GNGTS 2016 - Atti del 35° Convegno Nazionale

GNGTS 2016 S essione 3.1 487 modeling and by using a 50 Hz Ricker wavelet as the source signature. The Bayesian AVA inversion performed according to Buland and Omre (2003) returns the posterior probability distribution of the natural logarithm of the elastic properties ( m; seismic impedances and density) conditioned by the observed seismic data ( d ). However, density estimates are not used in the classification process because the linear AVA inversion cannot retrieve reliable information about density with realistic noise levels. In the following examples to qualitatively evaluate the ambiguity related to the different classification algorithms, we use as inputs for the classification methods different Monte Carlo realizations drawn from the posterior probability distribution p(m|d) . In addition, for the two Bayesian classification approaches we also show the posterior probability distribution representing the probability of occurrence of each facies at each given vertical position. The final results are represented in Fig. 2a. Comparing the results of DA and NN approaches we observe that they return very similar results, thus demonstrating that in this particular case the discriminant surfaces in the feature space (the 2D space containing the natural logarithm of Ip and Is ) can be conveniently approximated to quadratic surfaces. It can be seen that the gas sand layer and the most of the brine sand layers are correctly classified although some shale layers are erroneously classified as brine sand or gas sand. These misclassifications can be ascribed to the overlap between the elastic properties of each facies. Also note that the vertical facies profiles predicted by the DA and NN methods show some unphysical characteristics with a brine sand layer placed just above a gas sand interval. This is obviously an unphysical situation being the gas less dense than brine. If we analyze the SB method that considers the additional information about the a-priori occurrence of each facies, we observe that the predicted vertical facies profile is slightly closer to the true one, but some unphysical vertical successions of facies are already present. These unphysical characteristics are not present in the Bayesian classification with a 1D Markov chain prior model in which we have imposed a null probability for the transition from a brine sand to a gas sand. This additional a-priori information yields a predicted facies profile that is very close to the true one. In this case the majority of sand and shale intervals are correctly predicted, thus demonstrating that in case of a significant overlap between the elastic properties of each facies, it is crucial considering as many as prior information as possible to better constrain the final result. In Fig. 2b are shown the so called confusion matrices computed by considering the results obtained by classifying the maximum a posteriori (MAP) solution of AVA inversion. In a confusion matrix each column represents the instances in a predicted class while each row represents the instances in an actual class. Along the main diagonal we observe the percentage of samples belonging to a litho-fluid class that have been correctly classified in that class, whereas the off-diagonal terms indicate the percentage of samples that have been misclassified. It can be observed that the confusion matrices for the DA and the NN approaches are very similar with about 90% of shale, 80% of brine sands and 65% of gas sands correctly predicted. As expected, the overlap between the Ip and Is values of each facies produces a significant number of actual gas sand samples that have been erroneously classified as brine sand (35%, approximately). The confusion matrix resulting from the SB approach is similar to those derived from the NN and discriminant analysis. The great advantage in this case is offered by the posterior probability that indicates the probability of occurrence of each facies at each time sample. Finally, the MC method produces a confusion matrix with the 100% of gas sand correctly classified and negligible misclassification errors that can be primarily attributed to the different resolution between well log data and the elastic properties estimated by AVA inversion. Litho-fluid facies prediction on field data. The classification procedure is made even more complicated in the field data application by the narrow frequency bandwidth that characterizes the available seismic data. In fact, the strong attenuation of high frequencies produced by several gas clouds occurring in the shallow layers, determines a dominant frequency around 15 Hz at the depth of the target level. Fig. 3a represents the facies predicted along an In-line