Is it possible to optimize the traditional classification scheme of ultra-alkaline rocks by means of combined statistical methods?

The rare rocks-association of carbonatites, potassic melilitites, lamproites, lamprophyres and leucitites ("ultraalkaline" sensu Le Bas, 1987) have unique modal and chemical features that make impossible and misleading their grouping on a unique classification diagram. Many schemes of classification for igneous rocks are based on mineralogical and/or geochemical variables which vary with differentiation processes. However, the ultra-alkaline rocks often do not comply with common petrogenetic processes. The Recent Italian ultra-alkaline association occurs along the Apennines with monogenic volcanoes and the Vulture volcanic complex and along the Tyrrhenian coast in caldera and stratovolcanoes. Therefore, a correct classification of the ultra-alkaline rocks, would be very useful to define unique geologic pattern in the Italian area and in general for other similar occurrences worldwide. As they are not consistently classified by IUGS method, they have been studied using various statistical methods. The RHA method is based on three parameters. The first parameter (Rank) is the rock geochemical composition or mineralogical composition (mode/norm), ordered by atomic abundances or modal/normative volumetric percent. The other two parameters (Entropy and Anentropy) are used to discriminate rock types having the same rank formula. The second statistical approach employed is the Principal Component Analysis (PCA). PCA allows the definition of new latent variables (PCn) based on geochemical compositions through linear combinations of the major oxides. The number of new PCn is less than or equal to the number of original variables. Both statistical methods discriminate groups of lithotypes. In particular the PCA produced grouping of different ultra-alkaline rocks, having a direct correspondence with IUGS nomenclature but on chemical base. While using RHA method it has been possible to define a series of different groups of heterogeneous ultra-alkaline rocks, not related to current taxonomy but to petrogenetic system. As a whole, a simple chemical ternary classification diagram has been determined that outlines a possible genetic link between different rock types which may be used coupled with to the taxonomic IUGS classifying schemes.