Geophysics, 50(12), 2458-2472.