GNGTS 2016 - Atti del 35° Convegno Nazionale

490 GNGTS 2016 S essione 3.1 A Markov Chain Monte Carlo algorithm for litho-fluid facies prediction and petrophysical property estimation: An application for reservoir characterization in offshore Nile Delta M. Aleardi Earth Sciences Department, University of Pisa, Italy Introduction. Seismic reservoir characterization uses pre-stack reflection seismic data to describe the spatial variability of subsurface properties around the target zone. In this work, I implement a non linear, target-oriented, inversion algorithm that exploits the amplitude versus angle (AVA) variations of the seismic reflections to estimate in a single-step both the litho- fluid facies and the petrophysical properties. The inversion is casted in a Bayesian framework and given the non linearity of the forward modeling, it is formulated in terms of a Markov Chain Monte Carlo (MCMC) algorithm (Sambridge and Moosegard, 2002) in order to produce accurate and unbiased uncertainty estimations. I apply this algorithm in a clastic reservoir located in offshore Nile Delta where the reservoir zone is gas saturated and hosted in sand channels surrounded by shale sequences. A linear empirical rock physics model (RPM; see Aleardi et al. 2016) is used to link the petrophysical properties to the elastic parameters, whereas the non- linear Zoeppritz equations relate such elastic properties to the observed AVA response. The exact Zoeppritz equations allow me to take advantage of the long offset seismic acquisition and to consider a wide range of incidence angles (0 and 60 degrees) in the inversion. The Gaussian mixture (GM) distribution used to describe the a-priori information about the petrophysical properties takes into consideration the multimodality and the correlation that characterize the distribution of these properties in the reservoir zone. In the field data application the close match between the outcomes of the MCMC algorithm and the well log information demonstrates the applicability of the method and the reliability of the final results. In the following discussion, F indicates the litho-fluid facies that are shale, brine sand and gas sand, E represents the elastic properties that are P- wave, S-wave velocities ( Vp and Vs , respectively) and density, R indicates the petrophysical properties that are water saturation ( Sw ), porosity ( φ ) and shaliness ( Sh ), whereas d is the observed data that is the AVA response pertaining to the top of the interpreted reservoir extracted for each considered CMP gather. The implemented MCMC algorithm. Before discussing more in detail the MCMC algorithm I point out that my inversion procedure follows a strictly target-oriented approach, therefore only the AVA response associated to the interpreted top of the reservoir interval has been inverted. For each considered reflecting interface the properties of the underlying layers are considered as unknowns, whereas the properties of the cap-rock are kept fixed and equal to the average properties of the shales that are defined from well log data. The main advantage of MCMC methods is that they correctly sample the target posterior probability distribution (PPD) even if the a-priori distribution is not defined in a closed form and even for non-linear inverse problems in which the posterior distribution can not be analytically computed from the prior information and from the likelihood function. As MCMC algorithm I use the Metropolis-Hasting method. This method performs a random walk in the model space by applying a simple two-step procedure: in the first step a candidate model is drawn from the prior distribution, while in the second step this model is accepted with a probability that depends on its fit with the observed data. The ensemble of accepted models is the final output of the algorithm that can be used to numerically compute the final PPD. Once a candidate model is drawn, it is accepted following the so called Metropolis rule: (1) where m cand is the candidate model, m curr is the current model (that is the last model accepted during the random walk) and α is the acceptance probability. Usually, multiple random walks