In this paper, we propose a multivariate statistical method named Generalized Principal Component Analysis (GPCA) that computes components describing relationships between several sets of variables and also describing separately each set, while reducing the number of significant variables. GPCA is applied to three elastic parameters (P, Simpedances and densities) obtained after a joint prestack stratigraphic inversion of iso-angle cubes from a real seismic data set. The components extracted from GPCA are the new attributes representing the seismic character on the reservoir window. These new attributes are used to filter the initial parameters and are geologically interpreted with a supervised pattern recognition algorithm. They appear more relevant than more classical attributes extracted from a Principal Component Analysis (PCA) applied to the same data. First, the new attributes can be easily related to the groups of variables and therefore physically interpreted.