Comparison of different classification methods for litho-fluid facies identification in offshore Nile Delta.

Amplitude Versus Angle (AVA) inversion is usually applied to derive the elastic properties of the subsurface from pre-stack seismic data. Seismic reservoir characterization often uses the outcomes of AVA inversion to infer the litho-fluid facies around the target zone. In this work we test different classification methods for litho-fluid facies identification in a clastic reservoir located in offshore Nile Delta. The reservoir zone is gas saturated and is hosted in sands channels surrounded by shale sequences. This characteristic leads us to consider three different facies in the classification that are shales, brine sands and gas sands, while the available well log data enable us to separate the different facies in terms of petrophysical properties (water saturation, shaliness and porosity) and elastic properties (seismic impedances and density). The classification is performed on the feature space defined by the P- and S-wave impedances that are derived from the observed seismic data by means of a Bayesian linearized AVA inversion (Buland and Omre, 2003).The analyzed case is particularly challenging due to the significant overlap between the elastic characteristics of brine and gas sands. The classification methods we consider can be conveniently divided in two main categories: the methods that do not require any a-priori information about the overall proportions of the litho-fluid facies or about their vertical continuity in the investigated area and those methods that require such information. To the first group belong the quadratic discriminant analysis and the neural network approach, whereas to the second group belong the standard Bayesian approach and the Bayesian approach which include a 1D Markov chain prior model to constrain the vertical continuity of litho-fluid facies. The quadratic discriminant analysis (DA; Avseth et al. 2005) considers that the different classes are divided by quadratic discriminant surfaces in the feature space, while the neural network (NN) method is able to discriminate classes divided by highly non linear discriminant surfaces. This difference allows us to check if the assumption of quadratic discriminant surfaces yields a reliable classification in the investigated area or if more complicated non linear surfaces are required. These two methods return a deterministic classification in which each time sample is classified to one class or to another class without giving an idea on the probability that the sample effectively belongs to that class. Conversely, the two Bayesian classification methods exploit the seismic likelihood function and a set of a-priori information (derived from well log data) to produce a posterior probability that describes the probability that each given sample belongs to a particular litho-fluid class. The first Bayesian method we consider is what we call the standard Bayesian (SB) approach in which only the overall proportions of facies in the target interval is given as a-priori information (Avseth et al. 2005). If we consider a 1D vertical profile this approach classifies each given input sample independently from the adjacent classified samples. In the second Bayesian approach (that we indicate with the acronym MC) a 1D Markov chain prior model (in the form of a transition probability matrix) is given as additional prior information in order to constrain the vertical continuity of the litho-fluid facies along the vertical profile (Larsen et al. 2006). The ultimate goal of this study is to find an optimal classification method for the area under examination and to this end we first analyze the performances of the four classification algorithms in a synthetic AVA inversion in which the seismic data are computed on the basis of the available well log information, then the results obtained in the field data classification are discussed