GNGTS 2015 - Atti del 34° Convegno Nazionale

GNGTS 2015 S essione 3.1 23 expectation maximization algorithm. Fig. 1 represents the prior Gaussian mixture distribution of water saturation, porosity and shaliness for the three facies. In Fig. 1a we represent the prior distribution projected onto the Sw-φ plane, together with the associated two marginal prior distributions ( Mpdf ) computed along the Sw and φ directions. As expected, the shale correspond to high Sw values and low porosity, whereas both brine sands and gas sands are characterized by higher porosity, with the gas sands at lower water saturation values than brine sands. Fig. 1b shows the prior distribution of the petrophysical properties projected onto the Sw-Sh plane. Similarly to Fig. 1a, the marginal distributions are also represented. As expected, the shales are characterized by higher shaliness values with respect to brine sands and gas sands. To test the applicability of the petrophysical-seismic inversion and to check the reliability of the two considered rock-physics models, we show a synthetic inversion in which actual well- log measurements, pertaining to a well drilled in the target area, have been used to compute the synthetic seismic data. The synthetic data have been computed by means of a 1D convolutional forward modeling and using a 50 Hz Ricker wavelet as the source signature. Fig. 2a shows the synthetic CMP gather in which the offset has been converted to incident angles, whereas Figs. 2b, and 2c illustrate the results of the Bayesian AVA inversion. The green arrows in Fig. 2a at 2.46 s indicate the target gas-sand interval. The decrease of Ip and density and the increase of Is that characterize this gas-sand interval generate the typical class III AVA anomaly (Castagna and Swann, 1997) clearly visible in the synthetic seismogram. In Fig. 3a the blue curves depict the actual well-log data resampled at the seismic sample interval, the red curves illustrate the maximum a-posteriori (MAP) solution, and the gray curves are Monte Carlo realizations computed from the posterior distribution p(m|d obs ) (see Eq. 2). Each Monte Carlo realization represents a possible solution. As expected, the uncertainties increase passing from Ip , to Is and Fig. 1 – Prior probability distribution of the petrophysical variables (φ, Sw and Sh ) computed taking into account three different litho-fluid classes: brine-sand, gas-sand and shale. The prior is distributed according to a Gaussian mixture model that allows us to take into account the multimodality and the correlation that usually characterize the distribution of the petrophysical properties in the subsurface (see Eq. 4). a) Prior distribution projected onto the Sw-φ plane and the associated marginal distributions (Mpdf) computed along the Sw and φ directions. b) Same as (a) but considering the Sw-Sh plane.